Took some classes from the pandemonium engine.

core/containers/hash_map.h

@@ -0,0 +1,666 @@
+#ifndef HASH_MAP_H
+#define HASH_MAP_H
+
+/*************************************************************************/
+/*  hash_map.h                                                           */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/containers/hashfuncs.h"
+#include "core/containers/paged_allocator.h"
+#include "core/containers/pair.h"
+#include "core/math/math_funcs.h"
+#include "core/os/memory.h"
+
+/**
+ * A HashMap implementation that uses open addressing with Robin Hood hashing.
+ * Robin Hood hashing swaps out entries that have a smaller probing distance
+ * than the to-be-inserted entry, that evens out the average probing distance
+ * and enables faster lookups. Backward shift deletion is employed to further
+ * improve the performance and to avoid infinite loops in rare cases.
+ *
+ * Keys and values are stored in a double linked list by insertion order. This
+ * has a slight performance overhead on lookup, which can be mostly compensated
+ * using a paged allocator if required.
+ *
+ * The assignment operator copy the pairs from one map to the other.
+ */
+
+template <class TKey, class TValue, class Hasher = HashMapHasherDefault, class Comparator = HashMapComparatorDefault<TKey>>
+class HashMap {
+public:
+	const uint32_t MIN_CAPACITY_INDEX = 2; // Use a prime.
+	const float MAX_OCCUPANCY = 0.75;
+	const uint32_t EMPTY_HASH = 0;
+
+public:
+	struct Element {
+		Element *next = nullptr;
+		Element *prev = nullptr;
+		KeyValue<TKey, TValue> data;
+
+		const TKey &key() const {
+			return data.key;
+		}
+
+		TValue &value() {
+			return data.value;
+		}
+
+		const TValue &value() const {
+			return data.value;
+		}
+
+		TValue &get() {
+			return data.value;
+		};
+		const TValue &get() const {
+			return data.value;
+		};
+
+		Element() {}
+		Element(const TKey &p_key, const TValue &p_value) :
+				data(p_key, p_value) {}
+	};
+
+public:
+	_FORCE_INLINE_ uint32_t get_capacity() const { return hash_table_size_primes[capacity_index]; }
+	_FORCE_INLINE_ uint32_t size() const { return num_elements; }
+
+	/* Standard Godot Container API */
+
+	bool empty() const {
+		return num_elements == 0;
+	}
+
+	void clear() {
+		if (elements == nullptr || num_elements == 0) {
+			return;
+		}
+		uint32_t capacity = hash_table_size_primes[capacity_index];
+		for (uint32_t i = 0; i < capacity; i++) {
+			if (hashes[i] == EMPTY_HASH) {
+				continue;
+			}
+
+			hashes[i] = EMPTY_HASH;
+			memdelete(elements[i]);
+			elements[i] = nullptr;
+		}
+
+		tail_element = nullptr;
+		head_element = nullptr;
+		num_elements = 0;
+	}
+
+	TValue &get(const TKey &p_key) {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+		CRASH_COND_MSG(!exists, "HashMap key not found.");
+		return elements[pos]->data.value;
+	}
+
+	const TValue &get(const TKey &p_key) const {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+		CRASH_COND_MSG(!exists, "HashMap key not found.");
+		return elements[pos]->data.value;
+	}
+
+	const TValue *getptr(const TKey &p_key) const {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+
+		if (exists) {
+			return &elements[pos]->data.value;
+		}
+		return nullptr;
+	}
+
+	TValue *getptr(const TKey &p_key) {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+
+		if (exists) {
+			return &elements[pos]->data.value;
+		}
+		return nullptr;
+	}
+
+	const Element *get_element(const TKey &p_key) const {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+
+		if (exists) {
+			return elements[pos];
+		}
+
+		return NULL;
+	}
+
+	Element *get_element(const TKey &p_key) {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+
+		if (exists) {
+			return elements[pos];
+		}
+
+		return NULL;
+	}
+
+	_FORCE_INLINE_ const Element *find(const TKey &p_key) const {
+		return get_element(p_key);
+	}
+
+	_FORCE_INLINE_ Element *find(const TKey &p_key) {
+		return get_element(p_key);
+	}
+
+	/**
+	 * Same as get, except it can return NULL when item was not found.
+	 * This version is custom, will take a hash and a custom key (that should support operator==()
+	 */
+
+	template <class C>
+	_FORCE_INLINE_ TValue *custom_getptr(C p_custom_key, uint32_t p_custom_hash) {
+		if (unlikely(!elements)) {
+			return NULL;
+		}
+
+		const uint32_t capacity = hash_table_size_primes[capacity_index];
+		const uint64_t capacity_inv = hash_table_size_primes_inv[capacity_index];
+		uint32_t hash = p_custom_hash;
+		uint32_t pos = fastmod(hash, capacity_inv, capacity);
+		uint32_t distance = 0;
+
+		while (true) {
+			if (hashes[pos] == EMPTY_HASH) {
+				return NULL;
+			}
+
+			if (distance > _get_probe_length(pos, hashes[pos], capacity, capacity_inv)) {
+				return NULL;
+			}
+
+			if (hashes[pos] == hash && Comparator::compare(elements[pos]->data.key, p_custom_key)) {
+				return &elements[pos]->data.value;
+			}
+
+			pos = fastmod((pos + 1), capacity_inv, capacity);
+			distance++;
+		}
+
+		return NULL;
+	}
+
+	template <class C>
+	_FORCE_INLINE_ const TValue *custom_getptr(C p_custom_key, uint32_t p_custom_hash) const {
+		if (unlikely(!elements)) {
+			return NULL;
+		}
+
+		const uint32_t capacity = hash_table_size_primes[capacity_index];
+		const uint64_t capacity_inv = hash_table_size_primes_inv[capacity_index];
+		uint32_t hash = p_custom_hash;
+		uint32_t pos = fastmod(hash, capacity_inv, capacity);
+		uint32_t distance = 0;
+
+		while (true) {
+			if (hashes[pos] == EMPTY_HASH) {
+				return NULL;
+			}
+
+			if (distance > _get_probe_length(pos, hashes[pos], capacity, capacity_inv)) {
+				return NULL;
+			}
+
+			if (hashes[pos] == hash && Comparator::compare(elements[pos]->data.key, p_custom_key)) {
+				return &elements[pos]->data.value;
+			}
+
+			pos = fastmod((pos + 1), capacity_inv, capacity);
+			distance++;
+		}
+
+		return NULL;
+	}
+
+	_FORCE_INLINE_ bool has(const TKey &p_key) const {
+		uint32_t _pos = 0;
+		return _lookup_pos(p_key, _pos);
+	}
+
+	bool erase(const TKey &p_key) {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+
+		if (!exists) {
+			return false;
+		}
+
+		const uint32_t capacity = hash_table_size_primes[capacity_index];
+		const uint64_t capacity_inv = hash_table_size_primes_inv[capacity_index];
+		uint32_t next_pos = fastmod((pos + 1), capacity_inv, capacity);
+		while (hashes[next_pos] != EMPTY_HASH && _get_probe_length(next_pos, hashes[next_pos], capacity, capacity_inv) != 0) {
+			SWAP(hashes[next_pos], hashes[pos]);
+			SWAP(elements[next_pos], elements[pos]);
+			pos = next_pos;
+			next_pos = fastmod((pos + 1), capacity_inv, capacity);
+		}
+
+		hashes[pos] = EMPTY_HASH;
+
+		if (head_element == elements[pos]) {
+			head_element = elements[pos]->next;
+		}
+
+		if (tail_element == elements[pos]) {
+			tail_element = elements[pos]->prev;
+		}
+
+		if (elements[pos]->prev) {
+			elements[pos]->prev->next = elements[pos]->next;
+		}
+
+		if (elements[pos]->next) {
+			elements[pos]->next->prev = elements[pos]->prev;
+		}
+
+		memdelete(elements[pos]);
+		elements[pos] = nullptr;
+
+		num_elements--;
+		return true;
+	}
+
+	// Reserves space for a number of elements, useful to avoid many resizes and rehashes.
+	// If adding a known (possibly large) number of elements at once, must be larger than old capacity.
+	void reserve(uint32_t p_new_capacity) {
+		uint32_t new_index = capacity_index;
+
+		while (hash_table_size_primes[new_index] < p_new_capacity) {
+			ERR_FAIL_COND_MSG(new_index + 1 == (uint32_t)HASH_TABLE_SIZE_MAX, nullptr);
+			new_index++;
+		}
+
+		if (new_index == capacity_index) {
+			return;
+		}
+
+		if (elements == nullptr) {
+			capacity_index = new_index;
+			return; // Unallocated yet.
+		}
+		_resize_and_rehash(new_index);
+	}
+
+	_FORCE_INLINE_ Element *front() {
+		return head_element;
+	}
+	_FORCE_INLINE_ Element *back() {
+		return tail_element;
+	}
+
+	_FORCE_INLINE_ const Element *front() const {
+		return head_element;
+	}
+	_FORCE_INLINE_ const Element *back() const {
+		return tail_element;
+	}
+
+	/**
+	 * Get the next key to p_key, and the first key if p_key is null.
+	 * Returns a pointer to the next key if found, NULL otherwise.
+	 * Adding/Removing elements while iterating will, of course, have unexpected results, don't do it.
+	 *
+	 * Example:
+	 *
+	 * 	const TKey *k=NULL;
+	 *
+	 * 	while( (k=table.next(k)) ) {
+	 *
+	 * 		print( *k );
+	 * 	}
+	 *
+	 * This is for backwards compatibility. Use this syntax instead for new code:
+	 *
+	 * for (const HashMap<K, V>::Element *E = map.front(); E; E = E->next) {
+	 *     ...
+	 * }
+	 *
+	 */
+	const TKey *next(const TKey *p_key) const {
+		if (unlikely(!elements)) {
+			return nullptr;
+		}
+
+		if (!p_key) { /* get the first key */
+
+			if (unlikely(!front())) {
+				return nullptr;
+			}
+
+			return &front()->data.key;
+
+		} else { /* get the next key */
+
+			const Element *e = get_element(*p_key);
+			ERR_FAIL_COND_V_MSG(!e, nullptr, "Invalid key supplied.");
+			if (e->next) {
+				/* if there is a "next" in the list, return that */
+				return &e->next->data.key;
+			}
+
+			/* nothing found, was at end */
+		}
+
+		return nullptr; /* nothing found */
+	}
+
+	/* Indexing */
+
+	const TValue &operator[](const TKey &p_key) const {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+		CRASH_COND(!exists);
+		return elements[pos]->data.value;
+	}
+
+	TValue &operator[](const TKey &p_key) {
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+		if (!exists) {
+			return _insert(p_key, TValue())->data.value;
+		} else {
+			return elements[pos]->data.value;
+		}
+	}
+
+	/* Insert */
+
+	Element *insert(const TKey &p_key, const TValue &p_value, bool p_front_insert = false) {
+		return _insert(p_key, p_value, p_front_insert);
+	}
+
+	Element *set(const TKey &p_key, const TValue &p_value, bool p_front_insert = false) {
+		return _insert(p_key, p_value, p_front_insert);
+	}
+
+	/* Helpers */
+
+	void get_key_list(List<TKey> *p_keys) const {
+		if (unlikely(!elements)) {
+			return;
+		}
+
+		for (const Element *E = front(); E; E = E->next) {
+			p_keys->push_back(E->data.key);
+		}
+	}
+
+	/* Constructors */
+
+	HashMap(const HashMap &p_other) {
+		reserve(hash_table_size_primes[p_other.capacity_index]);
+
+		if (p_other.num_elements == 0) {
+			return;
+		}
+
+		for (const Element *E = p_other.front(); E; E = E->next) {
+			insert(E->data.key, E->data.value);
+		}
+	}
+
+	void operator=(const HashMap &p_other) {
+		if (this == &p_other) {
+			return; // Ignore self assignment.
+		}
+		if (num_elements != 0) {
+			clear();
+		}
+
+		reserve(hash_table_size_primes[p_other.capacity_index]);
+
+		if (p_other.elements == nullptr) {
+			return; // Nothing to copy.
+		}
+
+		for (const Element *E = p_other.front(); E; E = E->next) {
+			insert(E->data.key, E->data.value);
+		}
+	}
+
+	HashMap(uint32_t p_initial_capacity) {
+		// Capacity can't be 0.
+		capacity_index = 0;
+		reserve(p_initial_capacity);
+	}
+	HashMap() {
+		capacity_index = MIN_CAPACITY_INDEX;
+	}
+
+	uint32_t debug_get_hash(uint32_t p_index) {
+		if (num_elements == 0) {
+			return 0;
+		}
+		ERR_FAIL_INDEX_V(p_index, get_capacity(), 0);
+		return hashes[p_index];
+	}
+	Element *debug_get_element(uint32_t p_index) {
+		if (num_elements == 0) {
+			return NULL;
+		}
+
+		ERR_FAIL_INDEX_V(p_index, get_capacity(), NULL);
+
+		return elements[p_index];
+	}
+
+	~HashMap() {
+		clear();
+
+		if (elements != nullptr) {
+			Memory::free_static(elements);
+			Memory::free_static(hashes);
+		}
+	}
+
+private:
+	Element **elements = nullptr;
+	uint32_t *hashes = nullptr;
+	Element *head_element = nullptr;
+	Element *tail_element = nullptr;
+
+	uint32_t capacity_index = 0;
+	uint32_t num_elements = 0;
+
+	_FORCE_INLINE_ uint32_t _hash(const TKey &p_key) const {
+		uint32_t hash = Hasher::hash(p_key);
+
+		if (unlikely(hash == EMPTY_HASH)) {
+			hash = EMPTY_HASH + 1;
+		}
+
+		return hash;
+	}
+
+	static _FORCE_INLINE_ uint32_t _get_probe_length(const uint32_t p_pos, const uint32_t p_hash, const uint32_t p_capacity, const uint64_t p_capacity_inv) {
+		const uint32_t original_pos = fastmod(p_hash, p_capacity_inv, p_capacity);
+		return fastmod(p_pos - original_pos + p_capacity, p_capacity_inv, p_capacity);
+	}
+
+	bool _lookup_pos(const TKey &p_key, uint32_t &r_pos) const {
+		if (elements == nullptr || num_elements == 0) {
+			return false; // Failed lookups, no elements
+		}
+
+		const uint32_t capacity = hash_table_size_primes[capacity_index];
+		const uint64_t capacity_inv = hash_table_size_primes_inv[capacity_index];
+		uint32_t hash = _hash(p_key);
+		uint32_t pos = fastmod(hash, capacity_inv, capacity);
+		uint32_t distance = 0;
+
+		while (true) {
+			if (hashes[pos] == EMPTY_HASH) {
+				return false;
+			}
+
+			if (distance > _get_probe_length(pos, hashes[pos], capacity, capacity_inv)) {
+				return false;
+			}
+
+			if (hashes[pos] == hash && Comparator::compare(elements[pos]->data.key, p_key)) {
+				r_pos = pos;
+				return true;
+			}
+
+			pos = fastmod((pos + 1), capacity_inv, capacity);
+			distance++;
+		}
+	}
+
+	void _insert_with_hash(uint32_t p_hash, Element *p_value) {
+		const uint32_t capacity = hash_table_size_primes[capacity_index];
+		const uint64_t capacity_inv = hash_table_size_primes_inv[capacity_index];
+		uint32_t hash = p_hash;
+		Element *value = p_value;
+		uint32_t distance = 0;
+		uint32_t pos = fastmod(hash, capacity_inv, capacity);
+
+		while (true) {
+			if (hashes[pos] == EMPTY_HASH) {
+				elements[pos] = value;
+				hashes[pos] = hash;
+
+				num_elements++;
+
+				return;
+			}
+
+			// Not an empty slot, let's check the probing length of the existing one.
+			uint32_t existing_probe_len = _get_probe_length(pos, hashes[pos], capacity, capacity_inv);
+			if (existing_probe_len < distance) {
+				SWAP(hash, hashes[pos]);
+				SWAP(value, elements[pos]);
+				distance = existing_probe_len;
+			}
+
+			pos = fastmod((pos + 1), capacity_inv, capacity);
+			distance++;
+		}
+	}
+
+	void _resize_and_rehash(uint32_t p_new_capacity_index) {
+		uint32_t old_capacity = hash_table_size_primes[capacity_index];
+
+		// Capacity can't be 0.
+		capacity_index = MAX((uint32_t)MIN_CAPACITY_INDEX, p_new_capacity_index);
+
+		uint32_t capacity = hash_table_size_primes[capacity_index];
+
+		Element **old_elements = elements;
+		uint32_t *old_hashes = hashes;
+
+		num_elements = 0;
+		hashes = reinterpret_cast<uint32_t *>(Memory::alloc_static(sizeof(uint32_t) * capacity));
+		elements = reinterpret_cast<Element **>(Memory::alloc_static(sizeof(Element *) * capacity));
+
+		for (uint32_t i = 0; i < capacity; i++) {
+			hashes[i] = 0;
+			elements[i] = nullptr;
+		}
+
+		if (old_capacity == 0) {
+			// Nothing to do.
+			return;
+		}
+
+		for (uint32_t i = 0; i < old_capacity; i++) {
+			if (old_hashes[i] == EMPTY_HASH) {
+				continue;
+			}
+
+			_insert_with_hash(old_hashes[i], old_elements[i]);
+		}
+
+		Memory::free_static(old_elements);
+		Memory::free_static(old_hashes);
+	}
+
+	_FORCE_INLINE_ Element *_insert(const TKey &p_key, const TValue &p_value, bool p_front_insert = false) {
+		uint32_t capacity = hash_table_size_primes[capacity_index];
+		if (unlikely(elements == nullptr)) {
+			// Allocate on demand to save memory.
+
+			hashes = reinterpret_cast<uint32_t *>(Memory::alloc_static(sizeof(uint32_t) * capacity));
+			elements = reinterpret_cast<Element **>(Memory::alloc_static(sizeof(Element *) * capacity));
+
+			for (uint32_t i = 0; i < capacity; i++) {
+				hashes[i] = EMPTY_HASH;
+				elements[i] = nullptr;
+			}
+		}
+
+		uint32_t pos = 0;
+		bool exists = _lookup_pos(p_key, pos);
+
+		if (exists) {
+			elements[pos]->data.value = p_value;
+			return elements[pos];
+		} else {
+			if (num_elements + 1 > MAX_OCCUPANCY * capacity) {
+				ERR_FAIL_COND_V_MSG(capacity_index + 1 == HASH_TABLE_SIZE_MAX, nullptr, "Hash table maximum capacity reached, aborting insertion.");
+				_resize_and_rehash(capacity_index + 1);
+			}
+
+			Element *elem = memnew(Element(p_key, p_value));
+
+			if (tail_element == nullptr) {
+				head_element = elem;
+				tail_element = elem;
+			} else if (p_front_insert) {
+				head_element->prev = elem;
+				elem->next = head_element;
+				head_element = elem;
+			} else {
+				tail_element->next = elem;
+				elem->prev = tail_element;
+				tail_element = elem;
+			}
+
+			uint32_t hash = _hash(p_key);
+			_insert_with_hash(hash, elem);
+			return elem;
+		}
+	}
+};
+
+#endif // HASH_MAP_H

core/containers/hashfuncs.h

@@ -0,0 +1,532 @@
+#ifndef HASHFUNCS_H
+#define HASHFUNCS_H
+
+/*************************************************************************/
+/*  hashfuncs.h                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/containers/rid.h"
+#include "core/math/aabb.h"
+#include "core/math/math_defs.h"
+#include "core/math/math_funcs.h"
+#include "core/math/rect2.h"
+#include "core/math/rect2i.h"
+#include "core/math/vector2.h"
+#include "core/math/vector2i.h"
+#include "core/math/vector3.h"
+#include "core/math/vector3i.h"
+#include "core/math/vector4.h"
+#include "core/math/vector4i.h"
+#include "core/object/object_id.h"
+#include "core/string/node_path.h"
+#include "core/string/string_name.h"
+#include "core/string/ustring.h"
+#include "core/typedefs.h"
+
+/**
+ * Hashing functions
+ */
+
+/**
+ * DJB2 Hash function
+ * @param C String
+ * @return 32-bits hashcode
+ */
+static inline uint32_t hash_djb2(const char *p_cstr) {
+	const unsigned char *chr = (const unsigned char *)p_cstr;
+	uint32_t hash = 5381;
+	uint32_t c;
+
+	while ((c = *chr++)) {
+		hash = ((hash << 5) + hash) ^ c; /* hash * 33 ^ c */
+	}
+
+	return hash;
+}
+
+static inline uint32_t hash_djb2_buffer(const uint8_t *p_buff, int p_len, uint32_t p_prev = 5381) {
+	uint32_t hash = p_prev;
+
+	for (int i = 0; i < p_len; i++) {
+		hash = ((hash << 5) + hash) ^ p_buff[i]; /* hash * 33 ^ c */
+	}
+
+	return hash;
+}
+
+static inline uint32_t hash_djb2_one_32(uint32_t p_in, uint32_t p_prev = 5381) {
+	return ((p_prev << 5) + p_prev) ^ p_in;
+}
+
+/**
+ * Thomas Wang's 64-bit to 32-bit Hash function:
+ * https://web.archive.org/web/20071223173210/https:/www.concentric.net/~Ttwang/tech/inthash.htm
+ *
+ * @param p_int - 64-bit unsigned integer key to be hashed
+ * @return unsigned 32-bit value representing hashcode
+ */
+static inline uint32_t hash_one_uint64(const uint64_t p_int) {
+	uint64_t v = p_int;
+	v = (~v) + (v << 18); // v = (v << 18) - v - 1;
+	v = v ^ (v >> 31);
+	v = v * 21; // v = (v + (v << 2)) + (v << 4);
+	v = v ^ (v >> 11);
+	v = v + (v << 6);
+	v = v ^ (v >> 22);
+	return (uint32_t)v;
+}
+
+#define HASH_MURMUR3_SEED 0x7F07C65
+// Murmurhash3 32-bit version.
+// All MurmurHash versions are public domain software, and the author disclaims all copyright to their code.
+
+static _FORCE_INLINE_ uint32_t hash_murmur3_one_32(uint32_t p_in, uint32_t p_seed = HASH_MURMUR3_SEED) {
+	p_in *= 0xcc9e2d51;
+	p_in = (p_in << 15) | (p_in >> 17);
+	p_in *= 0x1b873593;
+
+	p_seed ^= p_in;
+	p_seed = (p_seed << 13) | (p_seed >> 19);
+	p_seed = p_seed * 5 + 0xe6546b64;
+
+	return p_seed;
+}
+
+static _FORCE_INLINE_ uint32_t hash_murmur3_one_float(float p_in, uint32_t p_seed = HASH_MURMUR3_SEED) {
+	union {
+		float f;
+		uint32_t i;
+	} u;
+
+	// Normalize +/- 0.0 and NaN values so they hash the same.
+	if (p_in == 0.0f) {
+		u.f = 0.0;
+	} else if (Math::is_nan(p_in)) {
+		u.f = NAN;
+	} else {
+		u.f = p_in;
+	}
+
+	return hash_murmur3_one_32(u.i, p_seed);
+}
+
+static _FORCE_INLINE_ uint32_t hash_murmur3_one_64(uint64_t p_in, uint32_t p_seed = HASH_MURMUR3_SEED) {
+	p_seed = hash_murmur3_one_32(p_in & 0xFFFFFFFF, p_seed);
+	return hash_murmur3_one_32(p_in >> 32, p_seed);
+}
+
+static _FORCE_INLINE_ uint32_t hash_murmur3_one_double(double p_in, uint32_t p_seed = HASH_MURMUR3_SEED) {
+	union {
+		double d;
+		uint64_t i;
+	} u;
+
+	// Normalize +/- 0.0 and NaN values so they hash the same.
+	if (p_in == 0.0f) {
+		u.d = 0.0;
+	} else if (Math::is_nan(p_in)) {
+		u.d = NAN;
+	} else {
+		u.d = p_in;
+	}
+
+	return hash_murmur3_one_64(u.i, p_seed);
+}
+
+static _FORCE_INLINE_ uint32_t hash_murmur3_one_real(real_t p_in, uint32_t p_seed = HASH_MURMUR3_SEED) {
+#ifdef REAL_T_IS_DOUBLE
+	return hash_murmur3_one_double(p_in, p_seed);
+#else
+	return hash_murmur3_one_float(p_in, p_seed);
+#endif
+}
+
+static _FORCE_INLINE_ uint32_t hash_rotl32(uint32_t x, int8_t r) {
+	return (x << r) | (x >> (32 - r));
+}
+
+static _FORCE_INLINE_ uint32_t hash_fmix32(uint32_t h) {
+	h ^= h >> 16;
+	h *= 0x85ebca6b;
+	h ^= h >> 13;
+	h *= 0xc2b2ae35;
+	h ^= h >> 16;
+
+	return h;
+}
+
+static _FORCE_INLINE_ uint32_t hash_murmur3_buffer(const void *key, int length, const uint32_t seed = HASH_MURMUR3_SEED) {
+	// Although not required, this is a random prime number.
+	const uint8_t *data = (const uint8_t *)key;
+	const int nblocks = length / 4;
+
+	uint32_t h1 = seed;
+
+	const uint32_t c1 = 0xcc9e2d51;
+	const uint32_t c2 = 0x1b873593;
+
+	const uint32_t *blocks = (const uint32_t *)(data + nblocks * 4);
+
+	for (int i = -nblocks; i; i++) {
+		uint32_t k1 = blocks[i];
+
+		k1 *= c1;
+		k1 = hash_rotl32(k1, 15);
+		k1 *= c2;
+
+		h1 ^= k1;
+		h1 = hash_rotl32(h1, 13);
+		h1 = h1 * 5 + 0xe6546b64;
+	}
+
+	const uint8_t *tail = (const uint8_t *)(data + nblocks * 4);
+
+	uint32_t k1 = 0;
+
+	switch (length & 3) {
+		case 3:
+			k1 ^= tail[2] << 16;
+			FALLTHROUGH;
+		case 2:
+			k1 ^= tail[1] << 8;
+			FALLTHROUGH;
+		case 1:
+			k1 ^= tail[0];
+			k1 *= c1;
+			k1 = hash_rotl32(k1, 15);
+			k1 *= c2;
+			h1 ^= k1;
+	};
+
+	// Finalize with additional bit mixing.
+	h1 ^= length;
+	return hash_fmix32(h1);
+}
+
+static inline uint32_t hash_djb2_one_float(double p_in, uint32_t p_prev = 5381) {
+	union {
+		double d;
+		uint64_t i;
+	} u;
+
+	// Normalize +/- 0.0 and NaN values so they hash the same.
+	if (p_in == 0.0f) {
+		u.d = 0.0;
+	} else if (Math::is_nan(p_in)) {
+		u.d = Math_NAN;
+	} else {
+		u.d = p_in;
+	}
+
+	return ((p_prev << 5) + p_prev) + hash_one_uint64(u.i);
+}
+
+template <class T>
+static inline uint32_t make_uint32_t(T p_in) {
+	union {
+		T t;
+		uint32_t _u32;
+	} _u;
+	_u._u32 = 0;
+	_u.t = p_in;
+	return _u._u32;
+}
+
+static _FORCE_INLINE_ uint64_t hash_djb2_one_float_64(double p_in, uint64_t p_prev = 5381) {
+	union {
+		double d;
+		uint64_t i;
+	} u;
+
+	// Normalize +/- 0.0 and NaN values so they hash the same.
+	if (p_in == 0.0f) {
+		u.d = 0.0;
+	} else if (Math::is_nan(p_in)) {
+		u.d = NAN;
+	} else {
+		u.d = p_in;
+	}
+
+	return ((p_prev << 5) + p_prev) + u.i;
+}
+
+static _FORCE_INLINE_ uint64_t hash_djb2_one_64(uint64_t p_in, uint64_t p_prev = 5381) {
+	return ((p_prev << 5) + p_prev) ^ p_in;
+}
+
+template <class T>
+static _FORCE_INLINE_ uint64_t hash_make_uint64_t(T p_in) {
+	union {
+		T t;
+		uint64_t _u64;
+	} _u;
+	_u._u64 = 0; // in case p_in is smaller
+
+	_u.t = p_in;
+	return _u._u64;
+}
+
+template <class T>
+static inline uint64_t make_uint64_t(T p_in) {
+	union {
+		T t;
+		uint64_t _u64;
+	} _u;
+	_u._u64 = 0; // in case p_in is smaller
+
+	_u.t = p_in;
+	return _u._u64;
+}
+
+template <class T>
+class Ref;
+
+struct HashMapHasherDefault {
+	// Generic hash function for any type.
+	template <class T>
+	static _FORCE_INLINE_ uint32_t hash(const T *p_pointer) { return hash_one_uint64((uint64_t)p_pointer); }
+
+	template <class T>
+	static _FORCE_INLINE_ uint32_t hash(const Ref<T> &p_ref) { return hash_one_uint64((uint64_t)p_ref.operator->()); }
+
+	static _FORCE_INLINE_ uint32_t hash(const String &p_string) { return p_string.hash(); }
+	static _FORCE_INLINE_ uint32_t hash(const char *p_cstr) { return hash_djb2(p_cstr); }
+	static _FORCE_INLINE_ uint32_t hash(const wchar_t p_wchar) { return hash_fmix32(p_wchar); }
+	static _FORCE_INLINE_ uint32_t hash(const char16_t p_uchar) { return hash_fmix32(p_uchar); }
+	static _FORCE_INLINE_ uint32_t hash(const char32_t p_uchar) { return hash_fmix32(p_uchar); }
+	static _FORCE_INLINE_ uint32_t hash(const RID &p_rid) { return hash_one_uint64(p_rid.get_id()); }
+	static _FORCE_INLINE_ uint32_t hash(const StringName &p_string_name) { return p_string_name.hash(); }
+	static _FORCE_INLINE_ uint32_t hash(const NodePath &p_path) { return p_path.hash(); }
+	//static _FORCE_INLINE_ uint32_t hash(const ObjectID &p_id) { return hash_one_uint64(p_id); }
+
+	static _FORCE_INLINE_ uint32_t hash(const uint64_t p_int) { return hash_one_uint64(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const int64_t p_int) { return hash_one_uint64(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const float p_float) { return hash_murmur3_one_float(p_float); }
+	static _FORCE_INLINE_ uint32_t hash(const double p_double) { return hash_murmur3_one_double(p_double); }
+	static _FORCE_INLINE_ uint32_t hash(const uint32_t p_int) { return hash_fmix32(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const int32_t p_int) { return hash_fmix32(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const uint16_t p_int) { return hash_fmix32(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const int16_t p_int) { return hash_fmix32(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const uint8_t p_int) { return hash_fmix32(p_int); }
+	static _FORCE_INLINE_ uint32_t hash(const int8_t p_int) { return hash_fmix32(p_int); }
+
+	static _FORCE_INLINE_ uint32_t hash(const Vector2i &p_vec) {
+		uint32_t h = hash_murmur3_one_32(p_vec.x);
+		h = hash_murmur3_one_32(p_vec.y, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Vector3i &p_vec) {
+		uint32_t h = hash_murmur3_one_32(p_vec.x);
+		h = hash_murmur3_one_32(p_vec.y, h);
+		h = hash_murmur3_one_32(p_vec.z, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Vector4i &p_vec) {
+		uint32_t h = hash_murmur3_one_32(p_vec.x);
+		h = hash_murmur3_one_32(p_vec.y, h);
+		h = hash_murmur3_one_32(p_vec.z, h);
+		h = hash_murmur3_one_32(p_vec.w, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Vector2 &p_vec) {
+		uint32_t h = hash_murmur3_one_real(p_vec.x);
+		h = hash_murmur3_one_real(p_vec.y, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Vector3 &p_vec) {
+		uint32_t h = hash_murmur3_one_real(p_vec.x);
+		h = hash_murmur3_one_real(p_vec.y, h);
+		h = hash_murmur3_one_real(p_vec.z, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Vector4 &p_vec) {
+		uint32_t h = hash_murmur3_one_real(p_vec.x);
+		h = hash_murmur3_one_real(p_vec.y, h);
+		h = hash_murmur3_one_real(p_vec.z, h);
+		h = hash_murmur3_one_real(p_vec.w, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Rect2i &p_rect) {
+		uint32_t h = hash_murmur3_one_32(p_rect.position.x);
+		h = hash_murmur3_one_32(p_rect.position.y, h);
+		h = hash_murmur3_one_32(p_rect.size.x, h);
+		h = hash_murmur3_one_32(p_rect.size.y, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const Rect2 &p_rect) {
+		uint32_t h = hash_murmur3_one_real(p_rect.position.x);
+		h = hash_murmur3_one_real(p_rect.position.y, h);
+		h = hash_murmur3_one_real(p_rect.size.x, h);
+		h = hash_murmur3_one_real(p_rect.size.y, h);
+		return hash_fmix32(h);
+	}
+	static _FORCE_INLINE_ uint32_t hash(const AABB &p_aabb) {
+		uint32_t h = hash_murmur3_one_real(p_aabb.position.x);
+		h = hash_murmur3_one_real(p_aabb.position.y, h);
+		h = hash_murmur3_one_real(p_aabb.position.z, h);
+		h = hash_murmur3_one_real(p_aabb.size.x, h);
+		h = hash_murmur3_one_real(p_aabb.size.y, h);
+		h = hash_murmur3_one_real(p_aabb.size.z, h);
+		return hash_fmix32(h);
+	}
+};
+
+template <typename T>
+struct HashMapComparatorDefault {
+	static bool compare(const T &p_lhs, const T &p_rhs) {
+		return p_lhs == p_rhs;
+	}
+};
+
+template <>
+struct HashMapComparatorDefault<float> {
+	static bool compare(const float &p_lhs, const float &p_rhs) {
+		return (p_lhs == p_rhs) || (Math::is_nan(p_lhs) && Math::is_nan(p_rhs));
+	}
+};
+
+template <>
+struct HashMapComparatorDefault<double> {
+	static bool compare(const double &p_lhs, const double &p_rhs) {
+		return (p_lhs == p_rhs) || (Math::is_nan(p_lhs) && Math::is_nan(p_rhs));
+	}
+};
+
+template <>
+struct HashMapComparatorDefault<Vector2> {
+	static bool compare(const Vector2 &p_lhs, const Vector2 &p_rhs) {
+		return ((p_lhs.x == p_rhs.x) || (Math::is_nan(p_lhs.x) && Math::is_nan(p_rhs.x))) && ((p_lhs.y == p_rhs.y) || (Math::is_nan(p_lhs.y) && Math::is_nan(p_rhs.y)));
+	}
+};
+
+template <>
+struct HashMapComparatorDefault<Vector3> {
+	static bool compare(const Vector3 &p_lhs, const Vector3 &p_rhs) {
+		return ((p_lhs.x == p_rhs.x) || (Math::is_nan(p_lhs.x) && Math::is_nan(p_rhs.x))) && ((p_lhs.y == p_rhs.y) || (Math::is_nan(p_lhs.y) && Math::is_nan(p_rhs.y))) && ((p_lhs.z == p_rhs.z) || (Math::is_nan(p_lhs.z) && Math::is_nan(p_rhs.z)));
+	}
+};
+
+constexpr uint32_t HASH_TABLE_SIZE_MAX = 29;
+
+const uint32_t hash_table_size_primes[HASH_TABLE_SIZE_MAX] = {
+	5,
+	13,
+	23,
+	47,
+	97,
+	193,
+	389,
+	769,
+	1543,
+	3079,
+	6151,
+	12289,
+	24593,
+	49157,
+	98317,
+	196613,
+	393241,
+	786433,
+	1572869,
+	3145739,
+	6291469,
+	12582917,
+	25165843,
+	50331653,
+	100663319,
+	201326611,
+	402653189,
+	805306457,
+	1610612741,
+};
+
+// Computed with elem_i = UINT64_C (0 x FFFFFFFF FFFFFFFF ) / d_i + 1, where d_i is the i-th element of the above array.
+const uint64_t hash_table_size_primes_inv[HASH_TABLE_SIZE_MAX] = {
+	3689348814741910324,
+	1418980313362273202,
+	802032351030850071,
+	392483916461905354,
+	190172619316593316,
+	95578984837873325,
+	47420935922132524,
+	23987963684927896,
+	11955116055547344,
+	5991147799191151,
+	2998982941588287,
+	1501077717772769,
+	750081082979285,
+	375261795343686,
+	187625172388393,
+	93822606204624,
+	46909513691883,
+	23456218233098,
+	11728086747027,
+	5864041509391,
+	2932024948977,
+	1466014921160,
+	733007198436,
+	366503839517,
+	183251896093,
+	91625960335,
+	45812983922,
+	22906489714,
+	11453246088
+};
+
+/**
+ * Fastmod computes ( n mod d ) given the precomputed c much faster than n % d.
+ * The implementation of fastmod is based on the following paper by Daniel Lemire et al.
+ * Faster Remainder by Direct Computation: Applications to Compilers and Software Libraries
+ * https://arxiv.org/abs/1902.01961
+ */
+static _FORCE_INLINE_ uint32_t fastmod(const uint32_t n, const uint64_t c, const uint32_t d) {
+#if defined(_MSC_VER)
+	// Returns the upper 64 bits of the product of two 64-bit unsigned integers.
+	// This intrinsic function is required since MSVC does not support unsigned 128-bit integers.
+#if defined(_M_X64) || defined(_M_ARM64)
+	return __umulh(c * n, d);
+#else
+	// Fallback to the slower method for 32-bit platforms.
+	return n % d;
+#endif // _M_X64 || _M_ARM64
+#else
+#ifdef __SIZEOF_INT128__
+	// Prevent compiler warning, because we know what we are doing.
+	uint64_t lowbits = c * n;
+	__extension__ typedef unsigned __int128 uint128;
+	return static_cast<uint64_t>(((uint128)lowbits * d) >> 64);
+#else
+	// Fallback to the slower method if no 128-bit unsigned integer type is available.
+	return n % d;
+#endif // __SIZEOF_INT128__
+#endif // _MSC_VER
+}
+
+#endif // HASHFUNCS_H

core/containers/paged_allocator.h

@@ -0,0 +1,134 @@
+#ifndef PAGED_ALLOCATOR_H
+#define PAGED_ALLOCATOR_H
+
+/*************************************************************************/
+/*  paged_allocator.h                                                    */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/os/memory.h"
+#include "core/os/spin_lock.h"
+#include "core/typedefs.h"
+
+template <class T, bool thread_safe = false>
+class PagedAllocator {
+	T **page_pool = nullptr;
+	T ***available_pool = nullptr;
+	uint32_t pages_allocated = 0;
+	uint32_t allocs_available = 0;
+
+	uint32_t page_shift = 0;
+	uint32_t page_mask = 0;
+	uint32_t page_size = 0;
+	SpinLock spin_lock;
+
+public:
+	T *alloc() {
+		if (thread_safe) {
+			spin_lock.lock();
+		}
+		if (unlikely(allocs_available == 0)) {
+			uint32_t pages_used = pages_allocated;
+
+			pages_allocated++;
+			page_pool = (T **)memrealloc(page_pool, sizeof(T *) * pages_allocated);
+			available_pool = (T ***)memrealloc(available_pool, sizeof(T **) * pages_allocated);
+
+			page_pool[pages_used] = (T *)memalloc(sizeof(T) * page_size);
+			available_pool[pages_used] = (T **)memalloc(sizeof(T *) * page_size);
+
+			for (uint32_t i = 0; i < page_size; i++) {
+				available_pool[0][i] = &page_pool[pages_used][i];
+			}
+			allocs_available += page_size;
+		}
+
+		allocs_available--;
+		T *alloc = available_pool[allocs_available >> page_shift][allocs_available & page_mask];
+		if (thread_safe) {
+			spin_lock.unlock();
+		}
+		memnew_placement(alloc, T);
+		return alloc;
+	}
+
+	void free(T *p_mem) {
+		if (thread_safe) {
+			spin_lock.lock();
+		}
+		p_mem->~T();
+		available_pool[allocs_available >> page_shift][allocs_available & page_mask] = p_mem;
+		if (thread_safe) {
+			spin_lock.unlock();
+		}
+		allocs_available++;
+	}
+
+	void reset(bool p_allow_unfreed = false) {
+		if (!p_allow_unfreed || !HAS_TRIVIAL_DESTRUCTOR(T)) {
+			ERR_FAIL_COND(allocs_available < pages_allocated * page_size);
+		}
+		if (pages_allocated) {
+			for (uint32_t i = 0; i < pages_allocated; i++) {
+				memfree(page_pool[i]);
+				memfree(available_pool[i]);
+			}
+			memfree(page_pool);
+			memfree(available_pool);
+			page_pool = nullptr;
+			available_pool = nullptr;
+			pages_allocated = 0;
+			allocs_available = 0;
+		}
+	}
+	bool is_configured() const {
+		return page_size > 0;
+	}
+
+	void configure(uint32_t p_page_size) {
+		ERR_FAIL_COND(page_pool != nullptr); //sanity check
+		ERR_FAIL_COND(p_page_size == 0);
+		page_size = nearest_power_of_2_templated(p_page_size);
+		page_mask = page_size - 1;
+		page_shift = get_shift_from_power_of_2(page_size);
+	}
+
+	// Power of 2 recommended because of alignment with OS page sizes.
+	// Even if element is bigger, its still a multiple and get rounded amount of pages
+	PagedAllocator(uint32_t p_page_size = 4096) {
+		configure(p_page_size);
+	}
+
+	~PagedAllocator() {
+		ERR_FAIL_COND_MSG(allocs_available < pages_allocated * page_size, "Pages in use exist at exit in PagedAllocator");
+		reset();
+	}
+};
+
+#endif // PAGED_ALLOCATOR_H

core/containers/pair.h

@@ -0,0 +1,116 @@
+#ifndef PAIR_H
+#define PAIR_H
+
+/*************************************************************************/
+/*  pair.h                                                               */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/containers/hashfuncs.h"
+#include "core/typedefs.h"
+
+template <class F, class S>
+struct Pair {
+	F first;
+	S second;
+
+	Pair() :
+			first(),
+			second() {
+	}
+
+	Pair(F p_first, const S &p_second) :
+			first(p_first),
+			second(p_second) {
+	}
+};
+
+template <class F, class S>
+bool operator==(const Pair<F, S> &pair, const Pair<F, S> &other) {
+	return (pair.first == other.first) && (pair.second == other.second);
+}
+
+template <class F, class S>
+bool operator!=(const Pair<F, S> &pair, const Pair<F, S> &other) {
+	return (pair.first != other.first) || (pair.second != other.second);
+}
+
+template <class F, class S>
+struct PairSort {
+	bool operator()(const Pair<F, S> &A, const Pair<F, S> &B) const {
+		if (A.first != B.first) {
+			return A.first < B.first;
+		}
+		return A.second < B.second;
+	}
+};
+
+template <class F, class S>
+struct PairHash {
+	static uint32_t hash(const Pair<F, S> &P) {
+		uint64_t h1 = HashMapHasherDefault::hash(P.first);
+		uint64_t h2 = HashMapHasherDefault::hash(P.second);
+		return hash_one_uint64((h1 << 32) | h2);
+	}
+};
+
+template <class K, class V>
+struct KeyValue {
+	const K key;
+	V value;
+
+	void operator=(const KeyValue &p_kv) = delete;
+	_FORCE_INLINE_ KeyValue(const KeyValue &p_kv) :
+			key(p_kv.key),
+			value(p_kv.value) {
+	}
+	_FORCE_INLINE_ KeyValue(const K &p_key, const V &p_value) :
+			key(p_key),
+			value(p_value) {
+	}
+};
+
+template <class K, class V>
+bool operator==(const KeyValue<K, V> &pair, const KeyValue<K, V> &other) {
+	return (pair.key == other.key) && (pair.value == other.value);
+}
+
+template <class K, class V>
+bool operator!=(const KeyValue<K, V> &pair, const KeyValue<K, V> &other) {
+	return (pair.key != other.key) || (pair.value != other.value);
+}
+
+template <class K, class V>
+struct KeyValueSort {
+	bool operator()(const KeyValue<K, V> &A, const KeyValue<K, V> &B) const {
+		return A.key < B.key;
+	}
+};
+
+#endif // PAIR_H

core/input/SCsub

@@ -0,0 +1,23 @@
+#!/usr/bin/env python
+
+import input_builders
+from platform_methods import run_in_subprocess
+
+Import("env")
+
+env_input = env.Clone()
+
+# Order matters here. Higher index controller database files write on top of lower index database files.
+controller_databases = [
+    "gamecontrollerdb.txt", 
+    "pandemoniumcontrollerdb.txt",
+]
+
+gensource = env_input.CommandNoCache(
+    "default_controller_mappings.gen.cpp",
+    controller_databases,
+    run_in_subprocess(input_builders.make_default_controller_mappings),
+)
+
+env_input.add_source_files(env.core_sources, "*.cpp")
+env_input.add_source_files(env.core_sources, gensource)

core/input/default_controller_mappings.h

@@ -0,0 +1,40 @@
+#ifndef DEFAULT_CONTROLLER_MAPPINGS_H
+#define DEFAULT_CONTROLLER_MAPPINGS_H
+
+/*************************************************************************/
+/*  default_controller_mappings.h                                        */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+class DefaultControllerMappings {
+public:
+	static const char *mappings[];
+};
+
+#endif // DEFAULT_CONTROLLER_MAPPINGS_H

core/input/input.cpp

@@ -0,0 +1,169 @@
+/*************************************************************************/
+/*  input.cpp                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "input.h"
+
+#include "core/config/project_settings.h"
+#include "core/input/input_map.h"
+#include "core/os/os.h"
+
+#ifdef TOOLS_ENABLED
+#include "editor/editor_settings.h"
+#endif
+
+Input *Input::singleton = nullptr;
+
+Input *Input::get_singleton() {
+	return singleton;
+}
+
+void Input::set_mouse_mode(MouseMode p_mode) {
+	ERR_FAIL_INDEX((int)p_mode, 4);
+	OS::get_singleton()->set_mouse_mode((OS::MouseMode)p_mode);
+}
+
+Input::MouseMode Input::get_mouse_mode() const {
+	return (MouseMode)OS::get_singleton()->get_mouse_mode();
+}
+
+void Input::_bind_methods() {
+	ClassDB::bind_method(D_METHOD("is_key_pressed", "scancode"), &Input::is_key_pressed);
+	ClassDB::bind_method(D_METHOD("is_physical_key_pressed", "scancode"), &Input::is_physical_key_pressed);
+	ClassDB::bind_method(D_METHOD("is_mouse_button_pressed", "button"), &Input::is_mouse_button_pressed);
+	ClassDB::bind_method(D_METHOD("is_joy_button_pressed", "device", "button"), &Input::is_joy_button_pressed);
+	ClassDB::bind_method(D_METHOD("is_action_pressed", "action", "exact"), &Input::is_action_pressed, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("is_action_just_pressed", "action", "exact"), &Input::is_action_just_pressed, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("is_action_just_released", "action", "exact"), &Input::is_action_just_released, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("get_action_strength", "action", "exact"), &Input::get_action_strength, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("get_action_raw_strength", "action", "exact"), &Input::get_action_raw_strength, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("get_axis", "negative_action", "positive_action"), &Input::get_axis);
+	ClassDB::bind_method(D_METHOD("get_vector", "negative_x", "positive_x", "negative_y", "positive_y", "deadzone"), &Input::get_vector, DEFVAL(-1.0f));
+	ClassDB::bind_method(D_METHOD("add_joy_mapping", "mapping", "update_existing"), &Input::add_joy_mapping, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("remove_joy_mapping", "guid"), &Input::remove_joy_mapping);
+	ClassDB::bind_method(D_METHOD("joy_connection_changed", "device", "connected", "name", "guid"), &Input::joy_connection_changed);
+	ClassDB::bind_method(D_METHOD("is_joy_known", "device"), &Input::is_joy_known);
+	ClassDB::bind_method(D_METHOD("get_joy_axis", "device", "axis"), &Input::get_joy_axis);
+	ClassDB::bind_method(D_METHOD("get_joy_name", "device"), &Input::get_joy_name);
+	ClassDB::bind_method(D_METHOD("get_joy_guid", "device"), &Input::get_joy_guid);
+	ClassDB::bind_method(D_METHOD("should_ignore_device", "vendor_id", "product_id"), &Input::should_ignore_device);
+	ClassDB::bind_method(D_METHOD("get_connected_joypads"), &Input::get_connected_joypads);
+	ClassDB::bind_method(D_METHOD("get_joy_vibration_strength", "device"), &Input::get_joy_vibration_strength);
+	ClassDB::bind_method(D_METHOD("get_joy_vibration_duration", "device"), &Input::get_joy_vibration_duration);
+	ClassDB::bind_method(D_METHOD("get_joy_button_string", "button_index"), &Input::get_joy_button_string);
+	ClassDB::bind_method(D_METHOD("get_joy_button_index_from_string", "button"), &Input::get_joy_button_index_from_string);
+	ClassDB::bind_method(D_METHOD("get_joy_axis_string", "axis_index"), &Input::get_joy_axis_string);
+	ClassDB::bind_method(D_METHOD("get_joy_axis_index_from_string", "axis"), &Input::get_joy_axis_index_from_string);
+	ClassDB::bind_method(D_METHOD("start_joy_vibration", "device", "weak_magnitude", "strong_magnitude", "duration"), &Input::start_joy_vibration, DEFVAL(0));
+	ClassDB::bind_method(D_METHOD("stop_joy_vibration", "device"), &Input::stop_joy_vibration);
+	ClassDB::bind_method(D_METHOD("vibrate_handheld", "duration_ms"), &Input::vibrate_handheld, DEFVAL(500));
+	ClassDB::bind_method(D_METHOD("get_gravity"), &Input::get_gravity);
+	ClassDB::bind_method(D_METHOD("get_accelerometer"), &Input::get_accelerometer);
+	ClassDB::bind_method(D_METHOD("get_magnetometer"), &Input::get_magnetometer);
+	ClassDB::bind_method(D_METHOD("get_gyroscope"), &Input::get_gyroscope);
+	ClassDB::bind_method(D_METHOD("set_gravity", "value"), &Input::set_gravity);
+	ClassDB::bind_method(D_METHOD("set_accelerometer", "value"), &Input::set_accelerometer);
+	ClassDB::bind_method(D_METHOD("set_magnetometer", "value"), &Input::set_magnetometer);
+	ClassDB::bind_method(D_METHOD("set_gyroscope", "value"), &Input::set_gyroscope);
+	//ClassDB::bind_method(D_METHOD("get_mouse_position"),&Input::get_mouse_position); - this is not the function you want
+	ClassDB::bind_method(D_METHOD("get_last_mouse_speed"), &Input::get_last_mouse_speed);
+	ClassDB::bind_method(D_METHOD("get_mouse_button_mask"), &Input::get_mouse_button_mask);
+	ClassDB::bind_method(D_METHOD("set_mouse_mode", "mode"), &Input::set_mouse_mode);
+	ClassDB::bind_method(D_METHOD("get_mouse_mode"), &Input::get_mouse_mode);
+	ClassDB::bind_method(D_METHOD("warp_mouse_position", "to"), &Input::warp_mouse_position);
+	ClassDB::bind_method(D_METHOD("action_press", "action", "strength"), &Input::action_press, DEFVAL(1.f));
+	ClassDB::bind_method(D_METHOD("action_release", "action"), &Input::action_release);
+	ClassDB::bind_method(D_METHOD("set_default_cursor_shape", "shape"), &Input::set_default_cursor_shape, DEFVAL(CURSOR_ARROW));
+	ClassDB::bind_method(D_METHOD("get_current_cursor_shape"), &Input::get_current_cursor_shape);
+	ClassDB::bind_method(D_METHOD("set_custom_mouse_cursor", "image", "shape", "hotspot"), &Input::set_custom_mouse_cursor, DEFVAL(CURSOR_ARROW), DEFVAL(Vector2()));
+	ClassDB::bind_method(D_METHOD("parse_input_event", "event"), &Input::parse_input_event);
+	ClassDB::bind_method(D_METHOD("set_use_accumulated_input", "enable"), &Input::set_use_accumulated_input);
+	ClassDB::bind_method(D_METHOD("is_using_accumulated_input"), &Input::is_using_accumulated_input);
+	ClassDB::bind_method(D_METHOD("flush_buffered_events"), &Input::flush_buffered_events);
+
+	ADD_PROPERTY(PropertyInfo(Variant::INT, "mouse_mode"), "set_mouse_mode", "get_mouse_mode");
+	ADD_PROPERTY(PropertyInfo(Variant::BOOL, "use_accumulated_input"), "set_use_accumulated_input", "is_using_accumulated_input");
+
+	BIND_ENUM_CONSTANT(MOUSE_MODE_VISIBLE);
+	BIND_ENUM_CONSTANT(MOUSE_MODE_HIDDEN);
+	BIND_ENUM_CONSTANT(MOUSE_MODE_CAPTURED);
+	BIND_ENUM_CONSTANT(MOUSE_MODE_CONFINED);
+
+	BIND_ENUM_CONSTANT(CURSOR_ARROW);
+	BIND_ENUM_CONSTANT(CURSOR_IBEAM);
+	BIND_ENUM_CONSTANT(CURSOR_POINTING_HAND);
+	BIND_ENUM_CONSTANT(CURSOR_CROSS);
+	BIND_ENUM_CONSTANT(CURSOR_WAIT);
+	BIND_ENUM_CONSTANT(CURSOR_BUSY);
+	BIND_ENUM_CONSTANT(CURSOR_DRAG);
+	BIND_ENUM_CONSTANT(CURSOR_CAN_DROP);
+	BIND_ENUM_CONSTANT(CURSOR_FORBIDDEN);
+	BIND_ENUM_CONSTANT(CURSOR_VSIZE);
+	BIND_ENUM_CONSTANT(CURSOR_HSIZE);
+	BIND_ENUM_CONSTANT(CURSOR_BDIAGSIZE);
+	BIND_ENUM_CONSTANT(CURSOR_FDIAGSIZE);
+	BIND_ENUM_CONSTANT(CURSOR_MOVE);
+	BIND_ENUM_CONSTANT(CURSOR_VSPLIT);
+	BIND_ENUM_CONSTANT(CURSOR_HSPLIT);
+	BIND_ENUM_CONSTANT(CURSOR_HELP);
+
+	ADD_SIGNAL(MethodInfo("joy_connection_changed", PropertyInfo(Variant::INT, "device"), PropertyInfo(Variant::BOOL, "connected")));
+}
+
+void Input::get_argument_options(const StringName &p_function, int p_idx, List<String> *r_options, const String &quote_style) const {
+#ifdef TOOLS_ENABLED
+	String pf = p_function;
+	if (p_idx == 0 &&
+			(pf == "is_action_pressed" || pf == "action_press" || pf == "action_release" ||
+					pf == "is_action_just_pressed" || pf == "is_action_just_released" ||
+					pf == "get_action_strength" || pf == "get_action_raw_strength" ||
+					pf == "get_axis" || pf == "get_vector")) {
+		List<PropertyInfo> pinfo;
+		ProjectSettings::get_singleton()->get_property_list(&pinfo);
+
+		for (List<PropertyInfo>::Element *E = pinfo.front(); E; E = E->next()) {
+			const PropertyInfo &pi = E->get();
+
+			if (!pi.name.begins_with("input/")) {
+				continue;
+			}
+
+			String name = pi.name.substr(pi.name.find("/") + 1, pi.name.length());
+			r_options->push_back(quote_style + name + quote_style);
+		}
+	}
+#endif
+}
+
+Input::Input() {
+	singleton = this;
+}
+
+//////////////////////////////////////////////////////////

core/input/input.h

@@ -0,0 +1,159 @@
+#ifndef INPUT_H
+#define INPUT_H
+
+/*************************************************************************/
+/*  input.h                                                              */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/vector2i.h"
+#include "core/object/object.h"
+#include "core/os/main_loop.h"
+#include "core/os/thread_safe.h"
+
+class Input : public Object {
+	GDCLASS(Input, Object);
+
+	static Input *singleton;
+
+protected:
+	static void _bind_methods();
+
+public:
+	enum MouseMode {
+		MOUSE_MODE_VISIBLE,
+		MOUSE_MODE_HIDDEN,
+		MOUSE_MODE_CAPTURED,
+		MOUSE_MODE_CONFINED
+	};
+
+#undef CursorShape
+	enum CursorShape {
+		CURSOR_ARROW,
+		CURSOR_IBEAM,
+		CURSOR_POINTING_HAND,
+		CURSOR_CROSS,
+		CURSOR_WAIT,
+		CURSOR_BUSY,
+		CURSOR_DRAG,
+		CURSOR_CAN_DROP,
+		CURSOR_FORBIDDEN,
+		CURSOR_VSIZE,
+		CURSOR_HSIZE,
+		CURSOR_BDIAGSIZE,
+		CURSOR_FDIAGSIZE,
+		CURSOR_MOVE,
+		CURSOR_VSPLIT,
+		CURSOR_HSPLIT,
+		CURSOR_HELP,
+		CURSOR_MAX
+	};
+
+	void set_mouse_mode(MouseMode p_mode);
+	MouseMode get_mouse_mode() const;
+
+	static Input *get_singleton();
+
+	virtual bool is_key_pressed(int p_scancode) const = 0;
+	virtual bool is_physical_key_pressed(int p_scancode) const = 0;
+	virtual bool is_mouse_button_pressed(int p_button) const = 0;
+	virtual bool is_joy_button_pressed(int p_device, int p_button) const = 0;
+	virtual bool is_action_pressed(const StringName &p_action, bool p_exact = false) const = 0;
+	virtual bool is_action_just_pressed(const StringName &p_action, bool p_exact = false) const = 0;
+	virtual bool is_action_just_released(const StringName &p_action, bool p_exact = false) const = 0;
+	virtual float get_action_strength(const StringName &p_action, bool p_exact = false) const = 0;
+	virtual float get_action_raw_strength(const StringName &p_action, bool p_exact = false) const = 0;
+
+	float get_axis(const StringName &p_negative_action, const StringName &p_positive_action) const;
+	Vector2 get_vector(const StringName &p_negative_x, const StringName &p_positive_x, const StringName &p_negative_y, const StringName &p_positive_y, float p_deadzone = -1.0f) const;
+
+	virtual float get_joy_axis(int p_device, int p_axis) const = 0;
+	virtual String get_joy_name(int p_idx) = 0;
+	virtual Array get_connected_joypads() = 0;
+	virtual void joy_connection_changed(int p_idx, bool p_connected, String p_name, String p_guid) = 0;
+	virtual void add_joy_mapping(String p_mapping, bool p_update_existing = false) = 0;
+	virtual void remove_joy_mapping(String p_guid) = 0;
+	virtual bool is_joy_known(int p_device) = 0;
+	virtual String get_joy_guid(int p_device) const = 0;
+	virtual bool should_ignore_device(int p_vendor_id, int p_product_id) const = 0;
+	virtual Vector2 get_joy_vibration_strength(int p_device) = 0;
+	virtual float get_joy_vibration_duration(int p_device) = 0;
+	virtual uint64_t get_joy_vibration_timestamp(int p_device) = 0;
+	virtual void start_joy_vibration(int p_device, float p_weak_magnitude, float p_strong_magnitude, float p_duration = 0) = 0;
+	virtual void stop_joy_vibration(int p_device) = 0;
+	virtual void vibrate_handheld(int p_duration_ms = 500) = 0;
+
+	virtual Point2 get_mouse_position() const = 0;
+	virtual Point2 get_last_mouse_speed() = 0;
+	virtual int get_mouse_button_mask() const = 0;
+
+	virtual void warp_mouse_position(const Vector2 &p_to) = 0;
+	virtual Point2i warp_mouse_motion(const Ref<InputEventMouseMotion> &p_motion, const Rect2 &p_rect) = 0;
+
+	virtual Vector3 get_gravity() const = 0;
+	virtual Vector3 get_accelerometer() const = 0;
+	virtual Vector3 get_magnetometer() const = 0;
+	virtual Vector3 get_gyroscope() const = 0;
+	virtual void set_gravity(const Vector3 &p_gravity) = 0;
+	virtual void set_accelerometer(const Vector3 &p_accel) = 0;
+	virtual void set_magnetometer(const Vector3 &p_magnetometer) = 0;
+	virtual void set_gyroscope(const Vector3 &p_gyroscope) = 0;
+
+	virtual void action_press(const StringName &p_action, float p_strength = 1.f) = 0;
+	virtual void action_release(const StringName &p_action) = 0;
+
+	void get_argument_options(const StringName &p_function, int p_idx, List<String> *r_options, const String &quote_style) const;
+
+	virtual bool is_emulating_touch_from_mouse() const = 0;
+	virtual bool is_emulating_mouse_from_touch() const = 0;
+
+	virtual CursorShape get_default_cursor_shape() const = 0;
+	virtual void set_default_cursor_shape(CursorShape p_shape) = 0;
+	virtual CursorShape get_current_cursor_shape() const = 0;
+	virtual void set_custom_mouse_cursor(const RES &p_cursor, CursorShape p_shape = CURSOR_ARROW, const Vector2 &p_hotspot = Vector2()) = 0;
+
+	virtual String get_joy_button_string(int p_button) = 0;
+	virtual String get_joy_axis_string(int p_axis) = 0;
+	virtual int get_joy_button_index_from_string(String p_button) = 0;
+	virtual int get_joy_axis_index_from_string(String p_axis) = 0;
+
+	virtual void parse_input_event(const Ref<InputEvent> &p_event) = 0;
+	virtual void flush_buffered_events() = 0;
+	virtual bool is_using_input_buffering() = 0;
+	virtual void set_use_input_buffering(bool p_enable) = 0;
+	virtual bool is_using_accumulated_input() = 0;
+	virtual void set_use_accumulated_input(bool p_enable) = 0;
+
+	Input();
+};
+
+VARIANT_ENUM_CAST(Input::MouseMode);
+VARIANT_ENUM_CAST(Input::CursorShape);
+
+#endif // INPUT_H

core/input/input_builders.py

@@ -0,0 +1,69 @@
+"""Functions used to generate source files during build time
+
+All such functions are invoked in a subprocess on Windows to prevent build flakiness.
+
+"""
+from platform_methods import subprocess_main
+from collections import OrderedDict
+
+def make_default_controller_mappings(target, source, env):
+    dst = target[0]
+    g = open(dst, "w")
+
+    g.write("/* THIS FILE IS GENERATED DO NOT EDIT */\n")
+    g.write('#include "core/typedefs.h"\n')
+    g.write('#include "core/input/default_controller_mappings.h"\n')
+
+    # ensure mappings have a consistent order
+    platform_mappings = OrderedDict()
+    for src_path in source:
+        with open(src_path, "r") as f:
+            # read mapping file and skip header
+            mapping_file_lines = f.readlines()[2:]
+
+        current_platform = None
+        for line in mapping_file_lines:
+            if not line:
+                continue
+            line = line.strip()
+            if len(line) == 0:
+                continue
+            if line[0] == "#":
+                current_platform = line[1:].strip()
+                if current_platform not in platform_mappings:
+                    platform_mappings[current_platform] = {}
+            elif current_platform:
+                line_parts = line.split(",")
+                guid = line_parts[0]
+                if guid in platform_mappings[current_platform]:
+                    g.write(
+                        "// WARNING - DATABASE {} OVERWROTE PRIOR MAPPING: {} {}\n".format(
+                            src_path, current_platform, platform_mappings[current_platform][guid]
+                        )
+                    )
+                platform_mappings[current_platform][guid] = line
+
+    platform_variables = {
+        "Linux": "#if X11_ENABLED",
+        "Windows": "#ifdef WINDOWS_ENABLED",
+        "Mac OS X": "#ifdef OSX_ENABLED",
+        "Android": "#if defined(__ANDROID__)",
+        "iOS": "#ifdef IPHONE_ENABLED",
+        "Javascript": "#ifdef JAVASCRIPT_ENABLED",
+        "UWP": "#ifdef UWP_ENABLED",
+    }
+
+    g.write("const char* DefaultControllerMappings::mappings[] = {\n")
+    for platform, mappings in platform_mappings.items():
+        variable = platform_variables[platform]
+        g.write("{}\n".format(variable))
+        for mapping in mappings.values():
+            g.write('\t"{}",\n'.format(mapping))
+        g.write("#endif\n")
+
+    g.write("\tNULL\n};\n")
+    g.close()
+
+
+if __name__ == "__main__":
+    subprocess_main(globals())

core/input/input_event.h

@@ -0,0 +1,677 @@
+#ifndef INPUT_EVENT_H
+#define INPUT_EVENT_H
+
+/*************************************************************************/
+/*  input_event.h                                                        */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/transform_2d.h"
+#include "core/object/resource.h"
+#include "core/string/ustring.h"
+#include "core/typedefs.h"
+
+/**
+ * Input Event classes. These are used in the main loop.
+ * The events are pretty obvious.
+ */
+
+class ShortCut;
+
+enum ButtonList {
+	BUTTON_LEFT = 1,
+	BUTTON_RIGHT = 2,
+	BUTTON_MIDDLE = 3,
+	BUTTON_WHEEL_UP = 4,
+	BUTTON_WHEEL_DOWN = 5,
+	BUTTON_WHEEL_LEFT = 6,
+	BUTTON_WHEEL_RIGHT = 7,
+	BUTTON_XBUTTON1 = 8,
+	BUTTON_XBUTTON2 = 9,
+	BUTTON_MASK_LEFT = (1 << (BUTTON_LEFT - 1)),
+	BUTTON_MASK_RIGHT = (1 << (BUTTON_RIGHT - 1)),
+	BUTTON_MASK_MIDDLE = (1 << (BUTTON_MIDDLE - 1)),
+	BUTTON_MASK_XBUTTON1 = (1 << (BUTTON_XBUTTON1 - 1)),
+	BUTTON_MASK_XBUTTON2 = (1 << (BUTTON_XBUTTON2 - 1))
+};
+
+enum JoystickList {
+
+	JOY_INVALID_OPTION = -1,
+
+	JOY_BUTTON_0 = 0,
+	JOY_BUTTON_1 = 1,
+	JOY_BUTTON_2 = 2,
+	JOY_BUTTON_3 = 3,
+	JOY_BUTTON_4 = 4,
+	JOY_BUTTON_5 = 5,
+	JOY_BUTTON_6 = 6,
+	JOY_BUTTON_7 = 7,
+	JOY_BUTTON_8 = 8,
+	JOY_BUTTON_9 = 9,
+	JOY_BUTTON_10 = 10,
+	JOY_BUTTON_11 = 11,
+	JOY_BUTTON_12 = 12,
+	JOY_BUTTON_13 = 13,
+	JOY_BUTTON_14 = 14,
+	JOY_BUTTON_15 = 15,
+	JOY_BUTTON_16 = 16,
+	JOY_BUTTON_17 = 17,
+	JOY_BUTTON_18 = 18,
+	JOY_BUTTON_19 = 19,
+	JOY_BUTTON_20 = 20,
+	JOY_BUTTON_21 = 21,
+	JOY_BUTTON_22 = 22,
+	JOY_BUTTON_MAX = 128, // Android supports up to 36 buttons. DirectInput supports up to 128 buttons.
+
+	JOY_L = JOY_BUTTON_4,
+	JOY_R = JOY_BUTTON_5,
+	JOY_L2 = JOY_BUTTON_6,
+	JOY_R2 = JOY_BUTTON_7,
+	JOY_L3 = JOY_BUTTON_8,
+	JOY_R3 = JOY_BUTTON_9,
+	JOY_SELECT = JOY_BUTTON_10,
+	JOY_START = JOY_BUTTON_11,
+	JOY_DPAD_UP = JOY_BUTTON_12,
+	JOY_DPAD_DOWN = JOY_BUTTON_13,
+	JOY_DPAD_LEFT = JOY_BUTTON_14,
+	JOY_DPAD_RIGHT = JOY_BUTTON_15,
+	JOY_GUIDE = JOY_BUTTON_16,
+	JOY_MISC1 = JOY_BUTTON_17,
+	JOY_PADDLE1 = JOY_BUTTON_18,
+	JOY_PADDLE2 = JOY_BUTTON_19,
+	JOY_PADDLE3 = JOY_BUTTON_20,
+	JOY_PADDLE4 = JOY_BUTTON_21,
+	JOY_TOUCHPAD = JOY_BUTTON_22,
+
+	JOY_SONY_CIRCLE = JOY_BUTTON_1,
+	JOY_SONY_X = JOY_BUTTON_0,
+	JOY_SONY_SQUARE = JOY_BUTTON_2,
+	JOY_SONY_TRIANGLE = JOY_BUTTON_3,
+
+	JOY_XBOX_A = JOY_BUTTON_0,
+	JOY_XBOX_B = JOY_BUTTON_1,
+	JOY_XBOX_X = JOY_BUTTON_2,
+	JOY_XBOX_Y = JOY_BUTTON_3,
+
+	JOY_DS_A = JOY_BUTTON_1,
+	JOY_DS_B = JOY_BUTTON_0,
+	JOY_DS_X = JOY_BUTTON_3,
+	JOY_DS_Y = JOY_BUTTON_2,
+
+	JOY_WII_C = JOY_BUTTON_5,
+	JOY_WII_Z = JOY_BUTTON_6,
+
+	JOY_WII_MINUS = JOY_BUTTON_10,
+	JOY_WII_PLUS = JOY_BUTTON_11,
+
+	JOY_VR_GRIP = JOY_BUTTON_2,
+	JOY_VR_PAD = JOY_BUTTON_14,
+	JOY_VR_TRIGGER = JOY_BUTTON_15,
+
+	JOY_OCULUS_AX = JOY_BUTTON_7,
+	JOY_OCULUS_BY = JOY_BUTTON_1,
+	JOY_OCULUS_MENU = JOY_BUTTON_3,
+
+	JOY_OPENVR_MENU = JOY_BUTTON_1,
+
+	// end of history
+
+	JOY_AXIS_0 = 0,
+	JOY_AXIS_1 = 1,
+	JOY_AXIS_2 = 2,
+	JOY_AXIS_3 = 3,
+	JOY_AXIS_4 = 4,
+	JOY_AXIS_5 = 5,
+	JOY_AXIS_6 = 6,
+	JOY_AXIS_7 = 7,
+	JOY_AXIS_8 = 8,
+	JOY_AXIS_9 = 9,
+	JOY_AXIS_MAX = 10,
+
+	JOY_ANALOG_LX = JOY_AXIS_0,
+	JOY_ANALOG_LY = JOY_AXIS_1,
+
+	JOY_ANALOG_RX = JOY_AXIS_2,
+	JOY_ANALOG_RY = JOY_AXIS_3,
+
+	JOY_ANALOG_L2 = JOY_AXIS_6,
+	JOY_ANALOG_R2 = JOY_AXIS_7,
+
+	JOY_VR_ANALOG_TRIGGER = JOY_AXIS_2,
+	JOY_VR_ANALOG_GRIP = JOY_AXIS_4,
+
+	JOY_OPENVR_TOUCHPADX = JOY_AXIS_0,
+	JOY_OPENVR_TOUCHPADY = JOY_AXIS_1,
+};
+
+enum MidiMessageList {
+	MIDI_MESSAGE_NOTE_OFF = 0x8,
+	MIDI_MESSAGE_NOTE_ON = 0x9,
+	MIDI_MESSAGE_AFTERTOUCH = 0xA,
+	MIDI_MESSAGE_CONTROL_CHANGE = 0xB,
+	MIDI_MESSAGE_PROGRAM_CHANGE = 0xC,
+	MIDI_MESSAGE_CHANNEL_PRESSURE = 0xD,
+	MIDI_MESSAGE_PITCH_BEND = 0xE,
+	MIDI_MESSAGE_SYSTEM_EXCLUSIVE = 0xF0,
+	MIDI_MESSAGE_QUARTER_FRAME = 0xF1,
+	MIDI_MESSAGE_SONG_POSITION_POINTER = 0xF2,
+	MIDI_MESSAGE_SONG_SELECT = 0xF3,
+	MIDI_MESSAGE_TUNE_REQUEST = 0xF6,
+	MIDI_MESSAGE_TIMING_CLOCK = 0xF8,
+	MIDI_MESSAGE_START = 0xFA,
+	MIDI_MESSAGE_CONTINUE = 0xFB,
+	MIDI_MESSAGE_STOP = 0xFC,
+	MIDI_MESSAGE_ACTIVE_SENSING = 0xFE,
+	MIDI_MESSAGE_SYSTEM_RESET = 0xFF,
+};
+
+/**
+ * Input Modifier Status
+ * for keyboard/mouse events.
+ */
+
+class InputEvent : public Resource {
+	GDCLASS(InputEvent, Resource);
+
+	int device;
+
+protected:
+	bool canceled;
+	bool pressed;
+
+	static void _bind_methods();
+
+public:
+	static const int DEVICE_ID_TOUCH_MOUSE;
+	static const int DEVICE_ID_INTERNAL;
+
+	void set_device(int p_device);
+	int get_device() const;
+
+	bool is_action(const StringName &p_action, bool p_exact_match = false) const;
+	bool is_action_pressed(const StringName &p_action, bool p_allow_echo = false, bool p_exact_match = false) const;
+	bool is_action_released(const StringName &p_action, bool p_exact_match = false) const;
+	float get_action_strength(const StringName &p_action, bool p_exact_match = false) const;
+	float get_action_raw_strength(const StringName &p_action, bool p_exact_match = false) const;
+
+	bool is_canceled() const;
+	bool is_pressed() const;
+	bool is_released() const;
+	virtual bool is_echo() const;
+	// ...-.
+
+	virtual String as_text() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+
+	virtual bool action_match(const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength, float p_deadzone) const;
+	virtual bool shortcut_match(const Ref<InputEvent> &p_event, bool p_exact_match = true) const;
+	virtual bool is_action_type() const;
+
+	virtual bool accumulate(const Ref<InputEvent> &p_event) { return false; }
+	InputEvent();
+};
+
+class InputEventWithModifiers : public InputEvent {
+	GDCLASS(InputEventWithModifiers, InputEvent);
+
+	bool shift;
+	bool alt;
+#ifdef APPLE_STYLE_KEYS
+	union {
+		bool command;
+		bool meta; //< windows/mac key
+	};
+
+	bool control;
+#else
+	union {
+		bool command; //< windows/mac key
+		bool control;
+	};
+	bool meta; //< windows/mac key
+
+#endif
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_shift(bool p_enabled);
+	bool get_shift() const;
+
+	void set_alt(bool p_enabled);
+	bool get_alt() const;
+
+	void set_control(bool p_enabled);
+	bool get_control() const;
+
+	void set_metakey(bool p_enabled);
+	bool get_metakey() const;
+
+	void set_command(bool p_enabled);
+	bool get_command() const;
+
+	void set_modifiers_from_event(const InputEventWithModifiers *event);
+
+	uint32_t get_modifiers_mask() const;
+
+	InputEventWithModifiers();
+};
+
+class InputEventKey : public InputEventWithModifiers {
+	GDCLASS(InputEventKey, InputEventWithModifiers);
+
+	uint32_t scancode; ///< check keyboard.h , KeyCode enum, without modifier masks
+	uint32_t physical_scancode;
+	uint32_t unicode; ///unicode
+
+	bool echo; /// true if this is an echo key
+
+	bool action_match_force_exact;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_pressed(bool p_pressed);
+
+	void set_scancode(uint32_t p_scancode);
+	uint32_t get_scancode() const;
+
+	void set_physical_scancode(uint32_t p_scancode);
+	uint32_t get_physical_scancode() const;
+
+	void set_unicode(uint32_t p_unicode);
+	uint32_t get_unicode() const;
+
+	void set_echo(bool p_enable);
+	virtual bool is_echo() const;
+
+	void set_action_match_force_exact(bool p_enable);
+	bool is_action_match_force_exact() const;
+
+	uint32_t get_scancode_with_modifiers() const;
+	uint32_t get_physical_scancode_with_modifiers() const;
+
+	virtual bool action_match(const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength, float p_deadzone) const;
+	virtual bool shortcut_match(const Ref<InputEvent> &p_event, bool p_exact_match = true) const;
+
+	virtual bool is_action_type() const { return true; }
+
+	virtual String as_text() const;
+
+	InputEventKey();
+};
+
+class InputEventMouse : public InputEventWithModifiers {
+	GDCLASS(InputEventMouse, InputEventWithModifiers);
+
+	int button_mask;
+
+	Vector2 pos;
+	Vector2 global_pos;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_button_mask(int p_mask);
+	int get_button_mask() const;
+
+	void set_position(const Vector2 &p_pos);
+	Vector2 get_position() const;
+
+	void set_global_position(const Vector2 &p_global_pos);
+	Vector2 get_global_position() const;
+
+	InputEventMouse();
+};
+
+class InputEventMouseButton : public InputEventMouse {
+	GDCLASS(InputEventMouseButton, InputEventMouse);
+
+	float factor;
+	int button_index;
+	bool doubleclick; //last even less than doubleclick time
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_factor(float p_factor);
+	float get_factor() const;
+
+	void set_button_index(int p_index);
+	int get_button_index() const;
+
+	void set_pressed(bool p_pressed);
+	void set_canceled(bool p_canceled);
+
+	void set_doubleclick(bool p_doubleclick);
+	bool is_doubleclick() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+	virtual bool action_match(const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength, float p_deadzone) const;
+	virtual bool shortcut_match(const Ref<InputEvent> &p_event, bool p_exact_match = true) const;
+
+	virtual bool is_action_type() const { return true; }
+	virtual String as_text() const;
+
+	InputEventMouseButton();
+};
+
+class InputEventMouseMotion : public InputEventMouse {
+	GDCLASS(InputEventMouseMotion, InputEventMouse);
+
+	Vector2 tilt;
+	float pressure;
+	Vector2 relative;
+	Vector2 speed;
+	bool pen_inverted;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_tilt(const Vector2 &p_tilt);
+	Vector2 get_tilt() const;
+
+	void set_pressure(float p_pressure);
+	float get_pressure() const;
+
+	void set_pen_inverted(bool p_inverted);
+	bool get_pen_inverted() const;
+
+	void set_relative(const Vector2 &p_relative);
+	Vector2 get_relative() const;
+
+	void set_speed(const Vector2 &p_speed);
+	Vector2 get_speed() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+	virtual String as_text() const;
+
+	virtual bool accumulate(const Ref<InputEvent> &p_event);
+
+	InputEventMouseMotion();
+};
+
+class InputEventJoypadMotion : public InputEvent {
+	GDCLASS(InputEventJoypadMotion, InputEvent);
+
+	int axis; ///< Joypad axis
+	float axis_value; ///< -1 to 1
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_axis(int p_axis);
+	int get_axis() const;
+
+	void set_axis_value(float p_value);
+	float get_axis_value() const;
+
+	virtual bool action_match(const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength, float p_deadzone) const;
+	virtual bool shortcut_match(const Ref<InputEvent> &p_event, bool p_exact_match = true) const;
+
+	virtual bool is_action_type() const { return true; }
+	virtual String as_text() const;
+
+	InputEventJoypadMotion();
+};
+
+class InputEventJoypadButton : public InputEvent {
+	GDCLASS(InputEventJoypadButton, InputEvent);
+
+	int button_index;
+	float pressure; //0 to 1
+protected:
+	static void _bind_methods();
+
+public:
+	void set_button_index(int p_index);
+	int get_button_index() const;
+
+	void set_pressed(bool p_pressed);
+
+	void set_pressure(float p_pressure);
+	float get_pressure() const;
+
+	virtual bool action_match(const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength, float p_deadzone) const;
+	virtual bool shortcut_match(const Ref<InputEvent> &p_event, bool p_exact_match = true) const;
+
+	virtual bool is_action_type() const { return true; }
+	virtual String as_text() const;
+
+	InputEventJoypadButton();
+};
+
+class InputEventScreenTouch : public InputEvent {
+	GDCLASS(InputEventScreenTouch, InputEvent);
+	int index;
+	Vector2 pos;
+	bool double_tap;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_index(int p_index);
+	int get_index() const;
+
+	void set_position(const Vector2 &p_pos);
+	Vector2 get_position() const;
+
+	void set_pressed(bool p_pressed);
+	void set_canceled(bool p_canceled);
+
+	void set_double_tap(bool p_double_tap);
+	bool is_double_tap() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+	virtual String as_text() const;
+
+	InputEventScreenTouch();
+};
+
+class InputEventScreenDrag : public InputEvent {
+	GDCLASS(InputEventScreenDrag, InputEvent);
+	int index;
+	Vector2 pos;
+	Vector2 relative;
+	Vector2 speed;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_index(int p_index);
+	int get_index() const;
+
+	void set_position(const Vector2 &p_pos);
+	Vector2 get_position() const;
+
+	void set_relative(const Vector2 &p_relative);
+	Vector2 get_relative() const;
+
+	void set_speed(const Vector2 &p_speed);
+	Vector2 get_speed() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+	virtual String as_text() const;
+
+	virtual bool accumulate(const Ref<InputEvent> &p_event);
+
+	InputEventScreenDrag();
+};
+
+class InputEventAction : public InputEvent {
+	GDCLASS(InputEventAction, InputEvent);
+
+	StringName action;
+	float strength;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_action(const StringName &p_action);
+	StringName get_action() const;
+
+	void set_pressed(bool p_pressed);
+
+	void set_strength(float p_strength);
+	float get_strength() const;
+
+	virtual bool is_action(const StringName &p_action) const;
+
+	virtual bool action_match(const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength, float p_deadzone) const;
+	virtual bool shortcut_match(const Ref<InputEvent> &p_event, bool p_exact_match = true) const;
+
+	virtual bool is_action_type() const { return true; }
+	virtual String as_text() const;
+
+	InputEventAction();
+};
+
+class InputEventGesture : public InputEventWithModifiers {
+	GDCLASS(InputEventGesture, InputEventWithModifiers);
+
+	Vector2 pos;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_position(const Vector2 &p_pos);
+	Vector2 get_position() const;
+};
+
+class InputEventMagnifyGesture : public InputEventGesture {
+	GDCLASS(InputEventMagnifyGesture, InputEventGesture);
+	real_t factor;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_factor(real_t p_factor);
+	real_t get_factor() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+	virtual String as_text() const;
+
+	InputEventMagnifyGesture();
+};
+
+class InputEventPanGesture : public InputEventGesture {
+	GDCLASS(InputEventPanGesture, InputEventGesture);
+	Vector2 delta;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_delta(const Vector2 &p_delta);
+	Vector2 get_delta() const;
+
+	virtual Ref<InputEvent> xformed_by(const Transform2D &p_xform, const Vector2 &p_local_ofs = Vector2()) const;
+	virtual String as_text() const;
+
+	InputEventPanGesture();
+};
+
+class InputEventMIDI : public InputEvent {
+	GDCLASS(InputEventMIDI, InputEvent);
+
+	int channel;
+	int message;
+	int pitch;
+	int velocity;
+	int instrument;
+	int pressure;
+	int controller_number;
+	int controller_value;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_channel(const int p_channel);
+	int get_channel() const;
+
+	void set_message(const int p_message);
+	int get_message() const;
+
+	void set_pitch(const int p_pitch);
+	int get_pitch() const;
+
+	void set_velocity(const int p_velocity);
+	int get_velocity() const;
+
+	void set_instrument(const int p_instrument);
+	int get_instrument() const;
+
+	void set_pressure(const int p_pressure);
+	int get_pressure() const;
+
+	void set_controller_number(const int p_controller_number);
+	int get_controller_number() const;
+
+	void set_controller_value(const int p_controller_value);
+	int get_controller_value() const;
+
+	virtual String as_text() const;
+
+	InputEventMIDI();
+};
+
+class InputEventShortCut : public InputEvent {
+	GDCLASS(InputEventShortCut, InputEvent);
+
+	Ref<ShortCut> shortcut;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_shortcut(Ref<ShortCut> p_shortcut);
+	Ref<ShortCut> get_shortcut();
+
+	virtual String as_text() const;
+	virtual String to_string();
+
+	InputEventShortCut();
+	~InputEventShortCut();
+};
+
+#endif

core/input/input_map.cpp

@@ -0,0 +1,376 @@
+/*************************************************************************/
+/*  input_map.cpp                                                        */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "input_map.h"
+
+#include "core/config/project_settings.h"
+#include "core/input/input.h"
+#include "core/os/keyboard.h"
+
+InputMap *InputMap::singleton = nullptr;
+
+int InputMap::ALL_DEVICES = -1;
+
+void InputMap::_bind_methods() {
+	ClassDB::bind_method(D_METHOD("has_action", "action"), &InputMap::has_action);
+	ClassDB::bind_method(D_METHOD("get_actions"), &InputMap::_get_actions);
+	ClassDB::bind_method(D_METHOD("add_action", "action", "deadzone"), &InputMap::add_action, DEFVAL(0.5f));
+	ClassDB::bind_method(D_METHOD("erase_action", "action"), &InputMap::erase_action);
+
+	ClassDB::bind_method(D_METHOD("action_set_deadzone", "action", "deadzone"), &InputMap::action_set_deadzone);
+	ClassDB::bind_method(D_METHOD("action_get_deadzone", "action"), &InputMap::action_get_deadzone);
+	ClassDB::bind_method(D_METHOD("action_add_event", "action", "event"), &InputMap::action_add_event);
+	ClassDB::bind_method(D_METHOD("action_has_event", "action", "event"), &InputMap::action_has_event);
+	ClassDB::bind_method(D_METHOD("action_erase_event", "action", "event"), &InputMap::action_erase_event);
+	ClassDB::bind_method(D_METHOD("action_erase_events", "action"), &InputMap::action_erase_events);
+	ClassDB::bind_method(D_METHOD("get_action_list", "action"), &InputMap::_get_action_list);
+	ClassDB::bind_method(D_METHOD("event_is_action", "event", "action", "exact_match"), &InputMap::event_is_action, DEFVAL(false));
+	ClassDB::bind_method(D_METHOD("load_from_globals"), &InputMap::load_from_globals);
+}
+
+/**
+ * Returns an nonexistent action error message with a suggestion of the closest
+ * matching action name (if possible).
+ */
+String InputMap::suggest_actions(const StringName &p_action) const {
+	List<StringName> actions = get_actions();
+	StringName closest_action;
+	float closest_similarity = 0.0;
+
+	// Find the most action with the most similar name.
+	for (List<StringName>::Element *E = actions.front(); E; E = E->next()) {
+		const float similarity = String(E->get()).similarity(p_action);
+
+		if (similarity > closest_similarity) {
+			closest_action = E->get();
+			closest_similarity = similarity;
+		}
+	}
+
+	String error_message = vformat("The InputMap action \"%s\" doesn't exist.", p_action);
+
+	if (closest_similarity >= 0.4) {
+		// Only include a suggestion in the error message if it's similar enough.
+		error_message += vformat(" Did you mean \"%s\"?", closest_action);
+	}
+	return error_message;
+}
+
+void InputMap::add_action(const StringName &p_action, float p_deadzone) {
+	ERR_FAIL_COND_MSG(input_map.has(p_action), "InputMap already has action \"" + String(p_action) + "\".");
+	input_map[p_action] = Action();
+	static int last_id = 1;
+	input_map[p_action].id = last_id;
+	input_map[p_action].deadzone = p_deadzone;
+	last_id++;
+}
+
+void InputMap::erase_action(const StringName &p_action) {
+	ERR_FAIL_COND_MSG(!input_map.has(p_action), suggest_actions(p_action));
+
+	input_map.erase(p_action);
+}
+
+Array InputMap::_get_actions() {
+	Array ret;
+	List<StringName> actions = get_actions();
+	if (actions.empty()) {
+		return ret;
+	}
+
+	for (const List<StringName>::Element *E = actions.front(); E; E = E->next()) {
+		ret.push_back(E->get());
+	}
+
+	return ret;
+}
+
+List<StringName> InputMap::get_actions() const {
+	List<StringName> actions = List<StringName>();
+	if (input_map.empty()) {
+		return actions;
+	}
+
+	for (RBMap<StringName, Action>::Element *E = input_map.front(); E; E = E->next()) {
+		actions.push_back(E->key());
+	}
+
+	return actions;
+}
+
+List<Ref<InputEvent>>::Element *InputMap::_find_event(Action &p_action, const Ref<InputEvent> &p_event, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength) const {
+	ERR_FAIL_COND_V(!p_event.is_valid(), nullptr);
+
+	for (List<Ref<InputEvent>>::Element *E = p_action.inputs.front(); E; E = E->next()) {
+		const Ref<InputEvent> e = E->get();
+
+		//if (e.type != Ref<InputEvent>::KEY && e.device != p_event.device) -- unsure about the KEY comparison, why is this here?
+		//	continue;
+
+		int device = e->get_device();
+		if (device == ALL_DEVICES || device == p_event->get_device()) {
+			if (e->action_match(p_event, p_exact_match, p_pressed, p_strength, p_raw_strength, p_action.deadzone)) {
+				return E;
+			}
+		}
+	}
+
+	return nullptr;
+}
+
+bool InputMap::has_action(const StringName &p_action) const {
+	return input_map.has(p_action);
+}
+
+float InputMap::action_get_deadzone(const StringName &p_action) {
+	ERR_FAIL_COND_V_MSG(!input_map.has(p_action), 0.0f, suggest_actions(p_action));
+
+	return input_map[p_action].deadzone;
+}
+
+void InputMap::action_set_deadzone(const StringName &p_action, float p_deadzone) {
+	ERR_FAIL_COND_MSG(!input_map.has(p_action), suggest_actions(p_action));
+
+	input_map[p_action].deadzone = p_deadzone;
+}
+
+void InputMap::action_add_event(const StringName &p_action, const Ref<InputEvent> &p_event) {
+	ERR_FAIL_COND_MSG(p_event.is_null(), "It's not a reference to a valid InputEvent object.");
+	ERR_FAIL_COND_MSG(!input_map.has(p_action), suggest_actions(p_action));
+
+	if (_find_event(input_map[p_action], p_event, true)) {
+		return; // Already added.
+	}
+
+	input_map[p_action].inputs.push_back(p_event);
+}
+
+bool InputMap::action_has_event(const StringName &p_action, const Ref<InputEvent> &p_event) {
+	ERR_FAIL_COND_V_MSG(!input_map.has(p_action), false, suggest_actions(p_action));
+
+	return (_find_event(input_map[p_action], p_event, true) != nullptr);
+}
+
+void InputMap::action_erase_event(const StringName &p_action, const Ref<InputEvent> &p_event) {
+	ERR_FAIL_COND_MSG(!input_map.has(p_action), suggest_actions(p_action));
+
+	List<Ref<InputEvent>>::Element *E = _find_event(input_map[p_action], p_event, true);
+	if (E) {
+		input_map[p_action].inputs.erase(E);
+		if (Input::get_singleton()->is_action_pressed(p_action)) {
+			Input::get_singleton()->action_release(p_action);
+		}
+	}
+}
+
+void InputMap::action_erase_events(const StringName &p_action) {
+	ERR_FAIL_COND_MSG(!input_map.has(p_action), suggest_actions(p_action));
+
+	input_map[p_action].inputs.clear();
+}
+
+Array InputMap::_get_action_list(const StringName &p_action) {
+	Array ret;
+	const List<Ref<InputEvent>> *al = get_action_list(p_action);
+	if (al) {
+		for (const List<Ref<InputEvent>>::Element *E = al->front(); E; E = E->next()) {
+			ret.push_back(E->get());
+		}
+	}
+
+	return ret;
+}
+
+const List<Ref<InputEvent>> *InputMap::get_action_list(const StringName &p_action) {
+	const RBMap<StringName, Action>::Element *E = input_map.find(p_action);
+	if (!E) {
+		return nullptr;
+	}
+
+	return &E->get().inputs;
+}
+
+bool InputMap::event_is_action(const Ref<InputEvent> &p_event, const StringName &p_action, bool p_exact_match) const {
+	return event_get_action_status(p_event, p_action, p_exact_match);
+}
+
+bool InputMap::event_get_action_status(const Ref<InputEvent> &p_event, const StringName &p_action, bool p_exact_match, bool *p_pressed, float *p_strength, float *p_raw_strength) const {
+	RBMap<StringName, Action>::Element *E = input_map.find(p_action);
+	ERR_FAIL_COND_V_MSG(!E, false, suggest_actions(p_action));
+
+	Ref<InputEventAction> input_event_action = p_event;
+	if (input_event_action.is_valid()) {
+		bool pressed = input_event_action->is_pressed();
+		if (p_pressed != nullptr) {
+			*p_pressed = pressed;
+		}
+		if (p_strength != nullptr) {
+			*p_strength = pressed ? input_event_action->get_strength() : 0.0f;
+		}
+		return input_event_action->get_action() == p_action;
+	}
+
+	bool pressed;
+	float strength;
+	float raw_strength;
+	List<Ref<InputEvent>>::Element *event = _find_event(E->get(), p_event, p_exact_match, &pressed, &strength, &raw_strength);
+	if (event != nullptr) {
+		if (p_pressed != nullptr) {
+			*p_pressed = pressed;
+		}
+		if (p_strength != nullptr) {
+			*p_strength = strength;
+		}
+		if (p_raw_strength != nullptr) {
+			*p_raw_strength = raw_strength;
+		}
+		return true;
+	} else {
+		return false;
+	}
+}
+
+const RBMap<StringName, InputMap::Action> &InputMap::get_action_map() const {
+	return input_map;
+}
+
+void InputMap::load_from_globals() {
+	input_map.clear();
+
+	List<PropertyInfo> pinfo;
+	ProjectSettings::get_singleton()->get_property_list(&pinfo);
+
+	for (List<PropertyInfo>::Element *E = pinfo.front(); E; E = E->next()) {
+		const PropertyInfo &pi = E->get();
+
+		if (!pi.name.begins_with("input/")) {
+			continue;
+		}
+
+		String name = pi.name.substr(pi.name.find("/") + 1, pi.name.length());
+
+		Dictionary action = ProjectSettings::get_singleton()->get(pi.name);
+		float deadzone = action.has("deadzone") ? (float)action["deadzone"] : 0.5f;
+		Array events = action["events"];
+
+		add_action(name, deadzone);
+		for (int i = 0; i < events.size(); i++) {
+			Ref<InputEvent> event = events[i];
+			if (event.is_null()) {
+				continue;
+			}
+			action_add_event(name, event);
+		}
+	}
+}
+
+void InputMap::load_default() {
+	Ref<InputEventKey> key;
+
+	add_action("ui_accept");
+	key.instance();
+	key->set_scancode(KEY_ENTER);
+	action_add_event("ui_accept", key);
+
+	key.instance();
+	key->set_scancode(KEY_KP_ENTER);
+	action_add_event("ui_accept", key);
+
+	key.instance();
+	key->set_scancode(KEY_SPACE);
+	action_add_event("ui_accept", key);
+
+	add_action("ui_select");
+	key.instance();
+	key->set_scancode(KEY_SPACE);
+	action_add_event("ui_select", key);
+
+	add_action("ui_cancel");
+	key.instance();
+	key->set_scancode(KEY_ESCAPE);
+	action_add_event("ui_cancel", key);
+
+	add_action("ui_focus_next");
+	key.instance();
+	key->set_scancode(KEY_TAB);
+	action_add_event("ui_focus_next", key);
+
+	add_action("ui_focus_prev");
+	key.instance();
+	key->set_scancode(KEY_TAB);
+	key->set_shift(true);
+	action_add_event("ui_focus_prev", key);
+
+	add_action("ui_left");
+	key.instance();
+	key->set_scancode(KEY_LEFT);
+	action_add_event("ui_left", key);
+
+	add_action("ui_right");
+	key.instance();
+	key->set_scancode(KEY_RIGHT);
+	action_add_event("ui_right", key);
+
+	add_action("ui_up");
+	key.instance();
+	key->set_scancode(KEY_UP);
+	action_add_event("ui_up", key);
+
+	add_action("ui_down");
+	key.instance();
+	key->set_scancode(KEY_DOWN);
+	action_add_event("ui_down", key);
+
+	add_action("ui_page_up");
+	key.instance();
+	key->set_scancode(KEY_PAGEUP);
+	action_add_event("ui_page_up", key);
+
+	add_action("ui_page_down");
+	key.instance();
+	key->set_scancode(KEY_PAGEDOWN);
+	action_add_event("ui_page_down", key);
+
+	add_action("ui_home");
+	key.instance();
+	key->set_scancode(KEY_HOME);
+	action_add_event("ui_home", key);
+
+	add_action("ui_end");
+	key.instance();
+	key->set_scancode(KEY_END);
+	action_add_event("ui_end", key);
+}
+
+InputMap::InputMap() {
+	ERR_FAIL_COND_MSG(singleton, "Singleton in InputMap already exist.");
+	singleton = this;
+}

core/input/input_map.h

@@ -0,0 +1,94 @@
+#ifndef INPUT_MAP_H
+#define INPUT_MAP_H
+
+/*************************************************************************/
+/*  input_map.h                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/input/input_event.h"
+#include "core/object/object.h"
+
+class InputMap : public Object {
+	GDCLASS(InputMap, Object);
+
+public:
+	/**
+	 * A special value used to signify that a given Action can be triggered by any device
+	 */
+	static int ALL_DEVICES;
+
+	struct Action {
+		int id;
+		float deadzone;
+		List<Ref<InputEvent>> inputs;
+	};
+
+private:
+	static InputMap *singleton;
+
+	mutable RBMap<StringName, Action> input_map;
+
+	List<Ref<InputEvent>>::Element *_find_event(Action &p_action, const Ref<InputEvent> &p_event, bool p_exact_match = false, bool *p_pressed = nullptr, float *p_strength = nullptr, float *p_raw_strength = nullptr) const;
+
+	Array _get_action_list(const StringName &p_action);
+	Array _get_actions();
+
+protected:
+	static void _bind_methods();
+
+public:
+	static _FORCE_INLINE_ InputMap *get_singleton() { return singleton; }
+
+	bool has_action(const StringName &p_action) const;
+	List<StringName> get_actions() const;
+	void add_action(const StringName &p_action, float p_deadzone = 0.5);
+	void erase_action(const StringName &p_action);
+
+	float action_get_deadzone(const StringName &p_action);
+	void action_set_deadzone(const StringName &p_action, float p_deadzone);
+	void action_add_event(const StringName &p_action, const Ref<InputEvent> &p_event);
+	bool action_has_event(const StringName &p_action, const Ref<InputEvent> &p_event);
+	void action_erase_event(const StringName &p_action, const Ref<InputEvent> &p_event);
+	void action_erase_events(const StringName &p_action);
+
+	const List<Ref<InputEvent>> *get_action_list(const StringName &p_action);
+	bool event_is_action(const Ref<InputEvent> &p_event, const StringName &p_action, bool p_exact_match = false) const;
+	bool event_get_action_status(const Ref<InputEvent> &p_event, const StringName &p_action, bool p_exact_match = false, bool *p_pressed = nullptr, float *p_strength = nullptr, float *p_raw_strength = nullptr) const;
+
+	const RBMap<StringName, Action> &get_action_map() const;
+	void load_from_globals();
+	void load_default();
+
+	String suggest_actions(const StringName &p_action) const;
+
+	InputMap();
+};
+
+#endif // INPUT_MAP_H

core/input/pandemoniumcontrollerdb.txt

@@ -0,0 +1,38 @@
+# Game Controller DB for Godot in SDL 2.0.16 format
+# Source: https://github.com/Relintai/pandemonium_engine
+
+# Windows
+__XINPUT_DEVICE__,XInput Gamepad,a:b12,b:b13,x:b14,y:b15,start:b4,back:b5,leftstick:b6,rightstick:b7,leftshoulder:b8,rightshoulder:b9,dpup:b0,dpdown:b1,dpleft:b2,dpright:b3,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:Windows,
+
+# Android
+Default Android Gamepad,Default Controller,leftx:a0,lefty:a1,dpdown:h0.4,rightstick:b8,rightshoulder:b10,rightx:a2,start:b6,righty:a3,dpleft:h0.8,lefttrigger:a4,x:b2,dpup:h0.1,back:b4,leftstick:b7,leftshoulder:b9,y:b3,a:b0,dpright:h0.2,righttrigger:a5,b:b1,platform:Android,
+
+# Javascript
+standard,Standard Gamepad Mapping,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:b6,righttrigger:b7,a:b0,b:b1,x:b2,y:b3,leftshoulder:b4,rightshoulder:b5,back:b8,start:b9,leftstick:b10,rightstick:b11,dpup:b12,dpdown:b13,dpleft:b14,dpright:b15,guide:b16,leftstick:b10,rightstick:b11,platform:Javascript,
+Linux24c6581a,PowerA Xbox One Cabled,a:b0,b:b1,y:b3,x:b2,start:b7,guide:b8,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript,
+Linux0e6f0301,Logic 3 Controller (xbox compatible),a:b0,b:b1,y:b3,x:b2,start:b7,guide:b8,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript,
+Linux045e028e,Microsoft X-Box 360 pad,a:b0,b:b1,y:b3,x:b2,start:b7,guide:b8,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript,
+Linux045e02d1,Microsoft X-Box One pad,a:b0,b:b1,y:b3,x:b2,start:b7,guide:b8,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript,
+Linux045e02ea,Microsoft X-Box One S pad,a:b0,b:b1,y:b3,x:b2,start:b7,guide:b8,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript,
+Linux045e0b12,Microsoft X-Box Series X pad,a:b0,b:b1,y:b3,x:b2,start:b7,guide:b8,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript,
+Linux044fb315,Thrustmaster dual analog 3.2,a:b0,b:b2,y:b3,x:b1,start:b9,back:b8,leftstick:b10,rightstick:b11,leftshoulder:b4,rightshoulder:b6,dpup:-a5,dpleft:-a4,dpdown:+a5,dpright:+a4,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:b5,righttrigger:b7,platform:Javascript,
+Linux0e8f0003,PS3 Controller,a:b2,b:b1,back:b8,dpdown:+a5,dpleft:-a4,dpright:+a4,dpup:-a5,leftshoulder:b4,leftstick:b10,lefttrigger:b6,leftx:a0,lefty:a1,rightshoulder:b5,rightstick:b11,righttrigger:b7,rightx:a2,righty:a3,start:b9,x:b3,y:b0,platform:Javascript,
+MacOSX24c6581a,PowerA Xbox One Cabled,a:b11,b:b12,y:b14,x:b13,start:b4,back:b5,leftstick:b6,rightstick:b7,leftshoulder:b8,rightshoulder:b9,dpup:b0,dpleft:b2,dpdown:b1,dpright:b3,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:Javascript
+MacOSX045e028e,Xbox 360 Wired Controller,a:b11,b:b12,y:b14,x:b13,start:b4,back:b5,leftstick:b6,rightstick:b7,leftshoulder:b8,rightshoulder:b9,dpup:b0,dpleft:b2,dpdown:b1,dpright:b3,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:Javascript
+MacOSX045e02d1,Xbox One Controller,a:b11,b:b12,y:b14,x:b13,start:b4,back:b5,leftstick:b6,rightstick:b7,leftshoulder:b8,rightshoulder:b9,dpup:b0,dpleft:b2,dpdown:b1,dpright:b3,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:Javascript
+MacOSX045e02ea,Xbox One S Controller,a:b11,b:b12,y:b14,x:b13,start:b4,back:b5,leftstick:b6,rightstick:b7,leftshoulder:b8,rightshoulder:b9,dpup:b0,dpleft:b2,dpdown:b1,dpright:b3,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:Javascript
+MacOSX045e0b12,Xbox Series X Controller,a:b11,b:b12,y:b14,x:b13,start:b4,back:b5,leftstick:b6,rightstick:b7,leftshoulder:b8,rightshoulder:b9,dpup:b0,dpleft:b2,dpdown:b1,dpright:b3,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:Javascript
+Linux15320a14,Razer Wolverine Ultimate,a:b0,b:b1,y:b3,x:b2,start:b7,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript
+Linux05832060,iBuffalo BSGP801,a:b1,b:b0,y:b2,x:b3,start:b7,back:b6,leftshoulder:b4,rightshoulder:b5,dpup:-a1,dpleft:-a0,dpdown:+a1,dpright:+a0,platform:Javascript
+MacOSX05832060,iBuffalo BSGP801,a:b1,b:b0,y:b2,x:b3,start:b7,back:b6,leftshoulder:b4,rightshoulder:b5,dpup:-a1,dpleft:-a0,dpdown:+a1,dpright:+a0,platform:Javascript
+Linux0e8f3013,HuiJia USB GamePad,a:b2,b:b1,y:b0,x:b3,start:b9,back:b8,leftshoulder:b6,rightshoulder:b7,dpup:-a1,dpleft:-a0,dpdown:+a1,dpright:+a0,platform:Javascript
+Windows0e8f3013,HuiJia USB GamePad,a:b2,b:b1,y:b0,x:b3,start:b9,back:b8,leftshoulder:b6,rightshoulder:b7,dpup:-a1,dpleft:-a0,dpdown:+a1,dpright:+a0,platform:Javascript
+MacOSX0e8f3013,HuiJia USB GamePad,a:b2,b:b1,y:b0,x:b3,start:b9,back:b8,leftshoulder:b6,rightshoulder:b7,dpup:-a4,dpleft:-a3,dpdown:+a4,dpright:+a3,platform:Javascript
+Linux046dc216,046d-c216-Logitech Logitech Dual Action,a:b1,b:b2,y:b3,x:b0,start:b9,back:b8,leftstick:b10,rightstick:b11,leftshoulder:b4,rightshoulder:b5,dpup:-a5,dpleft:-a4,dpdown:+a5,dpright:+a4,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:b6,righttrigger:b7,platform:Javascript
+Linux20d6a713,Bensussen Deutsch & Associates Inc.(BDA) NSW Wired controller,a:b1,b:b2,y:b3,x:b0,start:b9,back:b8,leftstick:b10,rightstick:b11,leftshoulder:b4,rightshoulder:b5,dpup:-a5,dpleft:-a4,dpdown:+a5,dpright:+a4,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:b6,righttrigger:b7,platform:Javascript
+Linux054c05c4,Sony Computer Entertainment Wireless Controller,a:b0,b:b1,y:b2,x:b3,start:b9,back:b8,leftstick:b11,rightstick:b12,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript
+Linux18d19400,18d1-9400-Google LLC Stadia Controller rev. A,a:b0,b:b1,y:b3,x:b2,start:b7,back:b6,leftstick:b9,rightstick:b10,leftshoulder:b4,rightshoulder:b5,dpup:-a7,dpleft:-a6,dpdown:+a7,dpright:+a6,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a5,righttrigger:a4,platform:Javascript
+Linux054c0268,054c-0268-Sony PLAYSTATION(R)3 Controller,a:b0,b:b1,y:b2,x:b3,start:b9,guide:b10,back:b8,leftstick:b11,rightstick:b12,leftshoulder:b4,rightshoulder:b5,dpup:b13,dpleft:b15,dpdown:b14,dpright:b16,leftx:a0,lefty:a1,rightx:a3,righty:a4,lefttrigger:a2,righttrigger:a5,platform:Javascript
+
+# UWP
+__UWP_GAMEPAD__,Xbox Controller,a:b2,b:b3,x:b4,y:b5,start:b0,back:b1,leftstick:b12,rightstick:b13,leftshoulder:b10,rightshoulder:b11,dpup:b6,dpdown:b7,dpleft:b8,dpright:b9,leftx:a0,lefty:a1,rightx:a2,righty:a3,lefttrigger:a4,righttrigger:a5,platform:UWP,

core/input/shortcut.cpp

@@ -0,0 +1,78 @@
+/*************************************************************************/
+/*  shortcut.cpp                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "shortcut.h"
+
+#include "core/input/input_event.h"
+#include "core/os/keyboard.h"
+
+void ShortCut::set_shortcut(const Ref<InputEvent> &p_shortcut) {
+	shortcut = p_shortcut;
+	emit_changed();
+}
+
+Ref<InputEvent> ShortCut::get_shortcut() const {
+	return shortcut;
+}
+
+bool ShortCut::is_shortcut(const Ref<InputEvent> &p_event) const {
+	return shortcut.is_valid() && shortcut->shortcut_match(p_event);
+}
+
+String ShortCut::get_as_text() const {
+	if (shortcut.is_valid()) {
+		return shortcut->as_text();
+	} else {
+		return "None";
+	}
+}
+
+bool ShortCut::is_valid() const {
+	return shortcut.is_valid();
+}
+
+void ShortCut::_bind_methods() {
+	ClassDB::bind_method(D_METHOD("set_shortcut", "event"), &ShortCut::set_shortcut);
+	ClassDB::bind_method(D_METHOD("get_shortcut"), &ShortCut::get_shortcut);
+
+	ClassDB::bind_method(D_METHOD("is_valid"), &ShortCut::is_valid);
+
+	ClassDB::bind_method(D_METHOD("is_shortcut", "event"), &ShortCut::is_shortcut);
+	ClassDB::bind_method(D_METHOD("get_as_text"), &ShortCut::get_as_text);
+
+	ADD_PROPERTY(PropertyInfo(Variant::OBJECT, "shortcut", PROPERTY_HINT_RESOURCE_TYPE, "InputEvent"), "set_shortcut", "get_shortcut");
+}
+
+ShortCut::ShortCut() {
+}
+
+ShortCut::~ShortCut() {
+}

core/input/shortcut.h

@@ -0,0 +1,59 @@
+#ifndef SHORTCUT_H
+#define SHORTCUT_H
+
+/*************************************************************************/
+/*  shortcut.h                                                           */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/object/resource.h"
+
+class InputEvent;
+
+class ShortCut : public Resource {
+	GDCLASS(ShortCut, Resource);
+
+	Ref<InputEvent> shortcut;
+
+protected:
+	static void _bind_methods();
+
+public:
+	void set_shortcut(const Ref<InputEvent> &p_shortcut);
+	Ref<InputEvent> get_shortcut() const;
+	bool is_shortcut(const Ref<InputEvent> &p_event) const;
+	bool is_valid() const;
+
+	String get_as_text() const;
+
+	ShortCut();
+	~ShortCut();
+};
+
+#endif // SHORTCUT_H

core/math/aabb.cpp

@@ -0,0 +1,431 @@
+/*************************************************************************/
+/*  aabb.cpp                                                             */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "aabb.h"
+
+#include "core/string/print_string.h"
+#include "core/variant/variant.h"
+
+real_t AABB::get_volume() const {
+	return size.x * size.y * size.z;
+}
+
+bool AABB::operator==(const AABB &p_rval) const {
+	return ((position == p_rval.position) && (size == p_rval.size));
+}
+bool AABB::operator!=(const AABB &p_rval) const {
+	return ((position != p_rval.position) || (size != p_rval.size));
+}
+
+bool AABB::create_from_points(const Vector<Vector3> &p_points) {
+	if (!p_points.size()) {
+		return false;
+	}
+
+	Vector3 begin = p_points[0];
+	Vector3 end = begin;
+
+	for (int n = 1; n < p_points.size(); n++) {
+		const Vector3 &pt = p_points[n];
+
+		if (pt.x < begin.x) {
+			begin.x = pt.x;
+		}
+		if (pt.y < begin.y) {
+			begin.y = pt.y;
+		}
+		if (pt.z < begin.z) {
+			begin.z = pt.z;
+		}
+
+		if (pt.x > end.x) {
+			end.x = pt.x;
+		}
+		if (pt.y > end.y) {
+			end.y = pt.y;
+		}
+		if (pt.z > end.z) {
+			end.z = pt.z;
+		}
+	}
+
+	position = begin;
+	size = end - begin;
+
+	return true;
+}
+
+void AABB::merge_with(const AABB &p_aabb) {
+	Vector3 beg_1, beg_2;
+	Vector3 end_1, end_2;
+	Vector3 min, max;
+
+	beg_1 = position;
+	beg_2 = p_aabb.position;
+	end_1 = Vector3(size.x, size.y, size.z) + beg_1;
+	end_2 = Vector3(p_aabb.size.x, p_aabb.size.y, p_aabb.size.z) + beg_2;
+
+	min.x = (beg_1.x < beg_2.x) ? beg_1.x : beg_2.x;
+	min.y = (beg_1.y < beg_2.y) ? beg_1.y : beg_2.y;
+	min.z = (beg_1.z < beg_2.z) ? beg_1.z : beg_2.z;
+
+	max.x = (end_1.x > end_2.x) ? end_1.x : end_2.x;
+	max.y = (end_1.y > end_2.y) ? end_1.y : end_2.y;
+	max.z = (end_1.z > end_2.z) ? end_1.z : end_2.z;
+
+	position = min;
+	size = max - min;
+}
+
+bool AABB::is_equal_approx(const AABB &p_aabb) const {
+	return position.is_equal_approx(p_aabb.position) && size.is_equal_approx(p_aabb.size);
+}
+
+AABB AABB::intersection(const AABB &p_aabb) const {
+	Vector3 src_min = position;
+	Vector3 src_max = position + size;
+	Vector3 dst_min = p_aabb.position;
+	Vector3 dst_max = p_aabb.position + p_aabb.size;
+
+	Vector3 min, max;
+
+	if (src_min.x > dst_max.x || src_max.x < dst_min.x) {
+		return AABB();
+	} else {
+		min.x = (src_min.x > dst_min.x) ? src_min.x : dst_min.x;
+		max.x = (src_max.x < dst_max.x) ? src_max.x : dst_max.x;
+	}
+
+	if (src_min.y > dst_max.y || src_max.y < dst_min.y) {
+		return AABB();
+	} else {
+		min.y = (src_min.y > dst_min.y) ? src_min.y : dst_min.y;
+		max.y = (src_max.y < dst_max.y) ? src_max.y : dst_max.y;
+	}
+
+	if (src_min.z > dst_max.z || src_max.z < dst_min.z) {
+		return AABB();
+	} else {
+		min.z = (src_min.z > dst_min.z) ? src_min.z : dst_min.z;
+		max.z = (src_max.z < dst_max.z) ? src_max.z : dst_max.z;
+	}
+
+	return AABB(min, max - min);
+}
+
+bool AABB::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip, Vector3 *r_normal) const {
+	Vector3 c1, c2;
+	Vector3 end = position + size;
+	real_t near = -1e20;
+	real_t far = 1e20;
+	int axis = 0;
+
+	for (int i = 0; i < 3; i++) {
+		if (p_dir[i] == 0) {
+			if ((p_from[i] < position[i]) || (p_from[i] > end[i])) {
+				return false;
+			}
+		} else { // ray not parallel to planes in this direction
+			c1[i] = (position[i] - p_from[i]) / p_dir[i];
+			c2[i] = (end[i] - p_from[i]) / p_dir[i];
+
+			if (c1[i] > c2[i]) {
+				SWAP(c1, c2);
+			}
+			if (c1[i] > near) {
+				near = c1[i];
+				axis = i;
+			}
+			if (c2[i] < far) {
+				far = c2[i];
+			}
+			if ((near > far) || (far < 0)) {
+				return false;
+			}
+		}
+	}
+
+	if (r_clip) {
+		*r_clip = c1;
+	}
+	if (r_normal) {
+		*r_normal = Vector3();
+		(*r_normal)[axis] = p_dir[axis] ? -1 : 1;
+	}
+
+	return true;
+}
+
+bool AABB::intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip, Vector3 *r_normal) const {
+	real_t min = 0, max = 1;
+	int axis = 0;
+	real_t sign = 0;
+
+	for (int i = 0; i < 3; i++) {
+		real_t seg_from = p_from[i];
+		real_t seg_to = p_to[i];
+		real_t box_begin = position[i];
+		real_t box_end = box_begin + size[i];
+		real_t cmin, cmax;
+		real_t csign;
+
+		if (seg_from < seg_to) {
+			if (seg_from > box_end || seg_to < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
+			cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
+			csign = -1.0;
+
+		} else {
+			if (seg_to > box_end || seg_from < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
+			cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
+			csign = 1.0;
+		}
+
+		if (cmin > min) {
+			min = cmin;
+			axis = i;
+			sign = csign;
+		}
+		if (cmax < max) {
+			max = cmax;
+		}
+		if (max < min) {
+			return false;
+		}
+	}
+
+	Vector3 rel = p_to - p_from;
+
+	if (r_normal) {
+		Vector3 normal;
+		normal[axis] = sign;
+		*r_normal = normal;
+	}
+
+	if (r_clip) {
+		*r_clip = p_from + rel * min;
+	}
+
+	return true;
+}
+
+bool AABB::intersects_plane(const Plane &p_plane) const {
+	Vector3 points[8] = {
+		Vector3(position.x, position.y, position.z),
+		Vector3(position.x, position.y, position.z + size.z),
+		Vector3(position.x, position.y + size.y, position.z),
+		Vector3(position.x, position.y + size.y, position.z + size.z),
+		Vector3(position.x + size.x, position.y, position.z),
+		Vector3(position.x + size.x, position.y, position.z + size.z),
+		Vector3(position.x + size.x, position.y + size.y, position.z),
+		Vector3(position.x + size.x, position.y + size.y, position.z + size.z),
+	};
+
+	bool over = false;
+	bool under = false;
+
+	for (int i = 0; i < 8; i++) {
+		if (p_plane.distance_to(points[i]) > 0) {
+			over = true;
+		} else {
+			under = true;
+		}
+	}
+
+	return under && over;
+}
+
+Vector3 AABB::get_longest_axis() const {
+	Vector3 axis(1, 0, 0);
+	real_t max_size = size.x;
+
+	if (size.y > max_size) {
+		axis = Vector3(0, 1, 0);
+		max_size = size.y;
+	}
+
+	if (size.z > max_size) {
+		axis = Vector3(0, 0, 1);
+	}
+
+	return axis;
+}
+int AABB::get_longest_axis_index() const {
+	int axis = 0;
+	real_t max_size = size.x;
+
+	if (size.y > max_size) {
+		axis = 1;
+		max_size = size.y;
+	}
+
+	if (size.z > max_size) {
+		axis = 2;
+	}
+
+	return axis;
+}
+
+Vector3 AABB::get_shortest_axis() const {
+	Vector3 axis(1, 0, 0);
+	real_t max_size = size.x;
+
+	if (size.y < max_size) {
+		axis = Vector3(0, 1, 0);
+		max_size = size.y;
+	}
+
+	if (size.z < max_size) {
+		axis = Vector3(0, 0, 1);
+	}
+
+	return axis;
+}
+int AABB::get_shortest_axis_index() const {
+	int axis = 0;
+	real_t max_size = size.x;
+
+	if (size.y < max_size) {
+		axis = 1;
+		max_size = size.y;
+	}
+
+	if (size.z < max_size) {
+		axis = 2;
+	}
+
+	return axis;
+}
+
+AABB AABB::merge(const AABB &p_with) const {
+	AABB aabb = *this;
+	aabb.merge_with(p_with);
+	return aabb;
+}
+AABB AABB::expand(const Vector3 &p_vector) const {
+	AABB aabb = *this;
+	aabb.expand_to(p_vector);
+	return aabb;
+}
+AABB AABB::grow(real_t p_by) const {
+	AABB aabb = *this;
+	aabb.grow_by(p_by);
+	return aabb;
+}
+
+void AABB::get_edge(int p_edge, Vector3 &r_from, Vector3 &r_to) const {
+	ERR_FAIL_INDEX(p_edge, 12);
+	switch (p_edge) {
+		case 0: {
+			r_from = Vector3(position.x + size.x, position.y, position.z);
+			r_to = Vector3(position.x, position.y, position.z);
+		} break;
+		case 1: {
+			r_from = Vector3(position.x + size.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x + size.x, position.y, position.z);
+		} break;
+		case 2: {
+			r_from = Vector3(position.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x + size.x, position.y, position.z + size.z);
+
+		} break;
+		case 3: {
+			r_from = Vector3(position.x, position.y, position.z);
+			r_to = Vector3(position.x, position.y, position.z + size.z);
+
+		} break;
+		case 4: {
+			r_from = Vector3(position.x, position.y + size.y, position.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z);
+		} break;
+		case 5: {
+			r_from = Vector3(position.x + size.x, position.y + size.y, position.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+		} break;
+		case 6: {
+			r_from = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z + size.z);
+
+		} break;
+		case 7: {
+			r_from = Vector3(position.x, position.y + size.y, position.z + size.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z);
+
+		} break;
+		case 8: {
+			r_from = Vector3(position.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z + size.z);
+
+		} break;
+		case 9: {
+			r_from = Vector3(position.x, position.y, position.z);
+			r_to = Vector3(position.x, position.y + size.y, position.z);
+
+		} break;
+		case 10: {
+			r_from = Vector3(position.x + size.x, position.y, position.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z);
+
+		} break;
+		case 11: {
+			r_from = Vector3(position.x + size.x, position.y, position.z + size.z);
+			r_to = Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+
+		} break;
+	}
+}
+
+Variant AABB::intersects_segmentv(const Vector3 &p_from, const Vector3 &p_to) const {
+	Vector3 inters;
+	if (intersects_segment(p_from, p_to, &inters)) {
+		return inters;
+	}
+	return Variant();
+}
+
+Variant AABB::intersects_rayv(const Vector3 &p_from, const Vector3 &p_dir) const {
+	Vector3 inters;
+	if (intersects_ray(p_from, p_dir, &inters)) {
+		return inters;
+	}
+	return Variant();
+}
+
+AABB::operator String() const {
+	return "[P: " + position.operator String() + ", S: " + size + "]";
+}

core/math/aabb.h

@@ -0,0 +1,463 @@
+#ifndef AABB_H
+#define AABB_H
+
+/*************************************************************************/
+/*  aabb.h                                                               */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/math_defs.h"
+#include "core/math/plane.h"
+#include "core/math/vector3.h"
+
+/**
+ * AABB / AABB (Axis Aligned Bounding Box)
+ * This is implemented by a point (position) and the box size
+ */
+
+class Variant;
+
+struct _NO_DISCARD_CLASS_ AABB {
+	Vector3 position;
+	Vector3 size;
+
+	real_t get_volume() const; /// get area
+	_FORCE_INLINE_ bool has_no_volume() const {
+		return (size.x <= 0 || size.y <= 0 || size.z <= 0);
+	}
+
+	_FORCE_INLINE_ bool has_no_surface() const {
+		return (size.x <= 0 && size.y <= 0 && size.z <= 0);
+	}
+
+	const Vector3 &get_position() const { return position; }
+	void set_position(const Vector3 &p_pos) { position = p_pos; }
+	const Vector3 &get_size() const { return size; }
+	void set_size(const Vector3 &p_size) { size = p_size; }
+
+	bool operator==(const AABB &p_rval) const;
+	bool operator!=(const AABB &p_rval) const;
+
+	bool is_equal_approx(const AABB &p_aabb) const;
+	_FORCE_INLINE_ bool intersects(const AABB &p_aabb) const; /// Both AABBs overlap
+	_FORCE_INLINE_ bool intersects_inclusive(const AABB &p_aabb) const; /// Both AABBs (or their faces) overlap
+	_FORCE_INLINE_ bool encloses(const AABB &p_aabb) const; /// p_aabb is completely inside this
+
+	AABB merge(const AABB &p_with) const;
+	void merge_with(const AABB &p_aabb); ///merge with another AABB
+	AABB intersection(const AABB &p_aabb) const; ///get box where two intersect, empty if no intersection occurs
+	bool intersects_segment(const Vector3 &p_from, const Vector3 &p_to, Vector3 *r_clip = nullptr, Vector3 *r_normal = nullptr) const;
+	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *r_clip = nullptr, Vector3 *r_normal = nullptr) const;
+	_FORCE_INLINE_ bool smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t t0, real_t t1) const;
+
+	_FORCE_INLINE_ bool intersects_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const;
+	_FORCE_INLINE_ bool inside_convex_shape(const Plane *p_planes, int p_plane_count) const;
+	bool intersects_plane(const Plane &p_plane) const;
+
+	_FORCE_INLINE_ bool has_point(const Vector3 &p_point) const;
+	_FORCE_INLINE_ Vector3 get_support(const Vector3 &p_normal) const;
+
+	Vector3 get_longest_axis() const;
+	int get_longest_axis_index() const;
+	_FORCE_INLINE_ real_t get_longest_axis_size() const;
+
+	Vector3 get_shortest_axis() const;
+	int get_shortest_axis_index() const;
+	_FORCE_INLINE_ real_t get_shortest_axis_size() const;
+
+	AABB grow(real_t p_by) const;
+	_FORCE_INLINE_ void grow_by(real_t p_amount);
+
+	void get_edge(int p_edge, Vector3 &r_from, Vector3 &r_to) const;
+	_FORCE_INLINE_ Vector3 get_endpoint(int p_point) const;
+
+	AABB expand(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ void project_range_in_plane(const Plane &p_plane, real_t &r_min, real_t &r_max) const;
+	_FORCE_INLINE_ void expand_to(const Vector3 &p_vector); /** expand to contain a point if necessary */
+	bool create_from_points(const Vector<Vector3> &p_points);
+
+	_FORCE_INLINE_ AABB abs() const {
+		return AABB(Vector3(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0), position.z + MIN(size.z, 0)), size.abs());
+	}
+
+	Variant intersects_segmentv(const Vector3 &p_from, const Vector3 &p_to) const;
+	Variant intersects_rayv(const Vector3 &p_from, const Vector3 &p_dir) const;
+
+	_FORCE_INLINE_ void quantize(real_t p_unit);
+	_FORCE_INLINE_ AABB quantized(real_t p_unit) const;
+
+	_FORCE_INLINE_ void set_end(const Vector3 &p_end) {
+		size = p_end - position;
+	}
+
+	_FORCE_INLINE_ Vector3 get_end() const {
+		return position + size;
+	}
+
+	_FORCE_INLINE_ Vector3 get_center() const {
+		return position + (size * 0.5f);
+	}
+
+	operator String() const;
+
+	_FORCE_INLINE_ AABB() {}
+	inline AABB(const Vector3 &p_pos, const Vector3 &p_size) :
+			position(p_pos),
+			size(p_size) {
+	}
+};
+
+inline bool AABB::intersects(const AABB &p_aabb) const {
+	if (position.x >= (p_aabb.position.x + p_aabb.size.x)) {
+		return false;
+	}
+	if ((position.x + size.x) <= p_aabb.position.x) {
+		return false;
+	}
+	if (position.y >= (p_aabb.position.y + p_aabb.size.y)) {
+		return false;
+	}
+	if ((position.y + size.y) <= p_aabb.position.y) {
+		return false;
+	}
+	if (position.z >= (p_aabb.position.z + p_aabb.size.z)) {
+		return false;
+	}
+	if ((position.z + size.z) <= p_aabb.position.z) {
+		return false;
+	}
+
+	return true;
+}
+
+inline bool AABB::intersects_inclusive(const AABB &p_aabb) const {
+	if (position.x > (p_aabb.position.x + p_aabb.size.x)) {
+		return false;
+	}
+	if ((position.x + size.x) < p_aabb.position.x) {
+		return false;
+	}
+	if (position.y > (p_aabb.position.y + p_aabb.size.y)) {
+		return false;
+	}
+	if ((position.y + size.y) < p_aabb.position.y) {
+		return false;
+	}
+	if (position.z > (p_aabb.position.z + p_aabb.size.z)) {
+		return false;
+	}
+	if ((position.z + size.z) < p_aabb.position.z) {
+		return false;
+	}
+
+	return true;
+}
+
+inline bool AABB::encloses(const AABB &p_aabb) const {
+	Vector3 src_min = position;
+	Vector3 src_max = position + size;
+	Vector3 dst_min = p_aabb.position;
+	Vector3 dst_max = p_aabb.position + p_aabb.size;
+
+	return (
+			(src_min.x <= dst_min.x) &&
+			(src_max.x > dst_max.x) &&
+			(src_min.y <= dst_min.y) &&
+			(src_max.y > dst_max.y) &&
+			(src_min.z <= dst_min.z) &&
+			(src_max.z > dst_max.z));
+}
+
+Vector3 AABB::get_support(const Vector3 &p_normal) const {
+	Vector3 half_extents = size * 0.5f;
+	Vector3 ofs = position + half_extents;
+
+	return Vector3(
+				   (p_normal.x > 0) ? -half_extents.x : half_extents.x,
+				   (p_normal.y > 0) ? -half_extents.y : half_extents.y,
+				   (p_normal.z > 0) ? -half_extents.z : half_extents.z) +
+			ofs;
+}
+
+Vector3 AABB::get_endpoint(int p_point) const {
+	switch (p_point) {
+		case 0:
+			return Vector3(position.x, position.y, position.z);
+		case 1:
+			return Vector3(position.x, position.y, position.z + size.z);
+		case 2:
+			return Vector3(position.x, position.y + size.y, position.z);
+		case 3:
+			return Vector3(position.x, position.y + size.y, position.z + size.z);
+		case 4:
+			return Vector3(position.x + size.x, position.y, position.z);
+		case 5:
+			return Vector3(position.x + size.x, position.y, position.z + size.z);
+		case 6:
+			return Vector3(position.x + size.x, position.y + size.y, position.z);
+		case 7:
+			return Vector3(position.x + size.x, position.y + size.y, position.z + size.z);
+	};
+
+	ERR_FAIL_V(Vector3());
+}
+
+bool AABB::intersects_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const {
+	Vector3 half_extents = size * 0.5f;
+	Vector3 ofs = position + half_extents;
+
+	for (int i = 0; i < p_plane_count; i++) {
+		const Plane &p = p_planes[i];
+		Vector3 point(
+				(p.normal.x > 0) ? -half_extents.x : half_extents.x,
+				(p.normal.y > 0) ? -half_extents.y : half_extents.y,
+				(p.normal.z > 0) ? -half_extents.z : half_extents.z);
+		point += ofs;
+		if (p.is_point_over(point)) {
+			return false;
+		}
+	}
+
+	// Make sure all points in the shape aren't fully separated from the AABB on
+	// each axis.
+	int bad_point_counts_positive[3] = { 0 };
+	int bad_point_counts_negative[3] = { 0 };
+
+	for (int k = 0; k < 3; k++) {
+		for (int i = 0; i < p_point_count; i++) {
+			if (p_points[i].coord[k] > ofs.coord[k] + half_extents.coord[k]) {
+				bad_point_counts_positive[k]++;
+			}
+			if (p_points[i].coord[k] < ofs.coord[k] - half_extents.coord[k]) {
+				bad_point_counts_negative[k]++;
+			}
+		}
+
+		if (bad_point_counts_negative[k] == p_point_count) {
+			return false;
+		}
+		if (bad_point_counts_positive[k] == p_point_count) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool AABB::inside_convex_shape(const Plane *p_planes, int p_plane_count) const {
+	Vector3 half_extents = size * 0.5f;
+	Vector3 ofs = position + half_extents;
+
+	for (int i = 0; i < p_plane_count; i++) {
+		const Plane &p = p_planes[i];
+		Vector3 point(
+				(p.normal.x < 0) ? -half_extents.x : half_extents.x,
+				(p.normal.y < 0) ? -half_extents.y : half_extents.y,
+				(p.normal.z < 0) ? -half_extents.z : half_extents.z);
+		point += ofs;
+		if (p.is_point_over(point)) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool AABB::has_point(const Vector3 &p_point) const {
+	if (p_point.x < position.x) {
+		return false;
+	}
+	if (p_point.y < position.y) {
+		return false;
+	}
+	if (p_point.z < position.z) {
+		return false;
+	}
+	if (p_point.x > position.x + size.x) {
+		return false;
+	}
+	if (p_point.y > position.y + size.y) {
+		return false;
+	}
+	if (p_point.z > position.z + size.z) {
+		return false;
+	}
+
+	return true;
+}
+
+inline void AABB::expand_to(const Vector3 &p_vector) {
+	Vector3 begin = position;
+	Vector3 end = position + size;
+
+	if (p_vector.x < begin.x) {
+		begin.x = p_vector.x;
+	}
+	if (p_vector.y < begin.y) {
+		begin.y = p_vector.y;
+	}
+	if (p_vector.z < begin.z) {
+		begin.z = p_vector.z;
+	}
+
+	if (p_vector.x > end.x) {
+		end.x = p_vector.x;
+	}
+	if (p_vector.y > end.y) {
+		end.y = p_vector.y;
+	}
+	if (p_vector.z > end.z) {
+		end.z = p_vector.z;
+	}
+
+	position = begin;
+	size = end - begin;
+}
+
+void AABB::project_range_in_plane(const Plane &p_plane, real_t &r_min, real_t &r_max) const {
+	Vector3 half_extents = size * 0.5f;
+	Vector3 center(position.x + half_extents.x, position.y + half_extents.y, position.z + half_extents.z);
+
+	real_t length = p_plane.normal.abs().dot(half_extents);
+	real_t distance = p_plane.distance_to(center);
+	r_min = distance - length;
+	r_max = distance + length;
+}
+
+inline real_t AABB::get_longest_axis_size() const {
+	real_t max_size = size.x;
+
+	if (size.y > max_size) {
+		max_size = size.y;
+	}
+
+	if (size.z > max_size) {
+		max_size = size.z;
+	}
+
+	return max_size;
+}
+
+inline real_t AABB::get_shortest_axis_size() const {
+	real_t max_size = size.x;
+
+	if (size.y < max_size) {
+		max_size = size.y;
+	}
+
+	if (size.z < max_size) {
+		max_size = size.z;
+	}
+
+	return max_size;
+}
+
+bool AABB::smits_intersect_ray(const Vector3 &p_from, const Vector3 &p_dir, real_t t0, real_t t1) const {
+	real_t divx = 1 / p_dir.x;
+	real_t divy = 1 / p_dir.y;
+	real_t divz = 1 / p_dir.z;
+
+	Vector3 upbound = position + size;
+	real_t tmin, tmax, tymin, tymax, tzmin, tzmax;
+	if (p_dir.x >= 0) {
+		tmin = (position.x - p_from.x) * divx;
+		tmax = (upbound.x - p_from.x) * divx;
+	} else {
+		tmin = (upbound.x - p_from.x) * divx;
+		tmax = (position.x - p_from.x) * divx;
+	}
+	if (p_dir.y >= 0) {
+		tymin = (position.y - p_from.y) * divy;
+		tymax = (upbound.y - p_from.y) * divy;
+	} else {
+		tymin = (upbound.y - p_from.y) * divy;
+		tymax = (position.y - p_from.y) * divy;
+	}
+	if ((tmin > tymax) || (tymin > tmax)) {
+		return false;
+	}
+	if (tymin > tmin) {
+		tmin = tymin;
+	}
+	if (tymax < tmax) {
+		tmax = tymax;
+	}
+	if (p_dir.z >= 0) {
+		tzmin = (position.z - p_from.z) * divz;
+		tzmax = (upbound.z - p_from.z) * divz;
+	} else {
+		tzmin = (upbound.z - p_from.z) * divz;
+		tzmax = (position.z - p_from.z) * divz;
+	}
+	if ((tmin > tzmax) || (tzmin > tmax)) {
+		return false;
+	}
+	if (tzmin > tmin) {
+		tmin = tzmin;
+	}
+	if (tzmax < tmax) {
+		tmax = tzmax;
+	}
+	return ((tmin < t1) && (tmax > t0));
+}
+
+void AABB::grow_by(real_t p_amount) {
+	position.x -= p_amount;
+	position.y -= p_amount;
+	position.z -= p_amount;
+	size.x += 2 * p_amount;
+	size.y += 2 * p_amount;
+	size.z += 2 * p_amount;
+}
+
+void AABB::quantize(real_t p_unit) {
+	size += position;
+
+	position.x -= Math::fposmodp(position.x, p_unit);
+	position.y -= Math::fposmodp(position.y, p_unit);
+	position.z -= Math::fposmodp(position.z, p_unit);
+
+	size.x -= Math::fposmodp(size.x, p_unit);
+	size.y -= Math::fposmodp(size.y, p_unit);
+	size.z -= Math::fposmodp(size.z, p_unit);
+
+	size.x += p_unit;
+	size.y += p_unit;
+	size.z += p_unit;
+
+	size -= position;
+}
+
+AABB AABB::quantized(real_t p_unit) const {
+	AABB ret = *this;
+	ret.quantize(p_unit);
+	return ret;
+}
+
+#endif // AABB_H

core/math/basis.h

@@ -0,0 +1,404 @@
+#ifndef BASIS_H
+#define BASIS_H
+
+/*************************************************************************/
+/*  basis.h                                                              */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/quaternion.h"
+#include "core/math/vector3.h"
+#include "core/math/vector3i.h"
+
+struct _NO_DISCARD_CLASS_ Basis {
+	Vector3 rows[3] = {
+		Vector3(1, 0, 0),
+		Vector3(0, 1, 0),
+		Vector3(0, 0, 1)
+	};
+
+	_FORCE_INLINE_ const Vector3 &operator[](int p_row) const {
+		return rows[p_row];
+	}
+	_FORCE_INLINE_ Vector3 &operator[](int p_row) {
+		return rows[p_row];
+	}
+
+	void invert();
+	void transpose();
+
+	Basis inverse() const;
+	Basis transposed() const;
+
+	_FORCE_INLINE_ real_t determinant() const;
+
+	void from_z(const Vector3 &p_z);
+
+	void rotate(const Vector3 &p_axis, real_t p_phi);
+	Basis rotated(const Vector3 &p_axis, real_t p_phi) const;
+
+	void rotate_local(const Vector3 &p_axis, real_t p_phi);
+	Basis rotated_local(const Vector3 &p_axis, real_t p_phi) const;
+
+	void rotate(const Vector3 &p_euler);
+	Basis rotated(const Vector3 &p_euler) const;
+
+	void rotate(const Quaternion &p_quat);
+	Basis rotated(const Quaternion &p_quat) const;
+
+	_FORCE_INLINE_ void rotatev(const Vector3 &p_euler) { rotate(p_euler); }
+	_FORCE_INLINE_ Basis rotatedv(const Vector3 &p_euler) const { return rotated(p_euler); }
+	_FORCE_INLINE_ void rotateq(const Quaternion &p_quat) { rotate(p_quat); }
+	_FORCE_INLINE_ Basis rotatedq(const Quaternion &p_quat) const { return rotated(p_quat); }
+
+	Vector3 get_rotation_euler() const;
+	void get_rotation_axis_angle(Vector3 &p_axis, real_t &p_angle) const;
+	void get_rotation_axis_angle_local(Vector3 &p_axis, real_t &p_angle) const;
+	Quaternion get_rotation_quaternion() const;
+	Vector3 get_rotation() const { return get_rotation_euler(); };
+
+	void rotate_to_align(const Vector3 &p_start_direction, const Vector3 &p_end_direction);
+
+	Vector3 rotref_posscale_decomposition(Basis &rotref) const;
+
+	Vector3 get_euler_xyz() const;
+	void set_euler_xyz(const Vector3 &p_euler);
+
+	Vector3 get_euler_xzy() const;
+	void set_euler_xzy(const Vector3 &p_euler);
+
+	Vector3 get_euler_yzx() const;
+	void set_euler_yzx(const Vector3 &p_euler);
+
+	Vector3 get_euler_yxz() const;
+	void set_euler_yxz(const Vector3 &p_euler);
+
+	Vector3 get_euler_zxy() const;
+	void set_euler_zxy(const Vector3 &p_euler);
+
+	Vector3 get_euler_zyx() const;
+	void set_euler_zyx(const Vector3 &p_euler);
+
+	Vector3 get_euler() const { return get_euler_yxz(); }
+	void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); }
+
+	Quaternion get_quaternion() const;
+	void set_quaternion(const Quaternion &p_quat);
+
+	void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const;
+	void set_axis_angle(const Vector3 &p_axis, real_t p_phi);
+
+	void scale(const Vector3 &p_scale);
+	Basis scaled(const Vector3 &p_scale) const;
+
+	void scale_local(const Vector3 &p_scale);
+	Basis scaled_local(const Vector3 &p_scale) const;
+
+	void scale_orthogonal(const Vector3 &p_scale);
+	Basis scaled_orthogonal(const Vector3 &p_scale) const;
+
+	void make_scale_uniform();
+	real_t get_uniform_scale() const;
+
+	Vector3 get_scale() const;
+	Vector3 get_scale_abs() const;
+	Vector3 get_scale_local() const;
+
+	void set_axis_angle_scale(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale);
+	void set_euler_scale(const Vector3 &p_euler, const Vector3 &p_scale);
+	void set_quaternion_scale(const Quaternion &p_quat, const Vector3 &p_scale);
+
+	// transposed dot products
+	_FORCE_INLINE_ real_t tdotx(const Vector3 &v) const {
+		return rows[0][0] * v[0] + rows[1][0] * v[1] + rows[2][0] * v[2];
+	}
+	_FORCE_INLINE_ real_t tdoty(const Vector3 &v) const {
+		return rows[0][1] * v[0] + rows[1][1] * v[1] + rows[2][1] * v[2];
+	}
+	_FORCE_INLINE_ real_t tdotz(const Vector3 &v) const {
+		return rows[0][2] * v[0] + rows[1][2] * v[1] + rows[2][2] * v[2];
+	}
+
+	bool is_equal_approx(const Basis &p_basis) const;
+	bool is_equal_approx_ratio(const Basis &a, const Basis &b, real_t p_epsilon = UNIT_EPSILON) const;
+
+	bool operator==(const Basis &p_matrix) const;
+	bool operator!=(const Basis &p_matrix) const;
+
+	_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
+
+	_FORCE_INLINE_ Vector3i xform(const Vector3i &p_vector) const;
+	_FORCE_INLINE_ Vector3i xform_inv(const Vector3i &p_vector) const;
+
+	_FORCE_INLINE_ void operator*=(const Basis &p_matrix);
+	_FORCE_INLINE_ Basis operator*(const Basis &p_matrix) const;
+	_FORCE_INLINE_ void operator+=(const Basis &p_matrix);
+	_FORCE_INLINE_ Basis operator+(const Basis &p_matrix) const;
+	_FORCE_INLINE_ void operator-=(const Basis &p_matrix);
+	_FORCE_INLINE_ Basis operator-(const Basis &p_matrix) const;
+	_FORCE_INLINE_ void operator*=(real_t p_val);
+	_FORCE_INLINE_ Basis operator*(real_t p_val) const;
+
+	int get_orthogonal_index() const;
+	void set_orthogonal_index(int p_index);
+
+	void set_diagonal(const Vector3 &p_diag);
+
+	bool is_orthogonal() const;
+	bool is_diagonal() const;
+	bool is_rotation() const;
+
+	Basis slerp(const Basis &p_to, const real_t &p_weight) const;
+	_FORCE_INLINE_ Basis lerp(const Basis &p_to, const real_t &p_weight) const;
+	void rotate_sh(real_t *p_values);
+
+	operator String() const;
+
+	/* create / set */
+
+	_FORCE_INLINE_ void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
+		rows[0][0] = xx;
+		rows[0][1] = xy;
+		rows[0][2] = xz;
+		rows[1][0] = yx;
+		rows[1][1] = yy;
+		rows[1][2] = yz;
+		rows[2][0] = zx;
+		rows[2][1] = zy;
+		rows[2][2] = zz;
+	}
+	_FORCE_INLINE_ void set(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
+		set_column(0, p_x);
+		set_column(1, p_y);
+		set_column(2, p_z);
+	}
+
+	_FORCE_INLINE_ Vector3 get_column(int i) const {
+		return Vector3(rows[0][i], rows[1][i], rows[2][i]);
+	}
+
+	_FORCE_INLINE_ void set_column(int p_index, const Vector3 &p_value) {
+		// Set actual basis axis column (we store transposed as rows for performance).
+		rows[0][p_index] = p_value.x;
+		rows[1][p_index] = p_value.y;
+		rows[2][p_index] = p_value.z;
+	}
+
+	_FORCE_INLINE_ void set_columns(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z) {
+		set_column(0, p_x);
+		set_column(1, p_y);
+		set_column(2, p_z);
+	}
+
+	_FORCE_INLINE_ Vector3 get_row(int i) const {
+		return Vector3(rows[i][0], rows[i][1], rows[i][2]);
+	}
+	_FORCE_INLINE_ void set_row(int i, const Vector3 &p_row) {
+		rows[i][0] = p_row.x;
+		rows[i][1] = p_row.y;
+		rows[i][2] = p_row.z;
+	}
+
+	_FORCE_INLINE_ Vector3 get_axis(int i) const {
+		return Vector3(rows[0][i], rows[1][i], rows[2][i]);
+	}
+
+	_FORCE_INLINE_ void set_axis(int p_index, const Vector3 &p_value) {
+		// Set actual basis axis column (we store transposed as rows for performance).
+		rows[0][p_index] = p_value.x;
+		rows[1][p_index] = p_value.y;
+		rows[2][p_index] = p_value.z;
+	}
+
+	_FORCE_INLINE_ Vector3 get_main_diagonal() const {
+		return Vector3(rows[0][0], rows[1][1], rows[2][2]);
+	}
+
+	_FORCE_INLINE_ void set_zero() {
+		rows[0].zero();
+		rows[1].zero();
+		rows[2].zero();
+	}
+
+	_FORCE_INLINE_ Basis transpose_xform(const Basis &m) const {
+		return Basis(
+				rows[0].x * m[0].x + rows[1].x * m[1].x + rows[2].x * m[2].x,
+				rows[0].x * m[0].y + rows[1].x * m[1].y + rows[2].x * m[2].y,
+				rows[0].x * m[0].z + rows[1].x * m[1].z + rows[2].x * m[2].z,
+				rows[0].y * m[0].x + rows[1].y * m[1].x + rows[2].y * m[2].x,
+				rows[0].y * m[0].y + rows[1].y * m[1].y + rows[2].y * m[2].y,
+				rows[0].y * m[0].z + rows[1].y * m[1].z + rows[2].y * m[2].z,
+				rows[0].z * m[0].x + rows[1].z * m[1].x + rows[2].z * m[2].x,
+				rows[0].z * m[0].y + rows[1].z * m[1].y + rows[2].z * m[2].y,
+				rows[0].z * m[0].z + rows[1].z * m[1].z + rows[2].z * m[2].z);
+	}
+	Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
+		set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+	}
+
+	void orthonormalize();
+	Basis orthonormalized() const;
+
+	void orthogonalize();
+	Basis orthogonalized() const;
+
+	bool is_symmetric() const;
+	Basis diagonalize();
+
+	// The following normal xform functions are correct for non-uniform scales.
+	// Use these two functions in combination to xform a series of normals.
+	// First use get_normal_xform_basis() to precalculate the inverse transpose.
+	// Then apply xform_normal_fast() multiple times using the inverse transpose basis.
+	Basis get_normal_xform_basis() const { return inverse().transposed(); }
+
+	// N.B. This only does a normal transform if the basis used is the inverse transpose!
+	// Otherwise use xform_normal().
+	Vector3 xform_normal_fast(const Vector3 &p_vector) const { return xform(p_vector).normalized(); }
+
+	// This function does the above but for a single normal vector. It is considerably slower, so should usually
+	// only be used in cases of single normals, or when the basis changes each time.
+	Vector3 xform_normal(const Vector3 &p_vector) const { return get_normal_xform_basis().xform_normal_fast(p_vector); }
+
+	static Basis looking_at(const Vector3 &p_target, const Vector3 &p_up = Vector3(0, 1, 0));
+	static Basis from_scale(const Vector3 &p_scale);
+
+	operator Quaternion() const { return get_quaternion(); }
+
+	Basis(const Quaternion &p_quat) { set_quaternion(p_quat); }
+	Basis(const Quaternion &p_quat, const Vector3 &p_scale) { set_quaternion_scale(p_quat, p_scale); }
+
+	Basis(const Vector3 &p_euler) { set_euler(p_euler); }
+	Basis(const Vector3 &p_euler, const Vector3 &p_scale) { set_euler_scale(p_euler, p_scale); }
+
+	Basis(const Vector3 &p_axis, real_t p_phi) { set_axis_angle(p_axis, p_phi); }
+	Basis(const Vector3 &p_axis, real_t p_phi, const Vector3 &p_scale) { set_axis_angle_scale(p_axis, p_phi, p_scale); }
+
+	_FORCE_INLINE_ Basis(const Vector3 &row0, const Vector3 &row1, const Vector3 &row2) {
+		rows[0] = row0;
+		rows[1] = row1;
+		rows[2] = row2;
+	}
+
+	_FORCE_INLINE_ Basis() {}
+};
+
+_FORCE_INLINE_ void Basis::operator*=(const Basis &p_matrix) {
+	set(
+			p_matrix.tdotx(rows[0]), p_matrix.tdoty(rows[0]), p_matrix.tdotz(rows[0]),
+			p_matrix.tdotx(rows[1]), p_matrix.tdoty(rows[1]), p_matrix.tdotz(rows[1]),
+			p_matrix.tdotx(rows[2]), p_matrix.tdoty(rows[2]), p_matrix.tdotz(rows[2]));
+}
+
+_FORCE_INLINE_ Basis Basis::operator*(const Basis &p_matrix) const {
+	return Basis(
+			p_matrix.tdotx(rows[0]), p_matrix.tdoty(rows[0]), p_matrix.tdotz(rows[0]),
+			p_matrix.tdotx(rows[1]), p_matrix.tdoty(rows[1]), p_matrix.tdotz(rows[1]),
+			p_matrix.tdotx(rows[2]), p_matrix.tdoty(rows[2]), p_matrix.tdotz(rows[2]));
+}
+
+_FORCE_INLINE_ void Basis::operator+=(const Basis &p_matrix) {
+	rows[0] += p_matrix.rows[0];
+	rows[1] += p_matrix.rows[1];
+	rows[2] += p_matrix.rows[2];
+}
+
+_FORCE_INLINE_ Basis Basis::operator+(const Basis &p_matrix) const {
+	Basis ret(*this);
+	ret += p_matrix;
+	return ret;
+}
+
+_FORCE_INLINE_ void Basis::operator-=(const Basis &p_matrix) {
+	rows[0] -= p_matrix.rows[0];
+	rows[1] -= p_matrix.rows[1];
+	rows[2] -= p_matrix.rows[2];
+}
+
+_FORCE_INLINE_ Basis Basis::operator-(const Basis &p_matrix) const {
+	Basis ret(*this);
+	ret -= p_matrix;
+	return ret;
+}
+
+_FORCE_INLINE_ void Basis::operator*=(real_t p_val) {
+	rows[0] *= p_val;
+	rows[1] *= p_val;
+	rows[2] *= p_val;
+}
+
+_FORCE_INLINE_ Basis Basis::operator*(real_t p_val) const {
+	Basis ret(*this);
+	ret *= p_val;
+	return ret;
+}
+
+Vector3 Basis::xform(const Vector3 &p_vector) const {
+	return Vector3(
+			rows[0].dot(p_vector),
+			rows[1].dot(p_vector),
+			rows[2].dot(p_vector));
+}
+
+Vector3i Basis::xform_inv(const Vector3i &p_vector) const {
+	return Vector3i(
+			(rows[0][0] * p_vector.x) + (rows[1][0] * p_vector.y) + (rows[2][0] * p_vector.z),
+			(rows[0][1] * p_vector.x) + (rows[1][1] * p_vector.y) + (rows[2][1] * p_vector.z),
+			(rows[0][2] * p_vector.x) + (rows[1][2] * p_vector.y) + (rows[2][2] * p_vector.z));
+}
+
+Vector3i Basis::xform(const Vector3i &p_vector) const {
+	return Vector3i(
+			rows[0].dot(p_vector),
+			rows[1].dot(p_vector),
+			rows[2].dot(p_vector));
+}
+
+Vector3 Basis::xform_inv(const Vector3 &p_vector) const {
+	return Vector3(
+			(rows[0][0] * p_vector.x) + (rows[1][0] * p_vector.y) + (rows[2][0] * p_vector.z),
+			(rows[0][1] * p_vector.x) + (rows[1][1] * p_vector.y) + (rows[2][1] * p_vector.z),
+			(rows[0][2] * p_vector.x) + (rows[1][2] * p_vector.y) + (rows[2][2] * p_vector.z));
+}
+
+real_t Basis::determinant() const {
+	return rows[0][0] * (rows[1][1] * rows[2][2] - rows[2][1] * rows[1][2]) -
+			rows[1][0] * (rows[0][1] * rows[2][2] - rows[2][1] * rows[0][2]) +
+			rows[2][0] * (rows[0][1] * rows[1][2] - rows[1][1] * rows[0][2]);
+}
+
+Basis Basis::lerp(const Basis &p_to, const real_t &p_weight) const {
+	Basis b;
+	b.rows[0] = rows[0].linear_interpolate(p_to.rows[0], p_weight);
+	b.rows[1] = rows[1].linear_interpolate(p_to.rows[1], p_weight);
+	b.rows[2] = rows[2].linear_interpolate(p_to.rows[2], p_weight);
+
+	return b;
+}
+#endif // BASIS_H

core/math/color.cpp

@@ -0,0 +1,573 @@
+/*************************************************************************/
+/*  color.cpp                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "color.h"
+
+#include "core/containers/rb_map.h"
+#include "core/math/color_names.inc"
+#include "core/math/math_funcs.h"
+#include "core/string/print_string.h"
+
+uint32_t Color::to_argb32() const {
+	uint32_t c = (uint8_t)Math::round(a * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(r * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(g * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(b * 255);
+
+	return c;
+}
+
+uint32_t Color::to_abgr32() const {
+	uint32_t c = (uint8_t)Math::round(a * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(b * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(g * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(r * 255);
+
+	return c;
+}
+
+uint32_t Color::to_rgba32() const {
+	uint32_t c = (uint8_t)Math::round(r * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(g * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(b * 255);
+	c <<= 8;
+	c |= (uint8_t)Math::round(a * 255);
+
+	return c;
+}
+
+uint64_t Color::to_abgr64() const {
+	uint64_t c = (uint16_t)Math::round(a * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(b * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(g * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(r * 65535);
+
+	return c;
+}
+
+uint64_t Color::to_argb64() const {
+	uint64_t c = (uint16_t)Math::round(a * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(r * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(g * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(b * 65535);
+
+	return c;
+}
+
+uint64_t Color::to_rgba64() const {
+	uint64_t c = (uint16_t)Math::round(r * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(g * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(b * 65535);
+	c <<= 16;
+	c |= (uint16_t)Math::round(a * 65535);
+
+	return c;
+}
+
+float Color::get_h() const {
+	float min = MIN(r, g);
+	min = MIN(min, b);
+	float max = MAX(r, g);
+	max = MAX(max, b);
+
+	float delta = max - min;
+
+	if (delta == 0) {
+		return 0;
+	}
+
+	float h;
+	if (r == max) {
+		h = (g - b) / delta; // between yellow & magenta
+	} else if (g == max) {
+		h = 2 + (b - r) / delta; // between cyan & yellow
+	} else {
+		h = 4 + (r - g) / delta; // between magenta & cyan
+	}
+
+	h /= 6.0;
+	if (h < 0) {
+		h += 1.0;
+	}
+
+	return h;
+}
+
+float Color::get_s() const {
+	float min = MIN(r, g);
+	min = MIN(min, b);
+	float max = MAX(r, g);
+	max = MAX(max, b);
+
+	float delta = max - min;
+
+	return (max != 0) ? (delta / max) : 0;
+}
+
+float Color::get_v() const {
+	float max = MAX(r, g);
+	max = MAX(max, b);
+	return max;
+}
+
+void Color::set_hsv(float p_h, float p_s, float p_v, float p_alpha) {
+	int i;
+	float f, p, q, t;
+	a = p_alpha;
+
+	if (p_s == 0) {
+		// acp_hromatic (grey)
+		r = g = b = p_v;
+		return;
+	}
+
+	p_h *= 6.0;
+	p_h = Math::fmod(p_h, 6);
+	i = Math::floor(p_h);
+
+	f = p_h - i;
+	p = p_v * (1 - p_s);
+	q = p_v * (1 - p_s * f);
+	t = p_v * (1 - p_s * (1 - f));
+
+	switch (i) {
+		case 0: // Red is the dominant color
+			r = p_v;
+			g = t;
+			b = p;
+			break;
+		case 1: // Green is the dominant color
+			r = q;
+			g = p_v;
+			b = p;
+			break;
+		case 2:
+			r = p;
+			g = p_v;
+			b = t;
+			break;
+		case 3: // Blue is the dominant color
+			r = p;
+			g = q;
+			b = p_v;
+			break;
+		case 4:
+			r = t;
+			g = p;
+			b = p_v;
+			break;
+		default: // (5) Red is the dominant color
+			r = p_v;
+			g = p;
+			b = q;
+			break;
+	}
+}
+
+bool Color::is_equal_approx(const Color &p_color) const {
+	return Math::is_equal_approx(r, p_color.r) && Math::is_equal_approx(g, p_color.g) && Math::is_equal_approx(b, p_color.b) && Math::is_equal_approx(a, p_color.a);
+}
+
+Color Color::clamp(const Color &p_min, const Color &p_max) const {
+	return Color(
+			CLAMP(r, p_min.r, p_max.r),
+			CLAMP(g, p_min.g, p_max.g),
+			CLAMP(b, p_min.b, p_max.b),
+			CLAMP(a, p_min.a, p_max.a));
+}
+
+void Color::invert() {
+	r = 1.0 - r;
+	g = 1.0 - g;
+	b = 1.0 - b;
+}
+void Color::contrast() {
+	r = Math::fmod(r + 0.5, 1.0);
+	g = Math::fmod(g + 0.5, 1.0);
+	b = Math::fmod(b + 0.5, 1.0);
+}
+
+Color Color::hex(uint32_t p_hex) {
+	float a = (p_hex & 0xFF) / 255.0;
+	p_hex >>= 8;
+	float b = (p_hex & 0xFF) / 255.0;
+	p_hex >>= 8;
+	float g = (p_hex & 0xFF) / 255.0;
+	p_hex >>= 8;
+	float r = (p_hex & 0xFF) / 255.0;
+
+	return Color(r, g, b, a);
+}
+
+Color Color::hex64(uint64_t p_hex) {
+	float a = (p_hex & 0xFFFF) / 65535.0;
+	p_hex >>= 16;
+	float b = (p_hex & 0xFFFF) / 65535.0;
+	p_hex >>= 16;
+	float g = (p_hex & 0xFFFF) / 65535.0;
+	p_hex >>= 16;
+	float r = (p_hex & 0xFFFF) / 65535.0;
+
+	return Color(r, g, b, a);
+}
+
+Color Color::from_rgbe9995(uint32_t p_rgbe) {
+	float r = p_rgbe & 0x1ff;
+	float g = (p_rgbe >> 9) & 0x1ff;
+	float b = (p_rgbe >> 18) & 0x1ff;
+	float e = (p_rgbe >> 27);
+	float m = Math::pow(2, e - 15.0 - 9.0);
+
+	float rd = r * m;
+	float gd = g * m;
+	float bd = b * m;
+
+	return Color(rd, gd, bd, 1.0f);
+}
+
+static float _parse_col(const String &p_str, int p_ofs) {
+	int ig = 0;
+
+	for (int i = 0; i < 2; i++) {
+		int c = p_str[i + p_ofs];
+		int v = 0;
+
+		if (c >= '0' && c <= '9') {
+			v = c - '0';
+		} else if (c >= 'a' && c <= 'f') {
+			v = c - 'a';
+			v += 10;
+		} else if (c >= 'A' && c <= 'F') {
+			v = c - 'A';
+			v += 10;
+		} else {
+			return -1;
+		}
+
+		if (i == 0) {
+			ig += v * 16;
+		} else {
+			ig += v;
+		}
+	}
+
+	return ig;
+}
+
+Color Color::inverted() const {
+	Color c = *this;
+	c.invert();
+	return c;
+}
+
+Color Color::contrasted() const {
+	Color c = *this;
+	c.contrast();
+	return c;
+}
+
+Color Color::html(const String &p_color) {
+	String color = p_color;
+	if (color.length() == 0) {
+		return Color();
+	}
+	if (color[0] == '#') {
+		color = color.substr(1, color.length() - 1);
+	}
+	if (color.length() == 3 || color.length() == 4) {
+		String exp_color;
+		for (int i = 0; i < color.length(); i++) {
+			exp_color += color[i];
+			exp_color += color[i];
+		}
+		color = exp_color;
+	}
+
+	bool alpha = false;
+
+	if (color.length() == 8) {
+		alpha = true;
+	} else if (color.length() == 6) {
+		alpha = false;
+	} else {
+		ERR_FAIL_V_MSG(Color(), "Invalid color code: " + p_color + ".");
+	}
+
+	int a = 255;
+	if (alpha) {
+		a = _parse_col(color, 0);
+		ERR_FAIL_COND_V_MSG(a < 0, Color(), "Invalid color code: " + p_color + ".");
+	}
+
+	int from = alpha ? 2 : 0;
+
+	int r = _parse_col(color, from + 0);
+	ERR_FAIL_COND_V_MSG(r < 0, Color(), "Invalid color code: " + p_color + ".");
+	int g = _parse_col(color, from + 2);
+	ERR_FAIL_COND_V_MSG(g < 0, Color(), "Invalid color code: " + p_color + ".");
+	int b = _parse_col(color, from + 4);
+	ERR_FAIL_COND_V_MSG(b < 0, Color(), "Invalid color code: " + p_color + ".");
+
+	return Color(r / 255.0, g / 255.0, b / 255.0, a / 255.0);
+}
+
+bool Color::html_is_valid(const String &p_color) {
+	String color = p_color;
+
+	if (color.length() == 0) {
+		return false;
+	}
+	if (color[0] == '#') {
+		color = color.substr(1, color.length() - 1);
+	}
+
+	bool alpha = false;
+
+	if (color.length() == 8) {
+		alpha = true;
+	} else if (color.length() == 6) {
+		alpha = false;
+	} else {
+		return false;
+	}
+
+	if (alpha) {
+		int a = _parse_col(color, 0);
+		if (a < 0) {
+			return false;
+		}
+	}
+
+	int from = alpha ? 2 : 0;
+
+	int r = _parse_col(color, from + 0);
+	if (r < 0) {
+		return false;
+	}
+	int g = _parse_col(color, from + 2);
+	if (g < 0) {
+		return false;
+	}
+	int b = _parse_col(color, from + 4);
+	if (b < 0) {
+		return false;
+	}
+
+	return true;
+}
+
+Color Color::named(const String &p_name) {
+	if (_named_colors.empty()) {
+		_populate_named_colors(); // from color_names.inc
+	}
+	String name = p_name;
+	// Normalize name
+	name = name.replace(" ", "");
+	name = name.replace("-", "");
+	name = name.replace("_", "");
+	name = name.replace("'", "");
+	name = name.replace(".", "");
+	name = name.to_lower();
+
+	const RBMap<String, Color>::Element *color = _named_colors.find(name);
+	ERR_FAIL_NULL_V_MSG(color, Color(), "Invalid color name: " + p_name + ".");
+	return color->value();
+}
+
+String _to_hex(float p_val) {
+	int v = Math::round(p_val * 255);
+	v = CLAMP(v, 0, 255);
+	String ret;
+
+	for (int i = 0; i < 2; i++) {
+		CharType c[2] = { 0, 0 };
+		int lv = v & 0xF;
+		if (lv < 10) {
+			c[0] = '0' + lv;
+		} else {
+			c[0] = 'a' + lv - 10;
+		}
+
+		v >>= 4;
+		String cs = (const CharType *)c;
+		ret = cs + ret;
+	}
+
+	return ret;
+}
+
+String Color::to_html(bool p_alpha) const {
+	String txt;
+	txt += _to_hex(r);
+	txt += _to_hex(g);
+	txt += _to_hex(b);
+	if (p_alpha) {
+		txt = _to_hex(a) + txt;
+	}
+	return txt;
+}
+
+Color Color::from_hsv(float p_h, float p_s, float p_v, float p_a) const {
+	Color c;
+	c.set_hsv(p_h, p_s, p_v, p_a);
+	return c;
+}
+
+// FIXME: Remove once Pandemonium 3.1 has been released
+float Color::gray() const {
+	WARN_DEPRECATED_MSG("'Color.gray()' is deprecated and will be removed in a future version. Use 'Color.v' for a better grayscale approximation.");
+	return (r + g + b) / 3.0;
+}
+
+Color::operator String() const {
+	return "(" + String::num(r, 4) + ", " + String::num(g, 4) + ", " + String::num(b, 4) + ", " + String::num(a, 4) + ")";
+}
+
+Color Color::operator+(const Color &p_color) const {
+	return Color(
+			r + p_color.r,
+			g + p_color.g,
+			b + p_color.b,
+			a + p_color.a);
+}
+
+void Color::operator+=(const Color &p_color) {
+	r = r + p_color.r;
+	g = g + p_color.g;
+	b = b + p_color.b;
+	a = a + p_color.a;
+}
+
+Color Color::operator-(const Color &p_color) const {
+	return Color(
+			r - p_color.r,
+			g - p_color.g,
+			b - p_color.b,
+			a - p_color.a);
+}
+
+void Color::operator-=(const Color &p_color) {
+	r = r - p_color.r;
+	g = g - p_color.g;
+	b = b - p_color.b;
+	a = a - p_color.a;
+}
+
+Color Color::operator*(const Color &p_color) const {
+	return Color(
+			r * p_color.r,
+			g * p_color.g,
+			b * p_color.b,
+			a * p_color.a);
+}
+
+Color Color::operator*(const real_t &rvalue) const {
+	return Color(
+			r * rvalue,
+			g * rvalue,
+			b * rvalue,
+			a * rvalue);
+}
+
+void Color::operator*=(const Color &p_color) {
+	r = r * p_color.r;
+	g = g * p_color.g;
+	b = b * p_color.b;
+	a = a * p_color.a;
+}
+
+void Color::operator*=(const real_t &rvalue) {
+	r = r * rvalue;
+	g = g * rvalue;
+	b = b * rvalue;
+	a = a * rvalue;
+}
+
+Color Color::operator/(const Color &p_color) const {
+	return Color(
+			r / p_color.r,
+			g / p_color.g,
+			b / p_color.b,
+			a / p_color.a);
+}
+
+Color Color::operator/(const real_t &rvalue) const {
+	return Color(
+			r / rvalue,
+			g / rvalue,
+			b / rvalue,
+			a / rvalue);
+}
+
+void Color::operator/=(const Color &p_color) {
+	r = r / p_color.r;
+	g = g / p_color.g;
+	b = b / p_color.b;
+	a = a / p_color.a;
+}
+
+void Color::operator/=(const real_t &rvalue) {
+	if (rvalue == 0) {
+		r = 1.0;
+		g = 1.0;
+		b = 1.0;
+		a = 1.0;
+	} else {
+		r = r / rvalue;
+		g = g / rvalue;
+		b = b / rvalue;
+		a = a / rvalue;
+	}
+};
+
+Color Color::operator-() const {
+	return Color(
+			1.0 - r,
+			1.0 - g,
+			1.0 - b,
+			1.0 - a);
+}

core/math/color.h

@@ -0,0 +1,269 @@
+#ifndef COLOR_H
+#define COLOR_H
+
+/*************************************************************************/
+/*  color.h                                                              */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/math_funcs.h"
+#include "core/string/ustring.h"
+
+struct _NO_DISCARD_CLASS_ Color {
+	union {
+		struct {
+			float r;
+			float g;
+			float b;
+			float a;
+		};
+		float components[4];
+	};
+
+	bool operator==(const Color &p_color) const { return (r == p_color.r && g == p_color.g && b == p_color.b && a == p_color.a); }
+	bool operator!=(const Color &p_color) const { return (r != p_color.r || g != p_color.g || b != p_color.b || a != p_color.a); }
+
+	uint32_t to_rgba32() const;
+	uint32_t to_argb32() const;
+	uint32_t to_abgr32() const;
+	uint64_t to_rgba64() const;
+	uint64_t to_argb64() const;
+	uint64_t to_abgr64() const;
+	float gray() const;
+	float get_h() const;
+	float get_s() const;
+	float get_v() const;
+	void set_hsv(float p_h, float p_s, float p_v, float p_alpha = 1.0);
+
+	_FORCE_INLINE_ float &operator[](int idx) {
+		return components[idx];
+	}
+	_FORCE_INLINE_ const float &operator[](int idx) const {
+		return components[idx];
+	}
+
+	Color operator+(const Color &p_color) const;
+	void operator+=(const Color &p_color);
+
+	Color operator-() const;
+	Color operator-(const Color &p_color) const;
+	void operator-=(const Color &p_color);
+
+	Color operator*(const Color &p_color) const;
+	Color operator*(const real_t &rvalue) const;
+	void operator*=(const Color &p_color);
+	void operator*=(const real_t &rvalue);
+
+	Color operator/(const Color &p_color) const;
+	Color operator/(const real_t &rvalue) const;
+	void operator/=(const Color &p_color);
+	void operator/=(const real_t &rvalue);
+
+	bool is_equal_approx(const Color &p_color) const;
+
+	Color clamp(const Color &p_min = Color(0, 0, 0, 0), const Color &p_max = Color(1, 1, 1, 1)) const;
+
+	void invert();
+	void contrast();
+	Color inverted() const;
+	Color contrasted() const;
+
+	_FORCE_INLINE_ float get_luminance() const {
+		return 0.2126 * r + 0.7152 * g + 0.0722 * b;
+	}
+
+	_FORCE_INLINE_ Color linear_interpolate(const Color &p_to, float p_weight) const {
+		Color res = *this;
+
+		res.r += (p_weight * (p_to.r - r));
+		res.g += (p_weight * (p_to.g - g));
+		res.b += (p_weight * (p_to.b - b));
+		res.a += (p_weight * (p_to.a - a));
+
+		return res;
+	}
+
+	_FORCE_INLINE_ Color darkened(float p_amount) const {
+		Color res = *this;
+		res.r = res.r * (1.0f - p_amount);
+		res.g = res.g * (1.0f - p_amount);
+		res.b = res.b * (1.0f - p_amount);
+		return res;
+	}
+
+	_FORCE_INLINE_ Color lightened(float p_amount) const {
+		Color res = *this;
+		res.r = res.r + (1.0f - res.r) * p_amount;
+		res.g = res.g + (1.0f - res.g) * p_amount;
+		res.b = res.b + (1.0f - res.b) * p_amount;
+		return res;
+	}
+
+	_FORCE_INLINE_ uint32_t to_rgbe9995() const {
+		const float pow2to9 = 512.0f;
+		const float B = 15.0f;
+		//const float Emax = 31.0f;
+		const float N = 9.0f;
+
+		float sharedexp = 65408.000f; //(( pow2to9  - 1.0f)/ pow2to9)*powf( 2.0f, 31.0f - 15.0f);
+
+		float cRed = MAX(0.0f, MIN(sharedexp, r));
+		float cGreen = MAX(0.0f, MIN(sharedexp, g));
+		float cBlue = MAX(0.0f, MIN(sharedexp, b));
+
+		float cMax = MAX(cRed, MAX(cGreen, cBlue));
+
+		// expp = MAX(-B - 1, log2(maxc)) + 1 + B
+
+		float expp = MAX(-B - 1.0f, floor(Math::log(cMax) / Math_LN2)) + 1.0f + B;
+
+		float sMax = (float)floor((cMax / Math::pow(2.0f, expp - B - N)) + 0.5f);
+
+		float exps = expp + 1.0f;
+
+		if (0.0 <= sMax && sMax < pow2to9) {
+			exps = expp;
+		}
+
+		float sRed = Math::floor((cRed / pow(2.0f, exps - B - N)) + 0.5f);
+		float sGreen = Math::floor((cGreen / pow(2.0f, exps - B - N)) + 0.5f);
+		float sBlue = Math::floor((cBlue / pow(2.0f, exps - B - N)) + 0.5f);
+
+		return (uint32_t(Math::fast_ftoi(sRed)) & 0x1FF) | ((uint32_t(Math::fast_ftoi(sGreen)) & 0x1FF) << 9) | ((uint32_t(Math::fast_ftoi(sBlue)) & 0x1FF) << 18) | ((uint32_t(Math::fast_ftoi(exps)) & 0x1F) << 27);
+	}
+
+	_FORCE_INLINE_ Color blend(const Color &p_over) const {
+		Color res;
+		float sa = 1.0 - p_over.a;
+		res.a = a * sa + p_over.a;
+		if (res.a == 0) {
+			return Color(0, 0, 0, 0);
+		} else {
+			res.r = (r * a * sa + p_over.r * p_over.a) / res.a;
+			res.g = (g * a * sa + p_over.g * p_over.a) / res.a;
+			res.b = (b * a * sa + p_over.b * p_over.a) / res.a;
+		}
+		return res;
+	}
+
+	_FORCE_INLINE_ Color to_linear() const {
+		return Color(
+				r < 0.04045 ? r * (1.0 / 12.92) : Math::pow((r + 0.055) * (1.0 / (1 + 0.055)), 2.4),
+				g < 0.04045 ? g * (1.0 / 12.92) : Math::pow((g + 0.055) * (1.0 / (1 + 0.055)), 2.4),
+				b < 0.04045 ? b * (1.0 / 12.92) : Math::pow((b + 0.055) * (1.0 / (1 + 0.055)), 2.4),
+				a);
+	}
+	_FORCE_INLINE_ Color to_srgb() const {
+		return Color(
+				r < 0.0031308 ? 12.92 * r : (1.0 + 0.055) * Math::pow(r, 1.0f / 2.4f) - 0.055,
+				g < 0.0031308 ? 12.92 * g : (1.0 + 0.055) * Math::pow(g, 1.0f / 2.4f) - 0.055,
+				b < 0.0031308 ? 12.92 * b : (1.0 + 0.055) * Math::pow(b, 1.0f / 2.4f) - 0.055, a);
+	}
+
+	static Color hex(uint32_t p_hex);
+	static Color hex64(uint64_t p_hex);
+	static Color html(const String &p_color);
+	static bool html_is_valid(const String &p_color);
+	static Color named(const String &p_name);
+	String to_html(bool p_alpha = true) const;
+	Color from_hsv(float p_h, float p_s, float p_v, float p_a) const;
+	static Color from_rgbe9995(uint32_t p_rgbe);
+
+	_FORCE_INLINE_ bool operator<(const Color &p_color) const; //used in set keys
+	operator String() const;
+
+	static _FORCE_INLINE_ Color color8(int r, int g, int b) {
+		return Color(static_cast<float>(r) / 255.0f, static_cast<float>(g) / 255.0f, static_cast<float>(b) / 255.0f);
+	}
+
+	static _FORCE_INLINE_ Color color8(int r, int g, int b, int a) {
+		return Color(static_cast<float>(r) / 255.0f, static_cast<float>(g) / 255.0f, static_cast<float>(b) / 255.0f, static_cast<float>(a) / 255.0f);
+	}
+
+	_FORCE_INLINE_ void set_r8(int32_t r8) { r = (CLAMP(r8, 0, 255) / 255.0f); }
+	_FORCE_INLINE_ int32_t get_r8() const { return int32_t(CLAMP(Math::round(r * 255.0f), 0.0f, 255.0f)); }
+	_FORCE_INLINE_ void set_g8(int32_t g8) { g = (CLAMP(g8, 0, 255) / 255.0f); }
+	_FORCE_INLINE_ int32_t get_g8() const { return int32_t(CLAMP(Math::round(g * 255.0f), 0.0f, 255.0f)); }
+	_FORCE_INLINE_ void set_b8(int32_t b8) { b = (CLAMP(b8, 0, 255) / 255.0f); }
+	_FORCE_INLINE_ int32_t get_b8() const { return int32_t(CLAMP(Math::round(b * 255.0f), 0.0f, 255.0f)); }
+	_FORCE_INLINE_ void set_a8(int32_t a8) { a = (CLAMP(a8, 0, 255) / 255.0f); }
+	_FORCE_INLINE_ int32_t get_a8() const { return int32_t(CLAMP(Math::round(a * 255.0f), 0.0f, 255.0f)); }
+
+	_FORCE_INLINE_ void set_h(float p_h) { set_hsv(p_h, get_s(), get_v(), a); }
+	_FORCE_INLINE_ void set_s(float p_s) { set_hsv(get_h(), p_s, get_v(), a); }
+	_FORCE_INLINE_ void set_v(float p_v) { set_hsv(get_h(), get_s(), p_v, a); }
+
+	/**
+	 * No construct parameters, r=0, g=0, b=0. a=255
+	 */
+	_FORCE_INLINE_ Color() {
+		r = 0;
+		g = 0;
+		b = 0;
+		a = 1.0;
+	}
+
+	/**
+	 * RGB / RGBA construct parameters. Alpha is optional, but defaults to 1.0
+	 */
+	_FORCE_INLINE_ Color(float p_r, float p_g, float p_b, float p_a = 1.0) {
+		r = p_r;
+		g = p_g;
+		b = p_b;
+		a = p_a;
+	}
+
+	/**
+	 * Construct a Color from another Color, but with the specified alpha value.
+	 */
+	_FORCE_INLINE_ Color(const Color &p_c, float p_a) {
+		r = p_c.r;
+		g = p_c.g;
+		b = p_c.b;
+		a = p_a;
+	}
+};
+
+bool Color::operator<(const Color &p_color) const {
+	if (r == p_color.r) {
+		if (g == p_color.g) {
+			if (b == p_color.b) {
+				return (a < p_color.a);
+			} else {
+				return (b < p_color.b);
+			}
+		} else {
+			return g < p_color.g;
+		}
+	} else {
+		return r < p_color.r;
+	}
+}
+
+#endif

core/math/color_names.inc

@@ -0,0 +1,162 @@
+
+#ifndef COLOR_NAMES_INC_H
+#define COLOR_NAMES_INC_H
+
+// Names from https://en.wikipedia.org/wiki/X11_color_names
+
+#include "core/containers/rb_map.h"
+
+static RBMap<String, Color> _named_colors;
+static void _populate_named_colors() {
+	if (!_named_colors.empty()) {
+		return;
+	}
+	_named_colors.insert("aliceblue", Color(0.94, 0.97, 1.00));
+	_named_colors.insert("antiquewhite", Color(0.98, 0.92, 0.84));
+	_named_colors.insert("aqua", Color(0.00, 1.00, 1.00));
+	_named_colors.insert("aquamarine", Color(0.50, 1.00, 0.83));
+	_named_colors.insert("azure", Color(0.94, 1.00, 1.00));
+	_named_colors.insert("beige", Color(0.96, 0.96, 0.86));
+	_named_colors.insert("bisque", Color(1.00, 0.89, 0.77));
+	_named_colors.insert("black", Color(0.00, 0.00, 0.00));
+	_named_colors.insert("blanchedalmond", Color(1.00, 0.92, 0.80));
+	_named_colors.insert("blue", Color(0.00, 0.00, 1.00));
+	_named_colors.insert("blueviolet", Color(0.54, 0.17, 0.89));
+	_named_colors.insert("brown", Color(0.65, 0.16, 0.16));
+	_named_colors.insert("burlywood", Color(0.87, 0.72, 0.53));
+	_named_colors.insert("cadetblue", Color(0.37, 0.62, 0.63));
+	_named_colors.insert("chartreuse", Color(0.50, 1.00, 0.00));
+	_named_colors.insert("chocolate", Color(0.82, 0.41, 0.12));
+	_named_colors.insert("coral", Color(1.00, 0.50, 0.31));
+	_named_colors.insert("cornflower", Color(0.39, 0.58, 0.93));
+	_named_colors.insert("cornsilk", Color(1.00, 0.97, 0.86));
+	_named_colors.insert("crimson", Color(0.86, 0.08, 0.24));
+	_named_colors.insert("cyan", Color(0.00, 1.00, 1.00));
+	_named_colors.insert("darkblue", Color(0.00, 0.00, 0.55));
+	_named_colors.insert("darkcyan", Color(0.00, 0.55, 0.55));
+	_named_colors.insert("darkgoldenrod", Color(0.72, 0.53, 0.04));
+	_named_colors.insert("darkgray", Color(0.66, 0.66, 0.66));
+	_named_colors.insert("darkgreen", Color(0.00, 0.39, 0.00));
+	_named_colors.insert("darkkhaki", Color(0.74, 0.72, 0.42));
+	_named_colors.insert("darkmagenta", Color(0.55, 0.00, 0.55));
+	_named_colors.insert("darkolivegreen", Color(0.33, 0.42, 0.18));
+	_named_colors.insert("darkorange", Color(1.00, 0.55, 0.00));
+	_named_colors.insert("darkorchid", Color(0.60, 0.20, 0.80));
+	_named_colors.insert("darkred", Color(0.55, 0.00, 0.00));
+	_named_colors.insert("darksalmon", Color(0.91, 0.59, 0.48));
+	_named_colors.insert("darkseagreen", Color(0.56, 0.74, 0.56));
+	_named_colors.insert("darkslateblue", Color(0.28, 0.24, 0.55));
+	_named_colors.insert("darkslategray", Color(0.18, 0.31, 0.31));
+	_named_colors.insert("darkturquoise", Color(0.00, 0.81, 0.82));
+	_named_colors.insert("darkviolet", Color(0.58, 0.00, 0.83));
+	_named_colors.insert("deeppink", Color(1.00, 0.08, 0.58));
+	_named_colors.insert("deepskyblue", Color(0.00, 0.75, 1.00));
+	_named_colors.insert("dimgray", Color(0.41, 0.41, 0.41));
+	_named_colors.insert("dodgerblue", Color(0.12, 0.56, 1.00));
+	_named_colors.insert("firebrick", Color(0.70, 0.13, 0.13));
+	_named_colors.insert("floralwhite", Color(1.00, 0.98, 0.94));
+	_named_colors.insert("forestgreen", Color(0.13, 0.55, 0.13));
+	_named_colors.insert("fuchsia", Color(1.00, 0.00, 1.00));
+	_named_colors.insert("gainsboro", Color(0.86, 0.86, 0.86));
+	_named_colors.insert("ghostwhite", Color(0.97, 0.97, 1.00));
+	_named_colors.insert("gold", Color(1.00, 0.84, 0.00));
+	_named_colors.insert("goldenrod", Color(0.85, 0.65, 0.13));
+	_named_colors.insert("gray", Color(0.75, 0.75, 0.75));
+	_named_colors.insert("webgray", Color(0.50, 0.50, 0.50));
+	_named_colors.insert("green", Color(0.00, 1.00, 0.00));
+	_named_colors.insert("webgreen", Color(0.00, 0.50, 0.00));
+	_named_colors.insert("greenyellow", Color(0.68, 1.00, 0.18));
+	_named_colors.insert("honeydew", Color(0.94, 1.00, 0.94));
+	_named_colors.insert("hotpink", Color(1.00, 0.41, 0.71));
+	_named_colors.insert("indianred", Color(0.80, 0.36, 0.36));
+	_named_colors.insert("indigo", Color(0.29, 0.00, 0.51));
+	_named_colors.insert("ivory", Color(1.00, 1.00, 0.94));
+	_named_colors.insert("khaki", Color(0.94, 0.90, 0.55));
+	_named_colors.insert("lavender", Color(0.90, 0.90, 0.98));
+	_named_colors.insert("lavenderblush", Color(1.00, 0.94, 0.96));
+	_named_colors.insert("lawngreen", Color(0.49, 0.99, 0.00));
+	_named_colors.insert("lemonchiffon", Color(1.00, 0.98, 0.80));
+	_named_colors.insert("lightblue", Color(0.68, 0.85, 0.90));
+	_named_colors.insert("lightcoral", Color(0.94, 0.50, 0.50));
+	_named_colors.insert("lightcyan", Color(0.88, 1.00, 1.00));
+	_named_colors.insert("lightgoldenrod", Color(0.98, 0.98, 0.82));
+	_named_colors.insert("lightgray", Color(0.83, 0.83, 0.83));
+	_named_colors.insert("lightgreen", Color(0.56, 0.93, 0.56));
+	_named_colors.insert("lightpink", Color(1.00, 0.71, 0.76));
+	_named_colors.insert("lightsalmon", Color(1.00, 0.63, 0.48));
+	_named_colors.insert("lightseagreen", Color(0.13, 0.70, 0.67));
+	_named_colors.insert("lightskyblue", Color(0.53, 0.81, 0.98));
+	_named_colors.insert("lightslategray", Color(0.47, 0.53, 0.60));
+	_named_colors.insert("lightsteelblue", Color(0.69, 0.77, 0.87));
+	_named_colors.insert("lightyellow", Color(1.00, 1.00, 0.88));
+	_named_colors.insert("lime", Color(0.00, 1.00, 0.00));
+	_named_colors.insert("limegreen", Color(0.20, 0.80, 0.20));
+	_named_colors.insert("linen", Color(0.98, 0.94, 0.90));
+	_named_colors.insert("magenta", Color(1.00, 0.00, 1.00));
+	_named_colors.insert("maroon", Color(0.69, 0.19, 0.38));
+	_named_colors.insert("webmaroon", Color(0.50, 0.00, 0.00));
+	_named_colors.insert("mediumaquamarine", Color(0.40, 0.80, 0.67));
+	_named_colors.insert("mediumblue", Color(0.00, 0.00, 0.80));
+	_named_colors.insert("mediumorchid", Color(0.73, 0.33, 0.83));
+	_named_colors.insert("mediumpurple", Color(0.58, 0.44, 0.86));
+	_named_colors.insert("mediumseagreen", Color(0.24, 0.70, 0.44));
+	_named_colors.insert("mediumslateblue", Color(0.48, 0.41, 0.93));
+	_named_colors.insert("mediumspringgreen", Color(0.00, 0.98, 0.60));
+	_named_colors.insert("mediumturquoise", Color(0.28, 0.82, 0.80));
+	_named_colors.insert("mediumvioletred", Color(0.78, 0.08, 0.52));
+	_named_colors.insert("midnightblue", Color(0.10, 0.10, 0.44));
+	_named_colors.insert("mintcream", Color(0.96, 1.00, 0.98));
+	_named_colors.insert("mistyrose", Color(1.00, 0.89, 0.88));
+	_named_colors.insert("moccasin", Color(1.00, 0.89, 0.71));
+	_named_colors.insert("navajowhite", Color(1.00, 0.87, 0.68));
+	_named_colors.insert("navyblue", Color(0.00, 0.00, 0.50));
+	_named_colors.insert("oldlace", Color(0.99, 0.96, 0.90));
+	_named_colors.insert("olive", Color(0.50, 0.50, 0.00));
+	_named_colors.insert("olivedrab", Color(0.42, 0.56, 0.14));
+	_named_colors.insert("orange", Color(1.00, 0.65, 0.00));
+	_named_colors.insert("orangered", Color(1.00, 0.27, 0.00));
+	_named_colors.insert("orchid", Color(0.85, 0.44, 0.84));
+	_named_colors.insert("palegoldenrod", Color(0.93, 0.91, 0.67));
+	_named_colors.insert("palegreen", Color(0.60, 0.98, 0.60));
+	_named_colors.insert("paleturquoise", Color(0.69, 0.93, 0.93));
+	_named_colors.insert("palevioletred", Color(0.86, 0.44, 0.58));
+	_named_colors.insert("papayawhip", Color(1.00, 0.94, 0.84));
+	_named_colors.insert("peachpuff", Color(1.00, 0.85, 0.73));
+	_named_colors.insert("peru", Color(0.80, 0.52, 0.25));
+	_named_colors.insert("pink", Color(1.00, 0.75, 0.80));
+	_named_colors.insert("plum", Color(0.87, 0.63, 0.87));
+	_named_colors.insert("powderblue", Color(0.69, 0.88, 0.90));
+	_named_colors.insert("purple", Color(0.63, 0.13, 0.94));
+	_named_colors.insert("webpurple", Color(0.50, 0.00, 0.50));
+	_named_colors.insert("rebeccapurple", Color(0.40, 0.20, 0.60));
+	_named_colors.insert("red", Color(1.00, 0.00, 0.00));
+	_named_colors.insert("rosybrown", Color(0.74, 0.56, 0.56));
+	_named_colors.insert("royalblue", Color(0.25, 0.41, 0.88));
+	_named_colors.insert("saddlebrown", Color(0.55, 0.27, 0.07));
+	_named_colors.insert("salmon", Color(0.98, 0.50, 0.45));
+	_named_colors.insert("sandybrown", Color(0.96, 0.64, 0.38));
+	_named_colors.insert("seagreen", Color(0.18, 0.55, 0.34));
+	_named_colors.insert("seashell", Color(1.00, 0.96, 0.93));
+	_named_colors.insert("sienna", Color(0.63, 0.32, 0.18));
+	_named_colors.insert("silver", Color(0.75, 0.75, 0.75));
+	_named_colors.insert("skyblue", Color(0.53, 0.81, 0.92));
+	_named_colors.insert("slateblue", Color(0.42, 0.35, 0.80));
+	_named_colors.insert("slategray", Color(0.44, 0.50, 0.56));
+	_named_colors.insert("snow", Color(1.00, 0.98, 0.98));
+	_named_colors.insert("springgreen", Color(0.00, 1.00, 0.50));
+	_named_colors.insert("steelblue", Color(0.27, 0.51, 0.71));
+	_named_colors.insert("tan", Color(0.82, 0.71, 0.55));
+	_named_colors.insert("teal", Color(0.00, 0.50, 0.50));
+	_named_colors.insert("thistle", Color(0.85, 0.75, 0.85));
+	_named_colors.insert("tomato", Color(1.00, 0.39, 0.28));
+	_named_colors.insert("turquoise", Color(0.25, 0.88, 0.82));
+	_named_colors.insert("transparent", Color(1.00, 1.00, 1.00, 0.00));
+	_named_colors.insert("violet", Color(0.93, 0.51, 0.93));
+	_named_colors.insert("wheat", Color(0.96, 0.87, 0.70));
+	_named_colors.insert("white", Color(1.00, 1.00, 1.00));
+	_named_colors.insert("whitesmoke", Color(0.96, 0.96, 0.96));
+	_named_colors.insert("yellow", Color(1.00, 1.00, 0.00));
+	_named_colors.insert("yellowgreen", Color(0.60, 0.80, 0.20));
+}
+
+#endif

core/math/face3.cpp

@@ -0,0 +1,392 @@
+/*************************************************************************/
+/*  face3.cpp                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "face3.h"
+
+#include "core/math/geometry.h"
+
+int Face3::split_by_plane(const Plane &p_plane, Face3 p_res[3], bool p_is_point_over[3]) const {
+	ERR_FAIL_COND_V(is_degenerate(), 0);
+
+	Vector3 above[4];
+	int above_count = 0;
+
+	Vector3 below[4];
+	int below_count = 0;
+
+	for (int i = 0; i < 3; i++) {
+		if (p_plane.has_point(vertex[i], (real_t)CMP_EPSILON)) { // point is in plane
+
+			ERR_FAIL_COND_V(above_count >= 4, 0);
+			above[above_count++] = vertex[i];
+			ERR_FAIL_COND_V(below_count >= 4, 0);
+			below[below_count++] = vertex[i];
+
+		} else {
+			if (p_plane.is_point_over(vertex[i])) {
+				//Point is over
+				ERR_FAIL_COND_V(above_count >= 4, 0);
+				above[above_count++] = vertex[i];
+
+			} else {
+				//Point is under
+				ERR_FAIL_COND_V(below_count >= 4, 0);
+				below[below_count++] = vertex[i];
+			}
+
+			/* Check for Intersection between this and the next vertex*/
+
+			Vector3 inters;
+			if (!p_plane.intersects_segment(vertex[i], vertex[(i + 1) % 3], &inters)) {
+				continue;
+			}
+
+			/* Intersection goes to both */
+			ERR_FAIL_COND_V(above_count >= 4, 0);
+			above[above_count++] = inters;
+			ERR_FAIL_COND_V(below_count >= 4, 0);
+			below[below_count++] = inters;
+		}
+	}
+
+	int polygons_created = 0;
+
+	ERR_FAIL_COND_V(above_count >= 4 && below_count >= 4, 0); //bug in the algo
+
+	if (above_count >= 3) {
+		p_res[polygons_created] = Face3(above[0], above[1], above[2]);
+		p_is_point_over[polygons_created] = true;
+		polygons_created++;
+
+		if (above_count == 4) {
+			p_res[polygons_created] = Face3(above[2], above[3], above[0]);
+			p_is_point_over[polygons_created] = true;
+			polygons_created++;
+		}
+	}
+
+	if (below_count >= 3) {
+		p_res[polygons_created] = Face3(below[0], below[1], below[2]);
+		p_is_point_over[polygons_created] = false;
+		polygons_created++;
+
+		if (below_count == 4) {
+			p_res[polygons_created] = Face3(below[2], below[3], below[0]);
+			p_is_point_over[polygons_created] = false;
+			polygons_created++;
+		}
+	}
+
+	return polygons_created;
+}
+
+bool Face3::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const {
+	return Geometry::ray_intersects_triangle(p_from, p_dir, vertex[0], vertex[1], vertex[2], p_intersection);
+}
+
+bool Face3::intersects_segment(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const {
+	return Geometry::segment_intersects_triangle(p_from, p_dir, vertex[0], vertex[1], vertex[2], p_intersection);
+}
+
+bool Face3::is_degenerate() const {
+	Vector3 normal = vec3_cross(vertex[0] - vertex[1], vertex[0] - vertex[2]);
+	return (normal.length_squared() < (real_t)CMP_EPSILON2);
+}
+
+Face3::Side Face3::get_side_of(const Face3 &p_face, ClockDirection p_clock_dir) const {
+	int over = 0, under = 0;
+
+	Plane plane = get_plane(p_clock_dir);
+
+	for (int i = 0; i < 3; i++) {
+		const Vector3 &v = p_face.vertex[i];
+
+		if (plane.has_point(v)) { //coplanar, don't bother
+			continue;
+		}
+
+		if (plane.is_point_over(v)) {
+			over++;
+		} else {
+			under++;
+		}
+	}
+
+	if (over > 0 && under == 0) {
+		return SIDE_OVER;
+	} else if (under > 0 && over == 0) {
+		return SIDE_UNDER;
+	} else if (under == 0 && over == 0) {
+		return SIDE_COPLANAR;
+	} else {
+		return SIDE_SPANNING;
+	}
+}
+
+Vector3 Face3::get_random_point_inside() const {
+	real_t a = Math::random(0, 1);
+	real_t b = Math::random(0, 1);
+	if (a > b) {
+		SWAP(a, b);
+	}
+
+	return vertex[0] * a + vertex[1] * (b - a) + vertex[2] * (1.0 - b);
+}
+
+Plane Face3::get_plane(ClockDirection p_dir) const {
+	return Plane(vertex[0], vertex[1], vertex[2], p_dir);
+}
+
+Vector3 Face3::get_median_point() const {
+	return (vertex[0] + vertex[1] + vertex[2]) / 3.0;
+}
+
+real_t Face3::get_area() const {
+	return vec3_cross(vertex[0] - vertex[1], vertex[0] - vertex[2]).length() * 0.5;
+}
+
+ClockDirection Face3::get_clock_dir() const {
+	Vector3 normal = vec3_cross(vertex[0] - vertex[1], vertex[0] - vertex[2]);
+	//printf("normal is %g,%g,%g x %g,%g,%g- wtfu is %g\n",tofloat(normal.x),tofloat(normal.y),tofloat(normal.z),tofloat(vertex[0].x),tofloat(vertex[0].y),tofloat(vertex[0].z),tofloat( normal.dot( vertex[0] ) ) );
+	return (normal.dot(vertex[0]) >= 0) ? CLOCKWISE : COUNTERCLOCKWISE;
+}
+
+bool Face3::intersects_aabb(const AABB &p_aabb) const {
+	/** TEST PLANE **/
+	if (!p_aabb.intersects_plane(get_plane())) {
+		return false;
+	}
+
+#define TEST_AXIS(m_ax)                                            \
+	/** TEST FACE AXIS */                                          \
+	{                                                              \
+		real_t aabb_min = p_aabb.position.m_ax;                    \
+		real_t aabb_max = p_aabb.position.m_ax + p_aabb.size.m_ax; \
+		real_t tri_min = vertex[0].m_ax;                           \
+		real_t tri_max = vertex[0].m_ax;                           \
+		for (int i = 1; i < 3; i++) {                              \
+			if (vertex[i].m_ax > tri_max)                          \
+				tri_max = vertex[i].m_ax;                          \
+			if (vertex[i].m_ax < tri_min)                          \
+				tri_min = vertex[i].m_ax;                          \
+		}                                                          \
+                                                                   \
+		if (tri_max < aabb_min || aabb_max < tri_min)              \
+			return false;                                          \
+	}
+
+	TEST_AXIS(x);
+	TEST_AXIS(y);
+	TEST_AXIS(z);
+
+	/** TEST ALL EDGES **/
+
+	Vector3 edge_norms[3] = {
+		vertex[0] - vertex[1],
+		vertex[1] - vertex[2],
+		vertex[2] - vertex[0],
+	};
+
+	for (int i = 0; i < 12; i++) {
+		Vector3 from, to;
+		p_aabb.get_edge(i, from, to);
+		Vector3 e1 = from - to;
+		for (int j = 0; j < 3; j++) {
+			Vector3 e2 = edge_norms[j];
+
+			Vector3 axis = vec3_cross(e1, e2);
+
+			if (axis.length_squared() < 0.0001f) {
+				continue; // coplanar
+			}
+			axis.normalize();
+
+			real_t minA, maxA, minB, maxB;
+			p_aabb.project_range_in_plane(Plane(axis, 0), minA, maxA);
+			project_range(axis, Transform(), minB, maxB);
+
+			if (maxA < minB || maxB < minA) {
+				return false;
+			}
+		}
+	}
+	return true;
+}
+
+Face3::operator String() const {
+	return String() + vertex[0] + ", " + vertex[1] + ", " + vertex[2];
+}
+
+void Face3::project_range(const Vector3 &p_normal, const Transform &p_transform, real_t &r_min, real_t &r_max) const {
+	for (int i = 0; i < 3; i++) {
+		Vector3 v = p_transform.xform(vertex[i]);
+		real_t d = p_normal.dot(v);
+
+		if (i == 0 || d > r_max) {
+			r_max = d;
+		}
+
+		if (i == 0 || d < r_min) {
+			r_min = d;
+		}
+	}
+}
+
+void Face3::get_support(const Vector3 &p_normal, const Transform &p_transform, Vector3 *p_vertices, int *p_count, int p_max) const {
+#define _FACE_IS_VALID_SUPPORT_THRESHOLD 0.98
+#define _EDGE_IS_VALID_SUPPORT_THRESHOLD 0.05
+
+	if (p_max <= 0) {
+		return;
+	}
+
+	Vector3 n = p_transform.basis.xform_inv(p_normal);
+
+	/** TEST FACE AS SUPPORT **/
+	if (get_plane().normal.dot(n) > (real_t)_FACE_IS_VALID_SUPPORT_THRESHOLD) {
+		*p_count = MIN(3, p_max);
+
+		for (int i = 0; i < *p_count; i++) {
+			p_vertices[i] = p_transform.xform(vertex[i]);
+		}
+
+		return;
+	}
+
+	/** FIND SUPPORT VERTEX **/
+
+	int vert_support_idx = -1;
+	real_t support_max = 0;
+
+	for (int i = 0; i < 3; i++) {
+		real_t d = n.dot(vertex[i]);
+
+		if (i == 0 || d > support_max) {
+			support_max = d;
+			vert_support_idx = i;
+		}
+	}
+
+	/** TEST EDGES AS SUPPORT **/
+
+	for (int i = 0; i < 3; i++) {
+		if (i != vert_support_idx && i + 1 != vert_support_idx) {
+			continue;
+		}
+
+		// check if edge is valid as a support
+		real_t dot = (vertex[i] - vertex[(i + 1) % 3]).normalized().dot(n);
+		dot = ABS(dot);
+		if (dot < (real_t)_EDGE_IS_VALID_SUPPORT_THRESHOLD) {
+			*p_count = MIN(2, p_max);
+
+			for (int j = 0; j < *p_count; j++) {
+				p_vertices[j] = p_transform.xform(vertex[(j + i) % 3]);
+			}
+
+			return;
+		}
+	}
+
+	*p_count = 1;
+	p_vertices[0] = p_transform.xform(vertex[vert_support_idx]);
+}
+
+Vector3 Face3::get_closest_point_to(const Vector3 &p_point) const {
+	Vector3 edge0 = vertex[1] - vertex[0];
+	Vector3 edge1 = vertex[2] - vertex[0];
+	Vector3 v0 = vertex[0] - p_point;
+
+	real_t a = edge0.dot(edge0);
+	real_t b = edge0.dot(edge1);
+	real_t c = edge1.dot(edge1);
+	real_t d = edge0.dot(v0);
+	real_t e = edge1.dot(v0);
+
+	real_t det = a * c - b * b;
+	real_t s = b * e - c * d;
+	real_t t = b * d - a * e;
+
+	if (s + t < det) {
+		if (s < 0.f) {
+			if (t < 0.f) {
+				if (d < 0.f) {
+					s = CLAMP(-d / a, 0.f, 1.f);
+					t = 0.f;
+				} else {
+					s = 0.f;
+					t = CLAMP(-e / c, 0.f, 1.f);
+				}
+			} else {
+				s = 0.f;
+				t = CLAMP(-e / c, 0.f, 1.f);
+			}
+		} else if (t < 0.f) {
+			s = CLAMP(-d / a, 0.f, 1.f);
+			t = 0.f;
+		} else {
+			real_t invDet = 1.f / det;
+			s *= invDet;
+			t *= invDet;
+		}
+	} else {
+		if (s < 0.f) {
+			real_t tmp0 = b + d;
+			real_t tmp1 = c + e;
+			if (tmp1 > tmp0) {
+				real_t numer = tmp1 - tmp0;
+				real_t denom = a - 2 * b + c;
+				s = CLAMP(numer / denom, 0.f, 1.f);
+				t = 1 - s;
+			} else {
+				t = CLAMP(-e / c, 0.f, 1.f);
+				s = 0.f;
+			}
+		} else if (t < 0.f) {
+			if (a + d > b + e) {
+				real_t numer = c + e - b - d;
+				real_t denom = a - 2 * b + c;
+				s = CLAMP(numer / denom, 0.f, 1.f);
+				t = 1 - s;
+			} else {
+				s = CLAMP(-d / a, 0.f, 1.f);
+				t = 0.f;
+			}
+		} else {
+			real_t numer = c + e - b - d;
+			real_t denom = a - 2 * b + c;
+			s = CLAMP(numer / denom, 0.f, 1.f);
+			t = 1.f - s;
+		}
+	}
+
+	return vertex[0] + s * edge0 + t * edge1;
+}

core/math/face3.h

@@ -0,0 +1,257 @@
+#ifndef FACE3_H
+#define FACE3_H
+
+/*************************************************************************/
+/*  face3.h                                                              */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/aabb.h"
+#include "core/math/plane.h"
+#include "core/math/transform.h"
+#include "core/math/vector3.h"
+
+struct _NO_DISCARD_CLASS_ Face3 {
+	enum Side {
+		SIDE_OVER,
+		SIDE_UNDER,
+		SIDE_SPANNING,
+		SIDE_COPLANAR
+	};
+
+	Vector3 vertex[3];
+
+	/**
+	 *
+	 * @param p_plane plane used to split the face
+	 * @param p_res array of at least 3 faces, amount used in function return
+	 * @param p_is_point_over array of at least 3 booleans, determining which face is over the plane, amount used in function return
+	 * @param _epsilon constant used for numerical error rounding, to add "thickness" to the plane (so coplanar points can happen)
+	 * @return amount of faces generated by the split, either 0 (means no split possible), 2 or 3
+	 */
+
+	int split_by_plane(const Plane &p_plane, Face3 *p_res, bool *p_is_point_over) const;
+
+	Plane get_plane(ClockDirection p_dir = CLOCKWISE) const;
+	Vector3 get_random_point_inside() const;
+
+	Side get_side_of(const Face3 &p_face, ClockDirection p_clock_dir = CLOCKWISE) const;
+
+	bool is_degenerate() const;
+	real_t get_area() const;
+	real_t get_twice_area_squared() const;
+
+	Vector3 get_median_point() const;
+	Vector3 get_closest_point_to(const Vector3 &p_point) const;
+
+	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection = nullptr) const;
+	bool intersects_segment(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection = nullptr) const;
+
+	ClockDirection get_clock_dir() const; ///< todo, test if this is returning the proper clockwisity
+
+	void get_support(const Vector3 &p_normal, const Transform &p_transform, Vector3 *p_vertices, int *p_count, int p_max) const;
+	void project_range(const Vector3 &p_normal, const Transform &p_transform, real_t &r_min, real_t &r_max) const;
+
+	AABB get_aabb() const {
+		AABB aabb(vertex[0], Vector3());
+		aabb.expand_to(vertex[1]);
+		aabb.expand_to(vertex[2]);
+		return aabb;
+	}
+
+	bool intersects_aabb(const AABB &p_aabb) const;
+	_FORCE_INLINE_ bool intersects_aabb2(const AABB &p_aabb) const;
+	operator String() const;
+
+	inline Face3() {}
+	inline Face3(const Vector3 &p_v1, const Vector3 &p_v2, const Vector3 &p_v3) {
+		vertex[0] = p_v1;
+		vertex[1] = p_v2;
+		vertex[2] = p_v3;
+	}
+};
+
+inline real_t Face3::get_twice_area_squared() const {
+	Vector3 edge1 = vertex[1] - vertex[0];
+	Vector3 edge2 = vertex[2] - vertex[0];
+	return edge1.cross(edge2).length_squared();
+}
+
+bool Face3::intersects_aabb2(const AABB &p_aabb) const {
+	Vector3 perp = (vertex[0] - vertex[2]).cross(vertex[0] - vertex[1]);
+
+	Vector3 half_extents = p_aabb.size * 0.5f;
+	Vector3 ofs = p_aabb.position + half_extents;
+
+	Vector3 sup = Vector3(
+			(perp.x > 0) ? -half_extents.x : half_extents.x,
+			(perp.y > 0) ? -half_extents.y : half_extents.y,
+			(perp.z > 0) ? -half_extents.z : half_extents.z);
+
+	real_t d = perp.dot(vertex[0]);
+	real_t dist_a = perp.dot(ofs + sup) - d;
+	real_t dist_b = perp.dot(ofs - sup) - d;
+
+	if (dist_a * dist_b > 0) {
+		return false; //does not intersect the plane
+	}
+
+#define TEST_AXIS(m_ax)                                            \
+	{                                                              \
+		real_t aabb_min = p_aabb.position.m_ax;                    \
+		real_t aabb_max = p_aabb.position.m_ax + p_aabb.size.m_ax; \
+		real_t tri_min, tri_max;                                   \
+		for (int i = 0; i < 3; i++) {                              \
+			if (i == 0 || vertex[i].m_ax > tri_max)                \
+				tri_max = vertex[i].m_ax;                          \
+			if (i == 0 || vertex[i].m_ax < tri_min)                \
+				tri_min = vertex[i].m_ax;                          \
+		}                                                          \
+                                                                   \
+		if (tri_max < aabb_min || aabb_max < tri_min)              \
+			return false;                                          \
+	}
+
+	TEST_AXIS(x);
+	TEST_AXIS(y);
+	TEST_AXIS(z);
+
+#undef TEST_AXIS
+
+	Vector3 edge_norms[3] = {
+		vertex[0] - vertex[1],
+		vertex[1] - vertex[2],
+		vertex[2] - vertex[0],
+	};
+
+	for (int i = 0; i < 12; i++) {
+		Vector3 from, to;
+		switch (i) {
+			case 0: {
+				from = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z);
+				to = Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z);
+			} break;
+			case 1: {
+				from = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z);
+				to = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z);
+			} break;
+			case 2: {
+				from = Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z);
+				to = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z);
+
+			} break;
+			case 3: {
+				from = Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z);
+				to = Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z);
+
+			} break;
+			case 4: {
+				from = Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z);
+				to = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z);
+			} break;
+			case 5: {
+				from = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z);
+				to = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z);
+			} break;
+			case 6: {
+				from = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z);
+				to = Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z);
+
+			} break;
+			case 7: {
+				from = Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z);
+				to = Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z);
+
+			} break;
+			case 8: {
+				from = Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z);
+				to = Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z);
+
+			} break;
+			case 9: {
+				from = Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z);
+				to = Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z);
+
+			} break;
+			case 10: {
+				from = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z);
+				to = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z);
+
+			} break;
+			case 11: {
+				from = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z);
+				to = Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z);
+
+			} break;
+		}
+
+		Vector3 e1 = from - to;
+		for (int j = 0; j < 3; j++) {
+			Vector3 e2 = edge_norms[j];
+
+			Vector3 axis = vec3_cross(e1, e2);
+
+			if (axis.length_squared() < 0.0001f) {
+				continue; // coplanar
+			}
+			//axis.normalize();
+
+			Vector3 sup2 = Vector3(
+					(axis.x > 0) ? -half_extents.x : half_extents.x,
+					(axis.y > 0) ? -half_extents.y : half_extents.y,
+					(axis.z > 0) ? -half_extents.z : half_extents.z);
+
+			real_t maxB = axis.dot(ofs + sup2);
+			real_t minB = axis.dot(ofs - sup2);
+			if (minB > maxB) {
+				SWAP(maxB, minB);
+			}
+
+			real_t minT = 1e20, maxT = -1e20;
+			for (int k = 0; k < 3; k++) {
+				real_t vert_d = axis.dot(vertex[k]);
+
+				if (vert_d > maxT) {
+					maxT = vert_d;
+				}
+
+				if (vert_d < minT) {
+					minT = vert_d;
+				}
+			}
+
+			if (maxB < minT || maxT < minB) {
+				return false;
+			}
+		}
+	}
+	return true;
+}
+
+#endif // FACE3_H

core/math/math_defs.h

@@ -0,0 +1,123 @@
+#ifndef MATH_DEFS_H
+#define MATH_DEFS_H
+
+/*************************************************************************/
+/*  math_defs.h                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#define CMP_EPSILON 0.00001
+#define CMP_EPSILON2 (CMP_EPSILON * CMP_EPSILON)
+
+#define CMP_NORMALIZE_TOLERANCE 0.000001
+#define CMP_POINT_IN_PLANE_EPSILON 0.00001
+
+#define Math_SQRT12 0.7071067811865475244008443621048490
+#define Math_SQRT2 1.4142135623730950488016887242
+#define Math_LN2 0.6931471805599453094172321215
+#define Math_TAU 6.2831853071795864769252867666
+#define Math_PI 3.1415926535897932384626433833
+#define Math_E 2.7182818284590452353602874714
+#define Math_INF INFINITY
+#define Math_NAN NAN
+
+#ifdef DEBUG_ENABLED
+#define MATH_CHECKS
+#endif
+
+//this epsilon is for values related to a unit size (scalar or vector len)
+#ifdef PRECISE_MATH_CHECKS
+#define UNIT_EPSILON 0.00001
+#else
+//tolerate some more floating point error normally
+#define UNIT_EPSILON 0.001
+#endif
+
+#define USEC_TO_SEC(m_usec) ((m_usec) / 1000000.0)
+
+enum ClockDirection {
+	CLOCKWISE,
+	COUNTERCLOCKWISE
+};
+
+enum Orientation {
+
+	HORIZONTAL,
+	VERTICAL
+};
+
+enum HAlign {
+
+	HALIGN_LEFT,
+	HALIGN_CENTER,
+	HALIGN_RIGHT
+};
+
+enum VAlign {
+
+	VALIGN_TOP,
+	VALIGN_CENTER,
+	VALIGN_BOTTOM
+};
+
+enum Margin {
+
+	MARGIN_LEFT,
+	MARGIN_TOP,
+	MARGIN_RIGHT,
+	MARGIN_BOTTOM
+};
+
+enum Side {
+	SIDE_LEFT,
+	SIDE_TOP,
+	SIDE_RIGHT,
+	SIDE_BOTTOM
+};
+
+enum Corner {
+
+	CORNER_TOP_LEFT,
+	CORNER_TOP_RIGHT,
+	CORNER_BOTTOM_RIGHT,
+	CORNER_BOTTOM_LEFT
+};
+
+/**
+ * The "Real" type is an abstract type used for real numbers, such as 1.5,
+ * in contrast to integer numbers. Precision can be controlled with the
+ * presence or absence of the REAL_T_IS_DOUBLE define.
+ */
+#ifdef REAL_T_IS_DOUBLE
+typedef double real_t;
+#else
+typedef float real_t;
+#endif
+
+#endif // MATH_DEFS_H

core/math/plane.cpp

@@ -0,0 +1,159 @@
+/*************************************************************************/
+/*  plane.cpp                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "plane.h"
+
+#include "core/math/math_funcs.h"
+#include "core/variant/variant.h"
+
+void Plane::set_normal(const Vector3 &p_normal) {
+	normal = p_normal;
+}
+
+void Plane::normalize() {
+	real_t l = normal.length();
+	if (l == 0) {
+		*this = Plane(0, 0, 0, 0);
+		return;
+	}
+	normal /= l;
+	d /= l;
+}
+
+Plane Plane::normalized() const {
+	Plane p = *this;
+	p.normalize();
+	return p;
+}
+
+Vector3 Plane::get_any_point() const {
+	return get_normal() * d;
+}
+
+Vector3 Plane::get_any_perpendicular_normal() const {
+	static const Vector3 p1 = Vector3(1, 0, 0);
+	static const Vector3 p2 = Vector3(0, 1, 0);
+	Vector3 p;
+
+	if (ABS(normal.dot(p1)) > 0.99f) { // if too similar to p1
+		p = p2; // use p2
+	} else {
+		p = p1; // use p1
+	}
+
+	p -= normal * normal.dot(p);
+	p.normalize();
+
+	return p;
+}
+
+/* intersections */
+
+bool Plane::intersect_3(const Plane &p_plane1, const Plane &p_plane2, Vector3 *r_result) const {
+	const Plane &p_plane0 = *this;
+	Vector3 normal0 = p_plane0.normal;
+	Vector3 normal1 = p_plane1.normal;
+	Vector3 normal2 = p_plane2.normal;
+
+	real_t denom = vec3_cross(normal0, normal1).dot(normal2);
+
+	if (Math::is_zero_approx(denom)) {
+		return false;
+	}
+
+	if (r_result) {
+		*r_result = ((vec3_cross(normal1, normal2) * p_plane0.d) +
+							(vec3_cross(normal2, normal0) * p_plane1.d) +
+							(vec3_cross(normal0, normal1) * p_plane2.d)) /
+				denom;
+	}
+
+	return true;
+}
+
+bool Plane::intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const {
+	Vector3 segment = p_dir;
+	real_t den = normal.dot(segment);
+
+	//printf("den is %i\n",den);
+	if (Math::is_zero_approx(den)) {
+		return false;
+	}
+
+	real_t dist = (normal.dot(p_from) - d) / den;
+	//printf("dist is %i\n",dist);
+
+	if (dist > (real_t)CMP_EPSILON) { //this is a ray, before the emitting pos (p_from) doesn't exist
+
+		return false;
+	}
+
+	dist = -dist;
+	*p_intersection = p_from + segment * dist;
+
+	return true;
+}
+
+bool Plane::intersects_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 *p_intersection) const {
+	Vector3 segment = p_begin - p_end;
+	real_t den = normal.dot(segment);
+
+	//printf("den is %i\n",den);
+	if (Math::is_zero_approx(den)) {
+		return false;
+	}
+
+	real_t dist = (normal.dot(p_begin) - d) / den;
+	//printf("dist is %i\n",dist);
+
+	if (dist < (real_t)-CMP_EPSILON || dist > (1 + (real_t)CMP_EPSILON)) {
+		return false;
+	}
+
+	dist = -dist;
+	*p_intersection = p_begin + segment * dist;
+
+	return true;
+}
+
+/* misc */
+
+bool Plane::is_equal_approx(const Plane &p_plane) const {
+	return normal.is_equal_approx(p_plane.normal) && Math::is_equal_approx(d, p_plane.d);
+}
+
+bool Plane::is_equal_approx_any_side(const Plane &p_plane) const {
+	return (normal.is_equal_approx(p_plane.normal) && Math::is_equal_approx(d, p_plane.d)) || (normal.is_equal_approx(-p_plane.normal) && Math::is_equal_approx(d, -p_plane.d));
+}
+
+Plane::operator String() const {
+	return "[N: " + normal.operator String() + ", D: " + String::num_real(d) + "]";
+}

core/math/plane.h

@@ -0,0 +1,133 @@
+#ifndef PLANE_H
+#define PLANE_H
+
+/*************************************************************************/
+/*  plane.h                                                              */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/vector3.h"
+
+class Variant;
+
+struct _NO_DISCARD_CLASS_ Plane {
+	Vector3 normal;
+	real_t d;
+
+	void set_normal(const Vector3 &p_normal);
+	_FORCE_INLINE_ Vector3 get_normal() const { return normal; }; ///Point is coplanar, CMP_EPSILON for precision
+
+	void normalize();
+	Plane normalized() const;
+
+	/* Plane-Point operations */
+
+	_FORCE_INLINE_ Vector3 center() const { return normal * d; }
+	Vector3 get_any_point() const;
+	Vector3 get_any_perpendicular_normal() const;
+
+	_FORCE_INLINE_ bool is_point_over(const Vector3 &p_point) const; ///< Point is over plane
+	_FORCE_INLINE_ real_t distance_to(const Vector3 &p_point) const;
+	_FORCE_INLINE_ bool has_point(const Vector3 &p_point, real_t _epsilon = CMP_EPSILON) const;
+
+	/* intersections */
+
+	bool intersect_3(const Plane &p_plane1, const Plane &p_plane2, Vector3 *r_result = nullptr) const;
+	bool intersects_ray(const Vector3 &p_from, const Vector3 &p_dir, Vector3 *p_intersection) const;
+	bool intersects_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 *p_intersection) const;
+
+	_FORCE_INLINE_ Vector3 project(const Vector3 &p_point) const {
+		return p_point - normal * distance_to(p_point);
+	}
+
+	/* misc */
+
+	Plane operator-() const { return Plane(-normal, -d); }
+	bool is_equal_approx(const Plane &p_plane) const;
+	bool is_equal_approx_any_side(const Plane &p_plane) const;
+
+	_FORCE_INLINE_ bool operator==(const Plane &p_plane) const;
+	_FORCE_INLINE_ bool operator!=(const Plane &p_plane) const;
+	operator String() const;
+
+	_FORCE_INLINE_ Plane() :
+			d(0) {}
+	_FORCE_INLINE_ Plane(real_t p_a, real_t p_b, real_t p_c, real_t p_d) :
+			normal(p_a, p_b, p_c),
+			d(p_d) {}
+
+	_FORCE_INLINE_ Plane(const Vector3 &p_normal, real_t p_d);
+	_FORCE_INLINE_ Plane(const Vector3 &p_point, const Vector3 &p_normal);
+	_FORCE_INLINE_ Plane(const Vector3 &p_point1, const Vector3 &p_point2, const Vector3 &p_point3, ClockDirection p_dir = CLOCKWISE);
+};
+
+bool Plane::is_point_over(const Vector3 &p_point) const {
+	return (normal.dot(p_point) > d);
+}
+
+real_t Plane::distance_to(const Vector3 &p_point) const {
+	return (normal.dot(p_point) - d);
+}
+
+bool Plane::has_point(const Vector3 &p_point, real_t _epsilon) const {
+	real_t dist = normal.dot(p_point) - d;
+	dist = ABS(dist);
+	return (dist <= _epsilon);
+}
+
+Plane::Plane(const Vector3 &p_normal, real_t p_d) :
+		normal(p_normal),
+		d(p_d) {
+}
+
+Plane::Plane(const Vector3 &p_point, const Vector3 &p_normal) :
+		normal(p_normal),
+		d(p_normal.dot(p_point)) {
+}
+
+Plane::Plane(const Vector3 &p_point1, const Vector3 &p_point2, const Vector3 &p_point3, ClockDirection p_dir) {
+	if (p_dir == CLOCKWISE) {
+		normal = (p_point1 - p_point3).cross(p_point1 - p_point2);
+	} else {
+		normal = (p_point1 - p_point2).cross(p_point1 - p_point3);
+	}
+
+	normal.normalize();
+	d = normal.dot(p_point1);
+}
+
+bool Plane::operator==(const Plane &p_plane) const {
+	return normal == p_plane.normal && d == p_plane.d;
+}
+
+bool Plane::operator!=(const Plane &p_plane) const {
+	return normal != p_plane.normal || d != p_plane.d;
+}
+
+#endif // PLANE_H

core/math/projection.h

@@ -0,0 +1,193 @@
+/*************************************************************************/
+/*  projection.h                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef PROJECTION_H
+#define PROJECTION_H
+
+#include "core/containers/vector.h"
+#include "core/math/math_defs.h"
+#include "core/math/vector3.h"
+#include "core/math/vector4.h"
+
+class Array;
+struct AABB;
+struct Plane;
+struct Rect2;
+struct Transform;
+struct Vector2;
+
+struct _NO_DISCARD_CLASS_ Projection {
+	enum Planes {
+		PLANE_NEAR,
+		PLANE_FAR,
+		PLANE_LEFT,
+		PLANE_TOP,
+		PLANE_RIGHT,
+		PLANE_BOTTOM
+	};
+
+	Vector4 matrix[4];
+
+	_FORCE_INLINE_ const Vector4 &operator[](const int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 4);
+		return matrix[p_axis];
+	}
+
+	_FORCE_INLINE_ Vector4 &operator[](const int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 4);
+		return matrix[p_axis];
+	}
+
+	float determinant() const;
+	void set_identity();
+	void set_zero();
+	void set_light_bias();
+	void set_depth_correction(bool p_flip_y = true);
+
+	void set_light_atlas_rect(const Rect2 &p_rect);
+	void set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov = false);
+	void set_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov, int p_eye, real_t p_intraocular_dist, real_t p_convergence_dist);
+	void set_for_hmd(int p_eye, real_t p_aspect, real_t p_intraocular_dist, real_t p_display_width, real_t p_display_to_lens, real_t p_oversample, real_t p_z_near, real_t p_z_far);
+	void set_orthogonal(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_znear, real_t p_zfar);
+	void set_orthogonal(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov = false);
+	void set_frustum(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far);
+	void set_frustum(real_t p_size, real_t p_aspect, Vector2 p_offset, real_t p_near, real_t p_far, bool p_flip_fov = false);
+	void adjust_perspective_znear(real_t p_new_znear);
+
+	static Projection create_depth_correction(bool p_flip_y);
+	static Projection create_light_atlas_rect(const Rect2 &p_rect);
+	static Projection create_perspective(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov = false);
+	static Projection create_perspective_hmd(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov, int p_eye, real_t p_intraocular_dist, real_t p_convergence_dist);
+	static Projection create_for_hmd(int p_eye, real_t p_aspect, real_t p_intraocular_dist, real_t p_display_width, real_t p_display_to_lens, real_t p_oversample, real_t p_z_near, real_t p_z_far);
+	static Projection create_orthogonal(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_znear, real_t p_zfar);
+	static Projection create_orthogonal_aspect(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov = false);
+	static Projection create_frustum(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far);
+	static Projection create_frustum_aspect(real_t p_size, real_t p_aspect, Vector2 p_offset, real_t p_near, real_t p_far, bool p_flip_fov = false);
+	static Projection create_fit_aabb(const AABB &p_aabb);
+
+	Projection perspective_znear_adjusted(real_t p_new_znear) const;
+	Plane get_projection_plane(Planes p_plane) const;
+	Projection flipped_y() const;
+	Projection jitter_offseted(const Vector2 &p_offset) const;
+
+	static real_t get_fovy(real_t p_fovx, real_t p_aspect) {
+		return Math::rad2deg(Math::atan(p_aspect * Math::tan(Math::deg2rad(p_fovx) * 0.5)) * 2.0);
+	}
+
+	real_t calculate_fovy(real_t p_fovx, real_t p_aspect) {
+		return Math::rad2deg(Math::atan(p_aspect * Math::tan(Math::deg2rad(p_fovx) * 0.5)) * 2.0);
+	}
+
+	real_t get_z_far() const;
+	real_t get_z_near() const;
+	real_t get_aspect() const;
+	real_t get_fov() const;
+	bool is_orthogonal() const;
+
+	Vector<Plane> get_projection_planes(const Transform &p_transform) const;
+	Array get_projection_planes_array(const Transform &p_transform) const;
+
+	bool get_endpoints(const Transform &p_transform, Vector3 *p_8points) const;
+	Vector2 get_viewport_half_extents() const;
+	Vector2 get_far_plane_half_extents() const;
+
+	void invert();
+	Projection inverse() const;
+
+	Projection operator*(const Projection &p_matrix) const;
+
+	Vector4 xform(const Vector4 &p_vec4) const;
+	Vector4 xform_inv(const Vector4 &p_vec4) const;
+
+	_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
+	Plane xform(const Plane &p_plane) const;
+
+	operator String() const;
+
+	void scale_translate_to_fit(const AABB &p_aabb);
+	void add_jitter_offset(const Vector2 &p_offset);
+	void make_scale(const Vector3 &p_scale);
+	int get_pixels_per_meter(int p_for_pixel_width) const;
+	operator Transform() const;
+
+	void flip_y();
+
+	bool operator==(const Projection &p_cam) const {
+		for (uint32_t i = 0; i < 4; i++) {
+			for (uint32_t j = 0; j < 4; j++) {
+				if (matrix[i][j] != p_cam.matrix[i][j]) {
+					return false;
+				}
+			}
+		}
+		return true;
+	}
+
+	bool operator!=(const Projection &p_cam) const {
+		return !(*this == p_cam);
+	}
+
+	float get_lod_multiplier() const;
+
+	_FORCE_INLINE_ void set_perspective1(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov = false) {
+		set_perspective(p_fovy_degrees, p_aspect, p_z_near, p_z_far, p_flip_fov);
+	}
+	_FORCE_INLINE_ void set_perspective2(real_t p_fovy_degrees, real_t p_aspect, real_t p_z_near, real_t p_z_far, bool p_flip_fov, int p_eye, real_t p_intraocular_dist, real_t p_convergence_dist) {
+		set_perspective(p_fovy_degrees, p_aspect, p_z_near, p_z_far, p_flip_fov, p_eye, p_intraocular_dist, p_convergence_dist);
+	}
+	_FORCE_INLINE_ void set_orthogonal1(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_znear, real_t p_zfar) {
+		set_orthogonal(p_left, p_right, p_bottom, p_top, p_znear, p_zfar);
+	}
+	_FORCE_INLINE_ void set_orthogonal2(real_t p_size, real_t p_aspect, real_t p_znear, real_t p_zfar, bool p_flip_fov = false) {
+		set_orthogonal(p_size, p_aspect, p_znear, p_zfar, p_flip_fov);
+	}
+	_FORCE_INLINE_ void set_frustum1(real_t p_left, real_t p_right, real_t p_bottom, real_t p_top, real_t p_near, real_t p_far) {
+		set_frustum(p_left, p_right, p_bottom, p_top, p_near, p_far);
+	}
+	//Vector2 is incomplete here
+	void set_frustum2(real_t p_size, real_t p_aspect, Vector2 p_offset, real_t p_near, real_t p_far, bool p_flip_fov = false);
+
+	Projection();
+	Projection(const Vector4 &p_x, const Vector4 &p_y, const Vector4 &p_z, const Vector4 &p_w);
+	Projection(const Transform &p_transform);
+	~Projection();
+};
+
+Vector3 Projection::xform(const Vector3 &p_vec3) const {
+	Vector3 ret;
+	ret.x = matrix[0][0] * p_vec3.x + matrix[1][0] * p_vec3.y + matrix[2][0] * p_vec3.z + matrix[3][0];
+	ret.y = matrix[0][1] * p_vec3.x + matrix[1][1] * p_vec3.y + matrix[2][1] * p_vec3.z + matrix[3][1];
+	ret.z = matrix[0][2] * p_vec3.x + matrix[1][2] * p_vec3.y + matrix[2][2] * p_vec3.z + matrix[3][2];
+	real_t w = matrix[0][3] * p_vec3.x + matrix[1][3] * p_vec3.y + matrix[2][3] * p_vec3.z + matrix[3][3];
+	return ret / w;
+}
+
+#endif // PROJECTION_H

core/math/quaternion.cpp

@@ -0,0 +1,336 @@
+/*************************************************************************/
+/*  quaternion.cpp                                                       */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "quaternion.h"
+
+#include "core/math/basis.h"
+#include "core/string/print_string.h"
+
+real_t Quaternion::angle_to(const Quaternion &p_to) const {
+	real_t d = dot(p_to);
+
+	// acos does clamping.
+	return Math::acos(d * d * 2 - 1);
+}
+
+// set_euler_xyz expects a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses XYZ convention (Z is the first rotation).
+void Quaternion::set_euler_xyz(const Vector3 &p_euler) {
+	real_t half_a1 = p_euler.x * 0.5f;
+	real_t half_a2 = p_euler.y * 0.5f;
+	real_t half_a3 = p_euler.z * 0.5f;
+
+	// R = X(a1).Y(a2).Z(a3) convention for Euler angles.
+	// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-2)
+	// a3 is the angle of the first rotation, following the notation in this reference.
+
+	real_t cos_a1 = Math::cos(half_a1);
+	real_t sin_a1 = Math::sin(half_a1);
+	real_t cos_a2 = Math::cos(half_a2);
+	real_t sin_a2 = Math::sin(half_a2);
+	real_t cos_a3 = Math::cos(half_a3);
+	real_t sin_a3 = Math::sin(half_a3);
+
+	set(sin_a1 * cos_a2 * cos_a3 + sin_a2 * sin_a3 * cos_a1,
+			-sin_a1 * sin_a3 * cos_a2 + sin_a2 * cos_a1 * cos_a3,
+			sin_a1 * sin_a2 * cos_a3 + sin_a3 * cos_a1 * cos_a2,
+			-sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
+}
+
+// get_euler_xyz returns a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses XYZ convention (Z is the first rotation).
+Vector3 Quaternion::get_euler_xyz() const {
+	Basis m(*this);
+	return m.get_euler_xyz();
+}
+
+// set_euler_yxz expects a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses YXZ convention (Z is the first rotation).
+void Quaternion::set_euler_yxz(const Vector3 &p_euler) {
+	real_t half_a1 = p_euler.y * 0.5f;
+	real_t half_a2 = p_euler.x * 0.5f;
+	real_t half_a3 = p_euler.z * 0.5f;
+
+	// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
+	// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
+	// a3 is the angle of the first rotation, following the notation in this reference.
+
+	real_t cos_a1 = Math::cos(half_a1);
+	real_t sin_a1 = Math::sin(half_a1);
+	real_t cos_a2 = Math::cos(half_a2);
+	real_t sin_a2 = Math::sin(half_a2);
+	real_t cos_a3 = Math::cos(half_a3);
+	real_t sin_a3 = Math::sin(half_a3);
+
+	set(sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
+			sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
+			-sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3,
+			sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
+}
+
+// get_euler_yxz returns a vector containing the Euler angles in the format
+// (ax,ay,az), where ax is the angle of rotation around x axis,
+// and similar for other axes.
+// This implementation uses YXZ convention (Z is the first rotation).
+Vector3 Quaternion::get_euler_yxz() const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
+#endif
+	Basis m(*this);
+	return m.get_euler_yxz();
+}
+
+void Quaternion::operator*=(const Quaternion &p_q) {
+	set(w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y,
+			w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z,
+			w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x,
+			w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z);
+}
+
+Quaternion Quaternion::operator*(const Quaternion &p_q) const {
+	Quaternion r = *this;
+	r *= p_q;
+	return r;
+}
+
+bool Quaternion::is_equal_approx(const Quaternion &p_quat) const {
+	return Math::is_equal_approx(x, p_quat.x) && Math::is_equal_approx(y, p_quat.y) && Math::is_equal_approx(z, p_quat.z) && Math::is_equal_approx(w, p_quat.w);
+}
+
+real_t Quaternion::length() const {
+	return Math::sqrt(length_squared());
+}
+
+void Quaternion::normalize() {
+	*this /= length();
+}
+
+Quaternion Quaternion::normalized() const {
+	return *this / length();
+}
+
+bool Quaternion::is_normalized() const {
+	return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON); //use less epsilon
+}
+
+Quaternion Quaternion::inverse() const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The quaternion must be normalized.");
+#endif
+	return Quaternion(-x, -y, -z, w);
+}
+
+Quaternion Quaternion::log() const {
+	Quaternion src = *this;
+	Vector3 src_v = src.get_axis() * src.get_angle();
+	return Quaternion(src_v.x, src_v.y, src_v.z, 0);
+}
+
+Quaternion Quaternion::exp() const {
+	Quaternion src = *this;
+	Vector3 src_v = Vector3(src.x, src.y, src.z);
+	float theta = src_v.length();
+	if (theta < CMP_EPSILON) {
+		return Quaternion(0, 0, 0, 1);
+	}
+	return Quaternion(src_v.normalized(), theta);
+}
+
+Quaternion Quaternion::slerp(const Quaternion &p_to, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
+#endif
+	Quaternion to1;
+	real_t omega, cosom, sinom, scale0, scale1;
+
+	// calc cosine
+	cosom = dot(p_to);
+
+	// adjust signs (if necessary)
+	if (cosom < 0) {
+		cosom = -cosom;
+		to1.x = -p_to.x;
+		to1.y = -p_to.y;
+		to1.z = -p_to.z;
+		to1.w = -p_to.w;
+	} else {
+		to1.x = p_to.x;
+		to1.y = p_to.y;
+		to1.z = p_to.z;
+		to1.w = p_to.w;
+	}
+
+	// calculate coefficients
+
+	if ((1 - cosom) > (real_t)CMP_EPSILON) {
+		// standard case (slerp)
+		omega = Math::acos(cosom);
+		sinom = Math::sin(omega);
+		scale0 = Math::sin((1 - p_weight) * omega) / sinom;
+		scale1 = Math::sin(p_weight * omega) / sinom;
+	} else {
+		// "from" and "to" quaternions are very close
+		//  ... so we can do a linear interpolation
+		scale0 = 1 - p_weight;
+		scale1 = p_weight;
+	}
+	// calculate final values
+	return Quaternion(
+			scale0 * x + scale1 * to1.x,
+			scale0 * y + scale1 * to1.y,
+			scale0 * z + scale1 * to1.z,
+			scale0 * w + scale1 * to1.w);
+}
+
+Quaternion Quaternion::slerpni(const Quaternion &p_to, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
+#endif
+	const Quaternion &from = *this;
+
+	real_t dot = from.dot(p_to);
+
+	if (Math::absf(dot) > 0.9999f) {
+		return from;
+	}
+
+	real_t theta = Math::acos(dot),
+		   sinT = 1 / Math::sin(theta),
+		   newFactor = Math::sin(p_weight * theta) * sinT,
+		   invFactor = Math::sin((1 - p_weight) * theta) * sinT;
+
+	return Quaternion(invFactor * from.x + newFactor * p_to.x,
+			invFactor * from.y + newFactor * p_to.y,
+			invFactor * from.z + newFactor * p_to.z,
+			invFactor * from.w + newFactor * p_to.w);
+}
+
+Quaternion Quaternion::cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
+#endif
+	//the only way to do slerp :|
+	real_t t2 = (1 - p_weight) * p_weight * 2;
+	Quaternion sp = this->slerp(p_b, p_weight);
+	Quaternion sq = p_pre_a.slerpni(p_post_b, p_weight);
+	return sp.slerpni(sq, t2);
+}
+
+Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
+	ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
+#endif
+	Quaternion from_q = *this;
+	Quaternion pre_q = p_pre_a;
+	Quaternion to_q = p_b;
+	Quaternion post_q = p_post_b;
+
+	// Align flip phases.
+	from_q = Basis(from_q).get_rotation_quaternion();
+	pre_q = Basis(pre_q).get_rotation_quaternion();
+	to_q = Basis(to_q).get_rotation_quaternion();
+	post_q = Basis(post_q).get_rotation_quaternion();
+
+	// Flip quaternions to shortest path if necessary.
+	bool flip1 = signbit(from_q.dot(pre_q));
+	pre_q = flip1 ? -pre_q : pre_q;
+	bool flip2 = signbit(from_q.dot(to_q));
+	to_q = flip2 ? -to_q : to_q;
+	bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
+	post_q = flip3 ? -post_q : post_q;
+
+	// Calc by Expmap in from_q space.
+	Quaternion ln_from = Quaternion(0, 0, 0, 0);
+	Quaternion ln_to = (from_q.inverse() * to_q).log();
+	Quaternion ln_pre = (from_q.inverse() * pre_q).log();
+	Quaternion ln_post = (from_q.inverse() * post_q).log();
+	Quaternion ln = Quaternion(0, 0, 0, 0);
+	ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
+	ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
+	ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
+	Quaternion q1 = from_q * ln.exp();
+
+	// Calc by Expmap in to_q space.
+	ln_from = (to_q.inverse() * from_q).log();
+	ln_to = Quaternion(0, 0, 0, 0);
+	ln_pre = (to_q.inverse() * pre_q).log();
+	ln_post = (to_q.inverse() * post_q).log();
+	ln = Quaternion(0, 0, 0, 0);
+	ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
+	ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
+	ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
+	Quaternion q2 = to_q * ln.exp();
+
+	// To cancel error made by Expmap ambiguity, do blends.
+	return q1.slerp(q2, p_weight);
+}
+
+Vector3 Quaternion::get_axis() const {
+	if (Math::abs(w) > 1 - CMP_EPSILON) {
+		return Vector3(x, y, z);
+	}
+	real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
+	return Vector3(x * r, y * r, z * r);
+}
+
+float Quaternion::get_angle() const {
+	return 2 * Math::acos(w);
+}
+
+Quaternion::operator String() const {
+	return "(" + String::num_real(x) + ", " + String::num_real(y) + ", " + String::num_real(z) + ", " + String::num_real(w) + ")";
+}
+
+void Quaternion::set_axis_angle(const Vector3 &axis, const real_t &angle) {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_MSG(!axis.is_normalized(), "The axis Vector3 must be normalized.");
+#endif
+	real_t d = axis.length();
+	if (d == 0) {
+		set(0, 0, 0, 0);
+	} else {
+		real_t sin_angle = Math::sin(angle * 0.5f);
+		real_t cos_angle = Math::cos(angle * 0.5f);
+		real_t s = sin_angle / d;
+		set(axis.x * s, axis.y * s, axis.z * s,
+				cos_angle);
+	}
+}

core/math/quaternion.h

@@ -0,0 +1,256 @@
+#ifndef QUATERNION_H
+#define QUATERNION_H
+
+/*************************************************************************/
+/*  quaternion.h                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/math_defs.h"
+#include "core/math/math_funcs.h"
+#include "core/math/vector3.h"
+#include "core/string/ustring.h"
+
+struct _NO_DISCARD_CLASS_ Quaternion {
+	union {
+		struct {
+			real_t x;
+			real_t y;
+			real_t z;
+			real_t w;
+		};
+		real_t components[4];
+	};
+
+	_FORCE_INLINE_ real_t &operator[](int idx) {
+		return components[idx];
+	}
+	_FORCE_INLINE_ const real_t &operator[](int idx) const {
+		return components[idx];
+	}
+
+	_FORCE_INLINE_ real_t length_squared() const;
+	bool is_equal_approx(const Quaternion &p_quat) const;
+	real_t length() const;
+	void normalize();
+	Quaternion normalized() const;
+	bool is_normalized() const;
+	Quaternion inverse() const;
+	Quaternion log() const;
+	Quaternion exp() const;
+	_FORCE_INLINE_ real_t dot(const Quaternion &p_q) const;
+	real_t angle_to(const Quaternion &p_to) const;
+
+	void set_euler_xyz(const Vector3 &p_euler);
+	Vector3 get_euler_xyz() const;
+	void set_euler_yxz(const Vector3 &p_euler);
+	Vector3 get_euler_yxz() const;
+
+	void set_euler(const Vector3 &p_euler) { set_euler_yxz(p_euler); };
+	Vector3 get_euler() const { return get_euler_yxz(); };
+
+	Quaternion slerp(const Quaternion &p_to, const real_t &p_weight) const;
+	Quaternion slerpni(const Quaternion &p_to, const real_t &p_weight) const;
+	Quaternion cubic_slerp(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const;
+	Quaternion spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight) const;
+
+	Vector3 get_axis() const;
+	float get_angle() const;
+
+	void set_axis_angle(const Vector3 &axis, const real_t &angle);
+	_FORCE_INLINE_ void get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
+		r_angle = 2 * Math::acos(w);
+		real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
+		r_axis.x = x * r;
+		r_axis.y = y * r;
+		r_axis.z = z * r;
+	}
+
+	void operator*=(const Quaternion &p_q);
+	Quaternion operator*(const Quaternion &p_q) const;
+
+	Quaternion operator*(const Vector3 &v) const {
+		return Quaternion(w * v.x + y * v.z - z * v.y,
+				w * v.y + z * v.x - x * v.z,
+				w * v.z + x * v.y - y * v.x,
+				-x * v.x - y * v.y - z * v.z);
+	}
+
+	_FORCE_INLINE_ Vector3 xform(const Vector3 &v) const {
+#ifdef MATH_CHECKS
+		ERR_FAIL_COND_V_MSG(!is_normalized(), v, "The quaternion must be normalized.");
+#endif
+		Vector3 u(x, y, z);
+		Vector3 uv = u.cross(v);
+		return v + ((uv * w) + u.cross(uv)) * ((real_t)2);
+	}
+
+	_FORCE_INLINE_ void operator+=(const Quaternion &p_q);
+	_FORCE_INLINE_ void operator-=(const Quaternion &p_q);
+	_FORCE_INLINE_ void operator*=(const real_t &s);
+	_FORCE_INLINE_ void operator/=(const real_t &s);
+	_FORCE_INLINE_ Quaternion operator+(const Quaternion &q2) const;
+	_FORCE_INLINE_ Quaternion operator-(const Quaternion &q2) const;
+	_FORCE_INLINE_ Quaternion operator-() const;
+	_FORCE_INLINE_ Quaternion operator*(const real_t &s) const;
+	_FORCE_INLINE_ Quaternion operator/(const real_t &s) const;
+
+	_FORCE_INLINE_ bool operator==(const Quaternion &p_quat) const;
+	_FORCE_INLINE_ bool operator!=(const Quaternion &p_quat) const;
+
+	operator String() const;
+
+	inline void set(real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+		w = p_w;
+	}
+	inline Quaternion(real_t p_x, real_t p_y, real_t p_z, real_t p_w) :
+			x(p_x),
+			y(p_y),
+			z(p_z),
+			w(p_w) {
+	}
+	Quaternion(const Vector3 &axis, const real_t &angle) {
+		set_axis_angle(axis, angle);
+	}
+
+	Quaternion(const Vector3 &euler) {
+		set_euler(euler);
+	}
+	Quaternion(const Quaternion &p_q) :
+			x(p_q.x),
+			y(p_q.y),
+			z(p_q.z),
+			w(p_q.w) {
+	}
+
+	Quaternion &operator=(const Quaternion &p_q) {
+		x = p_q.x;
+		y = p_q.y;
+		z = p_q.z;
+		w = p_q.w;
+		return *this;
+	}
+
+	Quaternion(const Vector3 &v0, const Vector3 &v1) // shortest arc
+	{
+		Vector3 c = v0.cross(v1);
+		real_t d = v0.dot(v1);
+
+		if (d < -1 + (real_t)CMP_EPSILON) {
+			x = 0;
+			y = 1;
+			z = 0;
+			w = 0;
+		} else {
+			real_t s = Math::sqrt((1 + d) * 2);
+			real_t rs = 1 / s;
+
+			x = c.x * rs;
+			y = c.y * rs;
+			z = c.z * rs;
+			w = s * 0.5f;
+		}
+	}
+
+	inline Quaternion() :
+			x(0),
+			y(0),
+			z(0),
+			w(1) {
+	}
+};
+
+real_t Quaternion::dot(const Quaternion &p_q) const {
+	return x * p_q.x + y * p_q.y + z * p_q.z + w * p_q.w;
+}
+
+real_t Quaternion::length_squared() const {
+	return dot(*this);
+}
+
+void Quaternion::operator+=(const Quaternion &p_q) {
+	x += p_q.x;
+	y += p_q.y;
+	z += p_q.z;
+	w += p_q.w;
+}
+
+void Quaternion::operator-=(const Quaternion &p_q) {
+	x -= p_q.x;
+	y -= p_q.y;
+	z -= p_q.z;
+	w -= p_q.w;
+}
+
+void Quaternion::operator*=(const real_t &s) {
+	x *= s;
+	y *= s;
+	z *= s;
+	w *= s;
+}
+
+void Quaternion::operator/=(const real_t &s) {
+	*this *= 1 / s;
+}
+
+Quaternion Quaternion::operator+(const Quaternion &q2) const {
+	const Quaternion &q1 = *this;
+	return Quaternion(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
+}
+
+Quaternion Quaternion::operator-(const Quaternion &q2) const {
+	const Quaternion &q1 = *this;
+	return Quaternion(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
+}
+
+Quaternion Quaternion::operator-() const {
+	const Quaternion &q2 = *this;
+	return Quaternion(-q2.x, -q2.y, -q2.z, -q2.w);
+}
+
+Quaternion Quaternion::operator*(const real_t &s) const {
+	return Quaternion(x * s, y * s, z * s, w * s);
+}
+
+Quaternion Quaternion::operator/(const real_t &s) const {
+	return *this * (1 / s);
+}
+
+bool Quaternion::operator==(const Quaternion &p_quat) const {
+	return x == p_quat.x && y == p_quat.y && z == p_quat.z && w == p_quat.w;
+}
+
+bool Quaternion::operator!=(const Quaternion &p_quat) const {
+	return x != p_quat.x || y != p_quat.y || z != p_quat.z || w != p_quat.w;
+}
+
+#endif

core/math/random_number_generator.cpp

@@ -0,0 +1,55 @@
+/*************************************************************************/
+/*  random_number_generator.cpp                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "random_number_generator.h"
+
+RandomNumberGenerator::RandomNumberGenerator() {}
+
+void RandomNumberGenerator::_bind_methods() {
+	ClassDB::bind_method(D_METHOD("set_seed", "seed"), &RandomNumberGenerator::set_seed);
+	ClassDB::bind_method(D_METHOD("get_seed"), &RandomNumberGenerator::get_seed);
+
+	ClassDB::bind_method(D_METHOD("set_state", "state"), &RandomNumberGenerator::set_state);
+	ClassDB::bind_method(D_METHOD("get_state"), &RandomNumberGenerator::get_state);
+
+	ClassDB::bind_method(D_METHOD("randi"), &RandomNumberGenerator::randi);
+	ClassDB::bind_method(D_METHOD("randf"), &RandomNumberGenerator::randf);
+	ClassDB::bind_method(D_METHOD("randfn", "mean", "deviation"), &RandomNumberGenerator::randfn, DEFVAL(0.0), DEFVAL(1.0));
+	ClassDB::bind_method(D_METHOD("randf_range", "from", "to"), &RandomNumberGenerator::randf_range);
+	ClassDB::bind_method(D_METHOD("randi_range", "from", "to"), &RandomNumberGenerator::randi_range);
+	ClassDB::bind_method(D_METHOD("randomize"), &RandomNumberGenerator::randomize);
+
+	ADD_PROPERTY(PropertyInfo(Variant::INT, "seed"), "set_seed", "get_seed");
+	ADD_PROPERTY(PropertyInfo(Variant::INT, "state"), "set_state", "get_state");
+	// Default values are non-deterministic, override for doc generation purposes.
+	ADD_PROPERTY_DEFAULT("seed", 0);
+	ADD_PROPERTY_DEFAULT("state", 0);
+}

core/math/random_number_generator.h

@@ -0,0 +1,67 @@
+#ifndef RANDOM_NUMBER_GENERATOR_H
+#define RANDOM_NUMBER_GENERATOR_H
+
+/*************************************************************************/
+/*  random_number_generator.h                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/random_pcg.h"
+#include "core/object/reference.h"
+
+class RandomNumberGenerator : public Reference {
+	GDCLASS(RandomNumberGenerator, Reference);
+
+protected:
+	RandomPCG randbase;
+
+	static void _bind_methods();
+
+public:
+	_FORCE_INLINE_ void set_seed(uint64_t seed) { randbase.seed(seed); }
+	_FORCE_INLINE_ uint64_t get_seed() { return randbase.get_seed(); }
+
+	_FORCE_INLINE_ void set_state(uint64_t p_state) { randbase.set_state(p_state); }
+	_FORCE_INLINE_ uint64_t get_state() const { return randbase.get_state(); }
+
+	_FORCE_INLINE_ void randomize() { randbase.randomize(); }
+
+	_FORCE_INLINE_ uint32_t randi() { return randbase.rand(); }
+	_FORCE_INLINE_ real_t randf() { return randbase.randf(); }
+	_FORCE_INLINE_ real_t randf_range(real_t from, real_t to) { return randbase.random(from, to); }
+	_FORCE_INLINE_ real_t randfn(real_t mean = 0.0, real_t deviation = 1.0) { return randbase.randfn(mean, deviation); }
+
+	_FORCE_INLINE_ int randi_range(int from, int to) {
+		return randbase.random(from, to);
+	}
+
+	RandomNumberGenerator();
+};
+
+#endif // RANDOM_NUMBER_GENERATOR_H

core/math/random_pcg.cpp

@@ -0,0 +1,59 @@
+/*************************************************************************/
+/*  random_pcg.cpp                                                       */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "random_pcg.h"
+
+#include "core/os/os.h"
+
+RandomPCG::RandomPCG(uint64_t p_seed, uint64_t p_inc) :
+		pcg(),
+		current_inc(p_inc) {
+	seed(p_seed);
+}
+
+void RandomPCG::randomize() {
+	seed((OS::get_singleton()->get_unix_time() + OS::get_singleton()->get_ticks_usec()) * pcg.state + PCG_DEFAULT_INC_64);
+}
+
+double RandomPCG::random(double p_from, double p_to) {
+	return randd() * (p_to - p_from) + p_from;
+}
+
+float RandomPCG::random(float p_from, float p_to) {
+	return randf() * (p_to - p_from) + p_from;
+}
+
+int RandomPCG::random(int p_from, int p_to) {
+	if (p_from == p_to) {
+		return p_from;
+	}
+	return rand(abs(p_from - p_to) + 1) + MIN(p_from, p_to);
+}

core/math/random_pcg.h

@@ -0,0 +1,142 @@
+#ifndef RANDOM_PCG_H
+#define RANDOM_PCG_H
+
+/*************************************************************************/
+/*  random_pcg.h                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include <math.h>
+
+#include "core/math/math_defs.h"
+
+#include "thirdparty/misc/pcg.h"
+
+#if defined(__GNUC__) || (_llvm_has_builtin(__builtin_clz))
+#define CLZ32(x) __builtin_clz(x)
+#elif defined(_MSC_VER)
+#include "intrin.h"
+static int __bsr_clz32(uint32_t x) {
+	unsigned long index;
+	_BitScanReverse(&index, x);
+	return 31 - index;
+}
+#define CLZ32(x) __bsr_clz32(x)
+#else
+#endif
+
+#if defined(__GNUC__) || (_llvm_has_builtin(__builtin_ldexp) && _llvm_has_builtin(__builtin_ldexpf))
+#define LDEXP(s, e) __builtin_ldexp(s, e)
+#define LDEXPF(s, e) __builtin_ldexpf(s, e)
+#else
+#include "math.h"
+#define LDEXP(s, e) ldexp(s, e)
+#define LDEXPF(s, e) ldexp(s, e)
+#endif
+
+class RandomPCG {
+	pcg32_random_t pcg;
+	uint64_t current_seed; // The seed the current generator state started from.
+	uint64_t current_inc;
+
+public:
+	static const uint64_t DEFAULT_SEED = 12047754176567800795U;
+	static const uint64_t DEFAULT_INC = PCG_DEFAULT_INC_64;
+
+	RandomPCG(uint64_t p_seed = DEFAULT_SEED, uint64_t p_inc = DEFAULT_INC);
+
+	_FORCE_INLINE_ void seed(uint64_t p_seed) {
+		current_seed = p_seed;
+		pcg32_srandom_r(&pcg, current_seed, current_inc);
+	}
+	_FORCE_INLINE_ uint64_t get_seed() { return current_seed; }
+
+	_FORCE_INLINE_ void set_state(uint64_t p_state) { pcg.state = p_state; }
+	_FORCE_INLINE_ uint64_t get_state() const { return pcg.state; }
+
+	void randomize();
+	_FORCE_INLINE_ uint32_t rand() {
+		return pcg32_random_r(&pcg);
+	}
+	_FORCE_INLINE_ uint32_t rand(uint32_t bounds) {
+		return pcg32_boundedrand_r(&pcg, bounds);
+	}
+
+	// Obtaining floating point numbers in [0, 1] range with "good enough" uniformity.
+	// These functions sample the output of rand() as the fraction part of an infinite binary number,
+	// with some tricks applied to reduce ops and branching:
+	// 1. Instead of shifting to the first 1 and connecting random bits, we simply set the MSB and LSB to 1.
+	//    Provided that the RNG is actually uniform bit by bit, this should have the exact same effect.
+	// 2. In order to compensate for exponent info loss, we count zeros from another random number,
+	//    and just add that to the initial offset.
+	//    This has the same probability as counting and shifting an actual bit stream: 2^-n for n zeroes.
+	// For all numbers above 2^-96 (2^-64 for floats), the functions should be uniform.
+	// However, all numbers below that threshold are floored to 0.
+	// The thresholds are chosen to minimize rand() calls while keeping the numbers within a totally subjective quality standard.
+	// If clz or ldexp isn't available, fall back to bit truncation for performance, sacrificing uniformity.
+	_FORCE_INLINE_ double randd() {
+#if defined(CLZ32)
+		uint32_t proto_exp_offset = rand();
+		if (unlikely(proto_exp_offset == 0)) {
+			return 0;
+		}
+		uint64_t significand = (((uint64_t)rand()) << 32) | rand() | 0x8000000000000001U;
+		return LDEXP((double)significand, -64 - CLZ32(proto_exp_offset));
+#else
+#pragma message("RandomPCG::randd - intrinsic clz is not available, falling back to bit truncation")
+		return (double)(((((uint64_t)rand()) << 32) | rand()) & 0x1FFFFFFFFFFFFFU) / (double)0x1FFFFFFFFFFFFFU;
+#endif
+	}
+	_FORCE_INLINE_ float randf() {
+#if defined(CLZ32)
+		uint32_t proto_exp_offset = rand();
+		if (unlikely(proto_exp_offset == 0)) {
+			return 0;
+		}
+		return LDEXPF((float)(rand() | 0x80000001), -32 - CLZ32(proto_exp_offset));
+#else
+#pragma message("RandomPCG::randf - intrinsic clz is not available, falling back to bit truncation")
+		return (float)(rand() & 0xFFFFFF) / (float)0xFFFFFF;
+#endif
+	}
+
+	_FORCE_INLINE_ double randfn(double p_mean, double p_deviation) {
+		return p_mean + p_deviation * (cos(Math_TAU * randd()) * sqrt(-2.0 * log(randd()))); // Box-Muller transform
+	}
+	_FORCE_INLINE_ float randfn(float p_mean, float p_deviation) {
+		return p_mean + p_deviation * (cos(Math_TAU * randf()) * sqrt(-2.0 * log(randf()))); // Box-Muller transform
+	}
+
+	double random(double p_from, double p_to);
+	float random(float p_from, float p_to);
+	real_t randomr(real_t p_from, real_t p_to) { return random(p_from, p_to); }
+	int random(int p_from, int p_to);
+};
+
+#endif // RANDOM_PCG_H

core/math/rect2.cpp

@@ -0,0 +1,272 @@
+/*************************************************************************/
+/*  rect2.cpp                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/transform_2d.h" // Includes rect2.h but Rect2 needs Transform2D
+
+#include "core/math/rect2i.h"
+
+bool Rect2::is_equal_approx(const Rect2 &p_rect) const {
+	return position.is_equal_approx(p_rect.position) && size.is_equal_approx(p_rect.size);
+}
+
+bool Rect2::intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos, Point2 *r_normal) const {
+	real_t min = 0, max = 1;
+	int axis = 0;
+	real_t sign = 0;
+
+	for (int i = 0; i < 2; i++) {
+		real_t seg_from = p_from[i];
+		real_t seg_to = p_to[i];
+		real_t box_begin = position[i];
+		real_t box_end = box_begin + size[i];
+		real_t cmin, cmax;
+		real_t csign;
+
+		if (seg_from < seg_to) {
+			if (seg_from > box_end || seg_to < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from < box_begin) ? ((box_begin - seg_from) / length) : 0;
+			cmax = (seg_to > box_end) ? ((box_end - seg_from) / length) : 1;
+			csign = -1.0;
+
+		} else {
+			if (seg_to > box_end || seg_from < box_begin) {
+				return false;
+			}
+			real_t length = seg_to - seg_from;
+			cmin = (seg_from > box_end) ? (box_end - seg_from) / length : 0;
+			cmax = (seg_to < box_begin) ? (box_begin - seg_from) / length : 1;
+			csign = 1.0;
+		}
+
+		if (cmin > min) {
+			min = cmin;
+			axis = i;
+			sign = csign;
+		}
+		if (cmax < max) {
+			max = cmax;
+		}
+		if (max < min) {
+			return false;
+		}
+	}
+
+	Vector2 rel = p_to - p_from;
+
+	if (r_normal) {
+		Vector2 normal;
+		normal[axis] = sign;
+		*r_normal = normal;
+	}
+
+	if (r_pos) {
+		*r_pos = p_from + rel * min;
+	}
+
+	return true;
+}
+
+bool Rect2::intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const {
+	//SAT intersection between local and transformed rect2
+
+	Vector2 xf_points[4] = {
+		p_xform.xform(p_rect.position),
+		p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y)),
+		p_xform.xform(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
+		p_xform.xform(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
+	};
+
+	real_t low_limit;
+
+	//base rect2 first (faster)
+
+	if (xf_points[0].y > position.y) {
+		goto next1;
+	}
+	if (xf_points[1].y > position.y) {
+		goto next1;
+	}
+	if (xf_points[2].y > position.y) {
+		goto next1;
+	}
+	if (xf_points[3].y > position.y) {
+		goto next1;
+	}
+
+	return false;
+
+next1:
+
+	low_limit = position.y + size.y;
+
+	if (xf_points[0].y < low_limit) {
+		goto next2;
+	}
+	if (xf_points[1].y < low_limit) {
+		goto next2;
+	}
+	if (xf_points[2].y < low_limit) {
+		goto next2;
+	}
+	if (xf_points[3].y < low_limit) {
+		goto next2;
+	}
+
+	return false;
+
+next2:
+
+	if (xf_points[0].x > position.x) {
+		goto next3;
+	}
+	if (xf_points[1].x > position.x) {
+		goto next3;
+	}
+	if (xf_points[2].x > position.x) {
+		goto next3;
+	}
+	if (xf_points[3].x > position.x) {
+		goto next3;
+	}
+
+	return false;
+
+next3:
+
+	low_limit = position.x + size.x;
+
+	if (xf_points[0].x < low_limit) {
+		goto next4;
+	}
+	if (xf_points[1].x < low_limit) {
+		goto next4;
+	}
+	if (xf_points[2].x < low_limit) {
+		goto next4;
+	}
+	if (xf_points[3].x < low_limit) {
+		goto next4;
+	}
+
+	return false;
+
+next4:
+
+	Vector2 xf_points2[4] = {
+		position,
+		Vector2(position.x + size.x, position.y),
+		Vector2(position.x, position.y + size.y),
+		Vector2(position.x + size.x, position.y + size.y),
+	};
+
+	real_t maxa = p_xform.columns[0].dot(xf_points2[0]);
+	real_t mina = maxa;
+
+	real_t dp = p_xform.columns[0].dot(xf_points2[1]);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
+
+	dp = p_xform.columns[0].dot(xf_points2[2]);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
+
+	dp = p_xform.columns[0].dot(xf_points2[3]);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
+
+	real_t maxb = p_xform.columns[0].dot(xf_points[0]);
+	real_t minb = maxb;
+
+	dp = p_xform.columns[0].dot(xf_points[1]);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
+
+	dp = p_xform.columns[0].dot(xf_points[2]);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
+
+	dp = p_xform.columns[0].dot(xf_points[3]);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
+
+	if (mina > maxb) {
+		return false;
+	}
+	if (minb > maxa) {
+		return false;
+	}
+
+	maxa = p_xform.columns[1].dot(xf_points2[0]);
+	mina = maxa;
+
+	dp = p_xform.columns[1].dot(xf_points2[1]);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
+
+	dp = p_xform.columns[1].dot(xf_points2[2]);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
+
+	dp = p_xform.columns[1].dot(xf_points2[3]);
+	maxa = MAX(dp, maxa);
+	mina = MIN(dp, mina);
+
+	maxb = p_xform.columns[1].dot(xf_points[0]);
+	minb = maxb;
+
+	dp = p_xform.columns[1].dot(xf_points[1]);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
+
+	dp = p_xform.columns[1].dot(xf_points[2]);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
+
+	dp = p_xform.columns[1].dot(xf_points[3]);
+	maxb = MAX(dp, maxb);
+	minb = MIN(dp, minb);
+
+	if (mina > maxb) {
+		return false;
+	}
+	if (minb > maxa) {
+		return false;
+	}
+
+	return true;
+}
+
+Rect2::operator String() const {
+	return "[P: " + position.operator String() + ", S: " + size + "]";
+}

core/math/rect2.h

@@ -0,0 +1,364 @@
+#ifndef RECT2_H
+#define RECT2_H
+
+/*************************************************************************/
+/*  rect2.h                                                              */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/vector2.h" // also includes math_funcs and ustring
+#include "core/math/vector2i.h"
+
+struct Transform2D;
+struct Rect2i;
+
+struct _NO_DISCARD_CLASS_ Rect2 {
+	Point2 position;
+	Size2 size;
+
+	const Vector2 &get_position() const { return position; }
+	void set_position(const Vector2 &p_pos) { position = p_pos; }
+	const Vector2 &get_size() const { return size; }
+	void set_size(const Vector2 &p_size) { size = p_size; }
+
+	real_t get_area() const { return size.width * size.height; }
+
+	_FORCE_INLINE_ Vector2 get_center() const { return position + (size * 0.5f); }
+
+	inline bool intersects(const Rect2 &p_rect, const bool p_include_borders = false) const {
+		if (p_include_borders) {
+			if (position.x > (p_rect.position.x + p_rect.size.width)) {
+				return false;
+			}
+			if ((position.x + size.width) < p_rect.position.x) {
+				return false;
+			}
+			if (position.y > (p_rect.position.y + p_rect.size.height)) {
+				return false;
+			}
+			if ((position.y + size.height) < p_rect.position.y) {
+				return false;
+			}
+		} else {
+			if (position.x >= (p_rect.position.x + p_rect.size.width)) {
+				return false;
+			}
+			if ((position.x + size.width) <= p_rect.position.x) {
+				return false;
+			}
+			if (position.y >= (p_rect.position.y + p_rect.size.height)) {
+				return false;
+			}
+			if ((position.y + size.height) <= p_rect.position.y) {
+				return false;
+			}
+		}
+
+		return true;
+	}
+
+	inline real_t distance_to(const Vector2 &p_point) const {
+		real_t dist = 0.0;
+		bool inside = true;
+
+		if (p_point.x < position.x) {
+			real_t d = position.x - p_point.x;
+			dist = d;
+			inside = false;
+		}
+		if (p_point.y < position.y) {
+			real_t d = position.y - p_point.y;
+			dist = inside ? d : MIN(dist, d);
+			inside = false;
+		}
+		if (p_point.x >= (position.x + size.x)) {
+			real_t d = p_point.x - (position.x + size.x);
+			dist = inside ? d : MIN(dist, d);
+			inside = false;
+		}
+		if (p_point.y >= (position.y + size.y)) {
+			real_t d = p_point.y - (position.y + size.y);
+			dist = inside ? d : MIN(dist, d);
+			inside = false;
+		}
+
+		if (inside) {
+			return 0;
+		} else {
+			return dist;
+		}
+	}
+
+	bool intersects_transformed(const Transform2D &p_xform, const Rect2 &p_rect) const;
+
+	bool intersects_segment(const Point2 &p_from, const Point2 &p_to, Point2 *r_pos = nullptr, Point2 *r_normal = nullptr) const;
+
+	inline bool encloses(const Rect2 &p_rect) const {
+		return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
+				((p_rect.position.x + p_rect.size.x) <= (position.x + size.x)) &&
+				((p_rect.position.y + p_rect.size.y) <= (position.y + size.y));
+	}
+
+	_FORCE_INLINE_ bool has_no_area() const {
+		return (size.x <= 0 || size.y <= 0);
+	}
+	inline Rect2 clip(const Rect2 &p_rect) const { /// return a clipped rect
+
+		Rect2 new_rect = p_rect;
+
+		if (!intersects(new_rect)) {
+			return Rect2();
+		}
+
+		new_rect.position.x = MAX(p_rect.position.x, position.x);
+		new_rect.position.y = MAX(p_rect.position.y, position.y);
+
+		Point2 p_rect_end = p_rect.position + p_rect.size;
+		Point2 end = position + size;
+
+		new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
+		new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
+
+		return new_rect;
+	}
+
+	inline Rect2 intersection(const Rect2 &p_rect) const {
+		Rect2 new_rect = p_rect;
+
+		if (!intersects(new_rect)) {
+			return Rect2();
+		}
+
+		new_rect.position.x = MAX(p_rect.position.x, position.x);
+		new_rect.position.y = MAX(p_rect.position.y, position.y);
+
+		Point2 p_rect_end = p_rect.position + p_rect.size;
+		Point2 end = position + size;
+
+		new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
+		new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
+
+		return new_rect;
+	}
+
+	inline Rect2 merge(const Rect2 &p_rect) const { ///< return a merged rect
+
+		Rect2 new_rect;
+
+		new_rect.position.x = MIN(p_rect.position.x, position.x);
+		new_rect.position.y = MIN(p_rect.position.y, position.y);
+
+		new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
+		new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
+
+		new_rect.size = new_rect.size - new_rect.position; //make relative again
+
+		return new_rect;
+	};
+	inline bool has_point(const Point2 &p_point) const {
+		if (p_point.x < position.x) {
+			return false;
+		}
+		if (p_point.y < position.y) {
+			return false;
+		}
+
+		if (p_point.x >= (position.x + size.x)) {
+			return false;
+		}
+		if (p_point.y >= (position.y + size.y)) {
+			return false;
+		}
+
+		return true;
+	}
+	bool is_equal_approx(const Rect2 &p_rect) const;
+
+	bool operator==(const Rect2 &p_rect) const { return position == p_rect.position && size == p_rect.size; }
+	bool operator!=(const Rect2 &p_rect) const { return position != p_rect.position || size != p_rect.size; }
+
+	inline Rect2 grow(real_t p_by) const {
+		Rect2 g = *this;
+		g.grow_by(p_by);
+		return g;
+	}
+
+	inline void grow_by(real_t p_by) {
+		position.x -= p_by;
+		position.y -= p_by;
+		size.width += p_by * 2;
+		size.height += p_by * 2;
+	}
+
+	inline Rect2 grow_margin(Margin p_margin, real_t p_amount) const {
+		Rect2 g = *this;
+		g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
+				(MARGIN_TOP == p_margin) ? p_amount : 0,
+				(MARGIN_RIGHT == p_margin) ? p_amount : 0,
+				(MARGIN_BOTTOM == p_margin) ? p_amount : 0);
+		return g;
+	}
+
+	inline Rect2 grow_side(Side p_side, real_t p_amount) const {
+		Rect2 g = *this;
+		g = g.grow_individual((SIDE_LEFT == p_side) ? p_amount : 0,
+				(SIDE_TOP == p_side) ? p_amount : 0,
+				(SIDE_RIGHT == p_side) ? p_amount : 0,
+				(SIDE_BOTTOM == p_side) ? p_amount : 0);
+		return g;
+	}
+
+	inline Rect2 grow_individual(real_t p_left, real_t p_top, real_t p_right, real_t p_bottom) const {
+		Rect2 g = *this;
+		g.position.x -= p_left;
+		g.position.y -= p_top;
+		g.size.width += p_left + p_right;
+		g.size.height += p_top + p_bottom;
+
+		return g;
+	}
+
+	_FORCE_INLINE_ Rect2 expand(const Vector2 &p_vector) const {
+		Rect2 r = *this;
+		r.expand_to(p_vector);
+		return r;
+	}
+
+	inline void expand_to(const Vector2 &p_vector) { //in place function for speed
+
+		Vector2 begin = position;
+		Vector2 end = position + size;
+
+		if (p_vector.x < begin.x) {
+			begin.x = p_vector.x;
+		}
+		if (p_vector.y < begin.y) {
+			begin.y = p_vector.y;
+		}
+
+		if (p_vector.x > end.x) {
+			end.x = p_vector.x;
+		}
+		if (p_vector.y > end.y) {
+			end.y = p_vector.y;
+		}
+
+		position = begin;
+		size = end - begin;
+	}
+
+	_FORCE_INLINE_ Rect2 abs() const {
+		return Rect2(Point2(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
+	}
+
+	Vector2 get_support(const Vector2 &p_normal) const {
+		Vector2 half_extents = size * 0.5f;
+		Vector2 ofs = position + half_extents;
+		return Vector2(
+					   (p_normal.x > 0) ? -half_extents.x : half_extents.x,
+					   (p_normal.y > 0) ? -half_extents.y : half_extents.y) +
+				ofs;
+	}
+
+	_FORCE_INLINE_ bool intersects_filled_polygon(const Vector2 *p_points, int p_point_count) const {
+		Vector2 center = get_center();
+		int side_plus = 0;
+		int side_minus = 0;
+		Vector2 end = position + size;
+
+		int i_f = p_point_count - 1;
+		for (int i = 0; i < p_point_count; i++) {
+			const Vector2 &a = p_points[i_f];
+			const Vector2 &b = p_points[i];
+			i_f = i;
+
+			Vector2 r = (b - a);
+			float l = r.length();
+			if (l == 0.0f) {
+				continue;
+			}
+
+			//check inside
+			Vector2 tg = r.orthogonal();
+			float s = tg.dot(center) - tg.dot(a);
+			if (s < 0.0f) {
+				side_plus++;
+			} else {
+				side_minus++;
+			}
+
+			//check ray box
+			r /= l;
+			Vector2 ir(1.0f / r.x, 1.0f / r.y);
+
+			// lb is the corner of AABB with minimal coordinates - left bottom, rt is maximal corner
+			// r.org is origin of ray
+			Vector2 t13 = (position - a) * ir;
+			Vector2 t24 = (end - a) * ir;
+
+			float tmin = MAX(MIN(t13.x, t24.x), MIN(t13.y, t24.y));
+			float tmax = MIN(MAX(t13.x, t24.x), MAX(t13.y, t24.y));
+
+			// if tmax < 0, ray (line) is intersecting AABB, but the whole AABB is behind us
+			if (tmax < 0 || tmin > tmax || tmin >= l) {
+				continue;
+			}
+
+			return true;
+		}
+
+		if (side_plus * side_minus == 0) {
+			return true; //all inside
+		} else {
+			return false;
+		}
+	}
+
+	_FORCE_INLINE_ void set_end(const Vector2 &p_end) {
+		size = p_end - position;
+	}
+
+	_FORCE_INLINE_ Vector2 get_end() const {
+		return position + size;
+	}
+
+	operator String() const;
+
+	Rect2() {}
+	Rect2(real_t p_x, real_t p_y, real_t p_width, real_t p_height) :
+			position(Point2(p_x, p_y)),
+			size(Size2(p_width, p_height)) {
+	}
+	Rect2(const Point2 &p_pos, const Size2 &p_size) :
+			position(p_pos),
+			size(p_size) {
+	}
+};
+
+#endif // RECT2_H

core/math/rect2i.cpp

@@ -0,0 +1,36 @@
+/*************************************************************************/
+/*  rect2i.cpp                                                           */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/transform_2d.h" // Includes rect2.h but Rect2 needs Transform2D
+
+Rect2i::operator String() const {
+	return "[P: " + position.operator String() + ", S: " + size + "]";
+}

core/math/rect2i.h

@@ -0,0 +1,257 @@
+#ifndef RECT2I_H
+#define RECT2I_H
+
+/*************************************************************************/
+/*  rect2i.h                                                             */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/vector2i.h" // also includes math_funcs and ustring
+
+struct _NO_DISCARD_CLASS_ Rect2i {
+	Point2i position;
+	Size2i size;
+
+	const Point2i &get_position() const { return position; }
+	void set_position(const Point2i &p_position) { position = p_position; }
+	const Size2i &get_size() const { return size; }
+	void set_size(const Size2i &p_size) { size = p_size; }
+
+	int get_area() const { return size.width * size.height; }
+
+	_FORCE_INLINE_ Vector2i get_center() const { return position + (size / 2); }
+
+	inline bool intersects(const Rect2i &p_rect) const {
+		if (position.x > (p_rect.position.x + p_rect.size.width)) {
+			return false;
+		}
+		if ((position.x + size.width) < p_rect.position.x) {
+			return false;
+		}
+		if (position.y > (p_rect.position.y + p_rect.size.height)) {
+			return false;
+		}
+		if ((position.y + size.height) < p_rect.position.y) {
+			return false;
+		}
+
+		return true;
+	}
+
+	inline bool encloses(const Rect2i &p_rect) const {
+		return (p_rect.position.x >= position.x) && (p_rect.position.y >= position.y) &&
+				((p_rect.position.x + p_rect.size.x) < (position.x + size.x)) &&
+				((p_rect.position.y + p_rect.size.y) < (position.y + size.y));
+	}
+
+	_FORCE_INLINE_ bool has_no_area() const {
+		return (size.x <= 0 || size.y <= 0);
+	}
+
+	inline Rect2i clip(const Rect2i &p_rect) const { /// return a clipped rect
+
+		Rect2i new_rect = p_rect;
+
+		if (!intersects(new_rect)) {
+			return Rect2i();
+		}
+
+		new_rect.position.x = MAX(p_rect.position.x, position.x);
+		new_rect.position.y = MAX(p_rect.position.y, position.y);
+
+		Point2 p_rect_end = p_rect.position + p_rect.size;
+		Point2 end = position + size;
+
+		new_rect.size.x = (int)(MIN(p_rect_end.x, end.x) - new_rect.position.x);
+		new_rect.size.y = (int)(MIN(p_rect_end.y, end.y) - new_rect.position.y);
+
+		return new_rect;
+	}
+
+	// Returns the instersection between two Rect2is or an empty Rect2i if there is no intersection
+	inline Rect2i intersection(const Rect2i &p_rect) const {
+		Rect2i new_rect = p_rect;
+
+		if (!intersects(new_rect)) {
+			return Rect2i();
+		}
+
+		new_rect.position.x = MAX(p_rect.position.x, position.x);
+		new_rect.position.y = MAX(p_rect.position.y, position.y);
+
+		Point2i p_rect_end = p_rect.position + p_rect.size;
+		Point2i end = position + size;
+
+		new_rect.size.x = MIN(p_rect_end.x, end.x) - new_rect.position.x;
+		new_rect.size.y = MIN(p_rect_end.y, end.y) - new_rect.position.y;
+
+		return new_rect;
+	}
+
+	inline Rect2i merge(const Rect2i &p_rect) const { ///< return a merged rect
+
+		Rect2i new_rect;
+
+		new_rect.position.x = MIN(p_rect.position.x, position.x);
+		new_rect.position.y = MIN(p_rect.position.y, position.y);
+
+		new_rect.size.x = MAX(p_rect.position.x + p_rect.size.x, position.x + size.x);
+		new_rect.size.y = MAX(p_rect.position.y + p_rect.size.y, position.y + size.y);
+
+		new_rect.size = new_rect.size - new_rect.position; //make relative again
+
+		return new_rect;
+	}
+
+	bool has_point(const Point2i &p_point) const {
+		if (p_point.x < position.x) {
+			return false;
+		}
+		if (p_point.y < position.y) {
+			return false;
+		}
+
+		if (p_point.x >= (position.x + size.x)) {
+			return false;
+		}
+		if (p_point.y >= (position.y + size.y)) {
+			return false;
+		}
+
+		return true;
+	}
+
+	bool operator==(const Rect2i &p_rect) const { return position == p_rect.position && size == p_rect.size; }
+	bool operator!=(const Rect2i &p_rect) const { return position != p_rect.position || size != p_rect.size; }
+
+	Rect2i grow(int p_by) const {
+		Rect2i g = *this;
+		g.position.x -= p_by;
+		g.position.y -= p_by;
+		g.size.width += p_by * 2;
+		g.size.height += p_by * 2;
+		return g;
+	}
+
+	void grow_by(int p_by) {
+		position.x -= p_by;
+		position.y -= p_by;
+		size.width += p_by * 2;
+		size.height += p_by * 2;
+	}
+
+	inline Rect2i grow_margin(Margin p_margin, int p_amount) const {
+		Rect2i g = *this;
+		g = g.grow_individual((MARGIN_LEFT == p_margin) ? p_amount : 0,
+				(MARGIN_TOP == p_margin) ? p_amount : 0,
+				(MARGIN_RIGHT == p_margin) ? p_amount : 0,
+				(MARGIN_BOTTOM == p_margin) ? p_amount : 0);
+		return g;
+	}
+
+	inline Rect2i grow_side(Side p_side, int p_amount) const {
+		Rect2i g = *this;
+		g = g.grow_individual((SIDE_LEFT == p_side) ? p_amount : 0,
+				(SIDE_TOP == p_side) ? p_amount : 0,
+				(SIDE_RIGHT == p_side) ? p_amount : 0,
+				(SIDE_BOTTOM == p_side) ? p_amount : 0);
+		return g;
+	}
+
+	inline Rect2i grow_individual(int p_left, int p_top, int p_right, int p_bottom) const {
+		Rect2i g = *this;
+		g.position.x -= p_left;
+		g.position.y -= p_top;
+		g.size.width += p_left + p_right;
+		g.size.height += p_top + p_bottom;
+
+		return g;
+	}
+
+	_FORCE_INLINE_ Rect2i expand(const Vector2i &p_vector) const {
+		Rect2i r = *this;
+		r.expand_to(p_vector);
+		return r;
+	}
+
+	inline void expand_to(const Point2i &p_vector) {
+		Point2i begin = position;
+		Point2i end = position + size;
+
+		if (p_vector.x < begin.x) {
+			begin.x = p_vector.x;
+		}
+		if (p_vector.y < begin.y) {
+			begin.y = p_vector.y;
+		}
+
+		if (p_vector.x > end.x) {
+			end.x = p_vector.x;
+		}
+		if (p_vector.y > end.y) {
+			end.y = p_vector.y;
+		}
+
+		position = begin;
+		size = end - begin;
+	}
+
+	_FORCE_INLINE_ Rect2i abs() const {
+		return Rect2i(Point2i(position.x + MIN(size.x, 0), position.y + MIN(size.y, 0)), size.abs());
+	}
+
+	_FORCE_INLINE_ void set_end(const Vector2i &p_end) {
+		size = p_end - position;
+	}
+
+	_FORCE_INLINE_ Vector2i get_end() const {
+		return position + size;
+	}
+
+	Rect2 to_rect2() const { return Rect2(position, size); }
+
+	operator String() const;
+	operator Rect2() const { return Rect2(position, size); }
+
+	Rect2i(const Rect2 &p_r2) :
+			position(p_r2.position),
+			size(p_r2.size) {
+	}
+	Rect2i() {}
+	Rect2i(int p_x, int p_y, int p_width, int p_height) :
+			position(Point2(p_x, p_y)),
+			size(Size2(p_width, p_height)) {
+	}
+	Rect2i(const Point2 &p_pos, const Size2 &p_size) :
+			position(p_pos),
+			size(p_size) {
+	}
+};
+
+#endif // RECT2_H

core/math/thirdparty/pcg.cpp

@@ -0,0 +1,58 @@
+// *Really* minimal PCG32 code / (c) 2014 M.E. O'Neill / pcg-random.org
+// Licensed under Apache License 2.0 (NO WARRANTY, etc. see website)
+
+#include "pcg.h"
+
+uint32_t pcg32_random_r(pcg32_random_t* rng)
+{
+    uint64_t oldstate = rng->state;
+    // Advance internal state
+    rng->state = oldstate * 6364136223846793005ULL + (rng->inc|1);
+    // Calculate output function (XSH RR), uses old state for max ILP
+    uint32_t xorshifted = ((oldstate >> 18u) ^ oldstate) >> 27u;
+    uint32_t rot = oldstate >> 59u;
+    return (xorshifted >> rot) | (xorshifted << ((-rot) & 31));
+}
+
+// Source from http://www.pcg-random.org/downloads/pcg-c-basic-0.9.zip
+void pcg32_srandom_r(pcg32_random_t* rng, uint64_t initstate, uint64_t initseq)
+{
+    rng->state = 0U;
+    rng->inc = (initseq << 1u) | 1u;
+    pcg32_random_r(rng);
+    rng->state += initstate;
+    pcg32_random_r(rng);
+}
+
+// Source from https://github.com/imneme/pcg-c-basic/blob/master/pcg_basic.c
+// pcg32_boundedrand_r(rng, bound):
+//     Generate a uniformly distributed number, r, where 0 <= r < bound
+uint32_t pcg32_boundedrand_r(pcg32_random_t *rng, uint32_t bound) {
+	// To avoid bias, we need to make the range of the RNG a multiple of
+	// bound, which we do by dropping output less than a threshold.
+	// A naive scheme to calculate the threshold would be to do
+	//
+	//     uint32_t threshold = 0x100000000ull % bound;
+	//
+	// but 64-bit div/mod is slower than 32-bit div/mod (especially on
+	// 32-bit platforms).  In essence, we do
+	//
+	//     uint32_t threshold = (0x100000000ull-bound) % bound;
+	//
+	// because this version will calculate the same modulus, but the LHS
+	// value is less than 2^32.
+	uint32_t threshold = -bound % bound;
+
+	// Uniformity guarantees that this loop will terminate.  In practice, it
+	// should usually terminate quickly; on average (assuming all bounds are
+	// equally likely), 82.25% of the time, we can expect it to require just
+	// one iteration.  In the worst case, someone passes a bound of 2^31 + 1
+	// (i.e., 2147483649), which invalidates almost 50% of the range.  In
+	// practice, bounds are typically small and only a tiny amount of the range
+	// is eliminated.
+	for (;;) {
+		uint32_t r = pcg32_random_r(rng);
+		if (r >= threshold)
+			return r % bound;
+	}
+}

core/math/thirdparty/pcg.h

@@ -0,0 +1,16 @@
+// *Really* minimal PCG32 code / (c) 2014 M.E. O'Neill / pcg-random.org
+// Licensed under Apache License 2.0 (NO WARRANTY, etc. see website)
+
+#ifndef RANDOM_H
+#define RANDOM_H
+
+#include "core/typedefs.h"
+
+#define PCG_DEFAULT_INC_64 1442695040888963407ULL
+
+typedef struct { uint64_t state;  uint64_t inc; } pcg32_random_t;
+uint32_t pcg32_random_r(pcg32_random_t* rng);
+void pcg32_srandom_r(pcg32_random_t* rng, uint64_t initstate, uint64_t initseq);
+uint32_t pcg32_boundedrand_r(pcg32_random_t* rng, uint32_t bound);
+
+#endif // RANDOM_H

core/math/transform.cpp

@@ -0,0 +1,283 @@
+/*************************************************************************/
+/*  transform.cpp                                                        */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "transform.h"
+
+#include "core/math/math_funcs.h"
+#include "core/string/print_string.h"
+
+void Transform::invert() {
+	basis.transpose();
+	origin = basis.xform(-origin);
+}
+
+Transform Transform::inverse() const {
+	// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
+	// Transform::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
+	Transform ret = *this;
+	ret.invert();
+	return ret;
+}
+
+void Transform::affine_invert() {
+	basis.invert();
+	origin = basis.xform(-origin);
+}
+
+Transform Transform::affine_inverse() const {
+	Transform ret = *this;
+	ret.affine_invert();
+	return ret;
+}
+
+Transform Transform::rotated(const Vector3 &p_axis, real_t p_angle) const {
+	// Equivalent to left multiplication
+	Basis p_basis(p_axis, p_angle);
+	return Transform(p_basis * basis, p_basis.xform(origin));
+}
+
+Transform Transform::rotated_local(const Vector3 &p_axis, real_t p_angle) const {
+	// Equivalent to right multiplication
+	Basis p_basis(p_axis, p_angle);
+	return Transform(basis * p_basis, origin);
+}
+
+void Transform::rotate(const Vector3 &p_axis, real_t p_phi) {
+	*this = rotated(p_axis, p_phi);
+}
+
+void Transform::rotate_local(const Vector3 &p_axis, real_t p_phi) {
+	*this = rotated_local(p_axis, p_phi);
+}
+
+void Transform::rotate_basis(const Vector3 &p_axis, real_t p_phi) {
+	basis.rotate(p_axis, p_phi);
+}
+
+void Transform::set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up) {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(p_eye == p_target);
+	ERR_FAIL_COND(p_up.length() == 0);
+#endif
+	// Reference: MESA source code
+	Vector3 v_x, v_y, v_z;
+
+	/* Make rotation matrix */
+
+	/* Z vector */
+	v_z = p_eye - p_target;
+
+	v_z.normalize();
+
+	v_y = p_up;
+
+	v_x = v_y.cross(v_z);
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(v_x.length() == 0);
+#endif
+
+	/* Recompute Y = Z cross X */
+	v_y = v_z.cross(v_x);
+
+	v_x.normalize();
+	v_y.normalize();
+
+	basis.set(v_x, v_y, v_z);
+
+	origin = p_eye;
+}
+
+Transform Transform::looking_at(const Vector3 &p_target, const Vector3 &p_up) const {
+	Transform t = *this;
+	t.set_look_at(origin, p_target, p_up);
+	return t;
+}
+
+void Transform::scale(const Vector3 &p_scale) {
+	basis.scale(p_scale);
+	origin *= p_scale;
+}
+
+Transform Transform::scaled(const Vector3 &p_scale) const {
+	// Equivalent to left multiplication
+	return Transform(basis.scaled(p_scale), origin * p_scale);
+}
+
+Transform Transform::scaled_local(const Vector3 &p_scale) const {
+	// Equivalent to right multiplication
+	return Transform(basis.scaled_local(p_scale), origin);
+}
+
+void Transform::scale_basis(const Vector3 &p_scale) {
+	basis.scale(p_scale);
+}
+
+void Transform::translate_local(real_t p_tx, real_t p_ty, real_t p_tz) {
+	translate_local(Vector3(p_tx, p_ty, p_tz));
+}
+void Transform::translate_local(const Vector3 &p_translation) {
+	for (int i = 0; i < 3; i++) {
+		origin[i] += basis[i].dot(p_translation);
+	}
+}
+
+void Transform::translate_localr(real_t p_tx, real_t p_ty, real_t p_tz) {
+	translate_local(Vector3(p_tx, p_ty, p_tz));
+}
+void Transform::translate_localv(const Vector3 &p_translation) {
+	for (int i = 0; i < 3; i++) {
+		origin[i] += basis[i].dot(p_translation);
+	}
+}
+
+Transform Transform::translated(const Vector3 &p_translation) const {
+	// Equivalent to left multiplication
+	return Transform(basis, origin + p_translation);
+}
+
+Transform Transform::translated_local(const Vector3 &p_translation) const {
+	// Equivalent to right multiplication
+	return Transform(basis, origin + basis.xform(p_translation));
+}
+
+void Transform::orthonormalize() {
+	basis.orthonormalize();
+}
+
+Transform Transform::orthonormalized() const {
+	Transform _copy = *this;
+	_copy.orthonormalize();
+	return _copy;
+}
+
+void Transform::orthogonalize() {
+	basis.orthogonalize();
+}
+
+Transform Transform::orthogonalized() const {
+	Transform _copy = *this;
+	_copy.orthogonalize();
+	return _copy;
+}
+
+bool Transform::is_equal_approx(const Transform &p_transform) const {
+	return basis.is_equal_approx(p_transform.basis) && origin.is_equal_approx(p_transform.origin);
+}
+
+bool Transform::operator==(const Transform &p_transform) const {
+	return (basis == p_transform.basis && origin == p_transform.origin);
+}
+bool Transform::operator!=(const Transform &p_transform) const {
+	return (basis != p_transform.basis || origin != p_transform.origin);
+}
+
+void Transform::operator*=(const Transform &p_transform) {
+	origin = xform(p_transform.origin);
+	basis *= p_transform.basis;
+}
+
+Transform Transform::operator*(const Transform &p_transform) const {
+	Transform t = *this;
+	t *= p_transform;
+	return t;
+}
+
+void Transform::operator*=(const real_t p_val) {
+	origin *= p_val;
+	basis *= p_val;
+}
+
+Transform Transform::operator*(const real_t p_val) const {
+	Transform ret(*this);
+	ret *= p_val;
+	return ret;
+}
+
+Transform Transform::spherical_interpolate_with(const Transform &p_transform, real_t p_c) const {
+	/* not sure if very "efficient" but good enough? */
+
+	Transform interp;
+
+	Vector3 src_scale = basis.get_scale();
+	Quaternion src_rot = basis.get_rotation_quaternion();
+	Vector3 src_loc = origin;
+
+	Vector3 dst_scale = p_transform.basis.get_scale();
+	Quaternion dst_rot = p_transform.basis.get_rotation_quaternion();
+	Vector3 dst_loc = p_transform.origin;
+
+	interp.basis.set_quaternion_scale(src_rot.slerp(dst_rot, p_c).normalized(), src_scale.linear_interpolate(dst_scale, p_c));
+	interp.origin = src_loc.linear_interpolate(dst_loc, p_c);
+
+	return interp;
+}
+
+Transform Transform::interpolate_with(const Transform &p_transform, real_t p_c) const {
+	/* not sure if very "efficient" but good enough? */
+
+	Vector3 src_scale = basis.get_scale();
+	Quaternion src_rot = basis.get_rotation_quaternion();
+	Vector3 src_loc = origin;
+
+	Vector3 dst_scale = p_transform.basis.get_scale();
+	Quaternion dst_rot = p_transform.basis.get_rotation_quaternion();
+	Vector3 dst_loc = p_transform.origin;
+
+	Transform interp;
+	interp.basis.set_quaternion_scale(src_rot.slerp(dst_rot, p_c).normalized(), src_scale.linear_interpolate(dst_scale, p_c));
+	interp.origin = src_loc.linear_interpolate(dst_loc, p_c);
+
+	return interp;
+}
+
+Transform::operator String() const {
+	return "[X: " + basis.get_axis(0).operator String() +
+			", Y: " + basis.get_axis(1).operator String() +
+			", Z: " + basis.get_axis(2).operator String() +
+			", O: " + origin.operator String() + "]";
+}
+
+Transform::Transform(const Basis &p_basis, const Vector3 &p_origin) :
+		basis(p_basis),
+		origin(p_origin) {
+}
+
+Transform::Transform(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz) {
+	basis = Basis(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+	origin = Vector3(ox, oy, oz);
+}
+
+Transform::Transform(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin) :
+		origin(p_origin) {
+	basis.set_column(0, p_x);
+	basis.set_column(1, p_y);
+	basis.set_column(2, p_z);
+}

core/math/transform.h

@@ -0,0 +1,326 @@
+#ifndef TRANSFORM_H
+#define TRANSFORM_H
+
+/*************************************************************************/
+/*  transform.h                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/containers/pool_vector.h"
+#include "core/math/aabb.h"
+#include "core/math/basis.h"
+#include "core/math/plane.h"
+#include "core/math/vector3i.h"
+
+struct _NO_DISCARD_CLASS_ Transform {
+	Basis basis;
+	Vector3 origin;
+
+	void invert();
+	Transform inverse() const;
+
+	void affine_invert();
+	Transform affine_inverse() const;
+
+	Transform rotated(const Vector3 &p_axis, real_t p_phi) const;
+	Transform rotated_local(const Vector3 &p_axis, real_t p_phi) const;
+
+	void rotate(const Vector3 &p_axis, real_t p_phi);
+	void rotate_local(const Vector3 &p_axis, real_t p_phi);
+	void rotate_basis(const Vector3 &p_axis, real_t p_phi);
+
+	void set_look_at(const Vector3 &p_eye, const Vector3 &p_target, const Vector3 &p_up);
+	Transform looking_at(const Vector3 &p_target, const Vector3 &p_up) const;
+
+	void scale(const Vector3 &p_scale);
+	Transform scaled(const Vector3 &p_scale) const;
+	Transform scaled_local(const Vector3 &p_scale) const;
+	void scale_basis(const Vector3 &p_scale);
+
+	void translate_local(real_t p_tx, real_t p_ty, real_t p_tz);
+	void translate_local(const Vector3 &p_translation);
+	void translate_localr(real_t p_tx, real_t p_ty, real_t p_tz);
+	void translate_localv(const Vector3 &p_translation);
+	Transform translated(const Vector3 &p_translation) const;
+	Transform translated_local(const Vector3 &p_translation) const;
+
+	const Basis &get_basis() const { return basis; }
+	void set_basis(const Basis &p_basis) { basis = p_basis; }
+
+	const Vector3 &get_origin() const { return origin; }
+	void set_origin(const Vector3 &p_origin) { origin = p_origin; }
+
+	void orthonormalize();
+	Transform orthonormalized() const;
+	void orthogonalize();
+	Transform orthogonalized() const;
+	bool is_equal_approx(const Transform &p_transform) const;
+
+	bool operator==(const Transform &p_transform) const;
+	bool operator!=(const Transform &p_transform) const;
+
+	_FORCE_INLINE_ Vector3 xform(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ Vector3i xform(const Vector3i &p_vector) const;
+	_FORCE_INLINE_ AABB xform(const AABB &p_aabb) const;
+	_FORCE_INLINE_ PoolVector<Vector3> xform(const PoolVector<Vector3> &p_array) const;
+	_FORCE_INLINE_ PoolVector<Vector3i> xform(const PoolVector<Vector3i> &p_array) const;
+
+	// NOTE: These are UNSAFE with non-uniform scaling, and will produce incorrect results.
+	// They use the transpose.
+	// For safe inverse transforms, xform by the affine_inverse.
+	_FORCE_INLINE_ Vector3 xform_inv(const Vector3 &p_vector) const;
+	_FORCE_INLINE_ Vector3i xform_inv(const Vector3i &p_vector) const;
+	_FORCE_INLINE_ AABB xform_inv(const AABB &p_aabb) const;
+	_FORCE_INLINE_ PoolVector<Vector3> xform_inv(const PoolVector<Vector3> &p_array) const;
+	_FORCE_INLINE_ PoolVector<Vector3i> xform_inv(const PoolVector<Vector3i> &p_array) const;
+
+	// Safe with non-uniform scaling (uses affine_inverse).
+	_FORCE_INLINE_ Plane xform(const Plane &p_plane) const;
+	_FORCE_INLINE_ Plane xform_inv(const Plane &p_plane) const;
+
+	// These fast versions use precomputed affine inverse, and should be used in bottleneck areas where
+	// multiple planes are to be transformed.
+	_FORCE_INLINE_ Plane xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const;
+	static _FORCE_INLINE_ Plane xform_inv_fast(const Plane &p_plane, const Transform &p_inverse, const Basis &p_basis_transpose);
+
+	void operator*=(const Transform &p_transform);
+	Transform operator*(const Transform &p_transform) const;
+	void operator*=(const real_t p_val);
+	Transform operator*(const real_t p_val) const;
+
+	Transform spherical_interpolate_with(const Transform &p_transform, real_t p_c) const;
+	Transform interpolate_with(const Transform &p_transform, real_t p_c) const;
+
+	_FORCE_INLINE_ Transform inverse_xform(const Transform &t) const {
+		Vector3 v = t.origin - origin;
+		return Transform(basis.transpose_xform(t.basis),
+				basis.xform(v));
+	}
+
+	void set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t tx, real_t ty, real_t tz) {
+		basis.set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
+		origin.x = tx;
+		origin.y = ty;
+		origin.z = tz;
+	}
+
+	operator String() const;
+
+	Transform(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz, real_t ox, real_t oy, real_t oz);
+	Transform(const Basis &p_basis, const Vector3 &p_origin = Vector3());
+	Transform(const Vector3 &p_x, const Vector3 &p_y, const Vector3 &p_z, const Vector3 &p_origin);
+	Transform() {}
+};
+
+_FORCE_INLINE_ Vector3 Transform::xform(const Vector3 &p_vector) const {
+	return Vector3(
+			basis[0].dot(p_vector) + origin.x,
+			basis[1].dot(p_vector) + origin.y,
+			basis[2].dot(p_vector) + origin.z);
+}
+
+_FORCE_INLINE_ Vector3 Transform::xform_inv(const Vector3 &p_vector) const {
+	Vector3 v = p_vector - origin;
+
+	return Vector3(
+			(basis.rows[0][0] * v.x) + (basis.rows[1][0] * v.y) + (basis.rows[2][0] * v.z),
+			(basis.rows[0][1] * v.x) + (basis.rows[1][1] * v.y) + (basis.rows[2][1] * v.z),
+			(basis.rows[0][2] * v.x) + (basis.rows[1][2] * v.y) + (basis.rows[2][2] * v.z));
+}
+
+_FORCE_INLINE_ Vector3i Transform::xform(const Vector3i &p_vector) const {
+	return Vector3i(
+			basis[0].dot(p_vector) + origin.x,
+			basis[1].dot(p_vector) + origin.y,
+			basis[2].dot(p_vector) + origin.z);
+}
+
+_FORCE_INLINE_ Vector3i Transform::xform_inv(const Vector3i &p_vector) const {
+	Vector3i v = p_vector;
+	v.x -= origin.x;
+	v.y -= origin.y;
+	v.z -= origin.z;
+
+	return Vector3i(
+			(basis.rows[0][0] * v.x) + (basis.rows[1][0] * v.y) + (basis.rows[2][0] * v.z),
+			(basis.rows[0][1] * v.x) + (basis.rows[1][1] * v.y) + (basis.rows[2][1] * v.z),
+			(basis.rows[0][2] * v.x) + (basis.rows[1][2] * v.y) + (basis.rows[2][2] * v.z));
+}
+
+// Neither the plane regular xform or xform_inv are particularly efficient,
+// as they do a basis inverse. For xforming a large number
+// of planes it is better to pre-calculate the inverse transpose basis once
+// and reuse it for each plane, by using the 'fast' version of the functions.
+_FORCE_INLINE_ Plane Transform::xform(const Plane &p_plane) const {
+	Basis b = basis.inverse();
+	b.transpose();
+	return xform_fast(p_plane, b);
+}
+
+_FORCE_INLINE_ Plane Transform::xform_inv(const Plane &p_plane) const {
+	Transform inv = affine_inverse();
+	Basis basis_transpose = basis.transposed();
+	return xform_inv_fast(p_plane, inv, basis_transpose);
+}
+
+_FORCE_INLINE_ AABB Transform::xform(const AABB &p_aabb) const {
+	/* http://dev.theomader.com/transform-bounding-boxes/ */
+	Vector3 min = p_aabb.position;
+	Vector3 max = p_aabb.position + p_aabb.size;
+	Vector3 tmin, tmax;
+	for (int i = 0; i < 3; i++) {
+		tmin[i] = tmax[i] = origin[i];
+		for (int j = 0; j < 3; j++) {
+			real_t e = basis[i][j] * min[j];
+			real_t f = basis[i][j] * max[j];
+			if (e < f) {
+				tmin[i] += e;
+				tmax[i] += f;
+			} else {
+				tmin[i] += f;
+				tmax[i] += e;
+			}
+		}
+	}
+	AABB r_aabb;
+	r_aabb.position = tmin;
+	r_aabb.size = tmax - tmin;
+	return r_aabb;
+}
+
+_FORCE_INLINE_ AABB Transform::xform_inv(const AABB &p_aabb) const {
+	/* define vertices */
+	Vector3 vertices[8] = {
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x + p_aabb.size.x, p_aabb.position.y, p_aabb.position.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y + p_aabb.size.y, p_aabb.position.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z + p_aabb.size.z),
+		Vector3(p_aabb.position.x, p_aabb.position.y, p_aabb.position.z)
+	};
+
+	AABB ret;
+
+	ret.position = xform_inv(vertices[0]);
+
+	for (int i = 1; i < 8; i++) {
+		ret.expand_to(xform_inv(vertices[i]));
+	}
+
+	return ret;
+}
+
+PoolVector<Vector3> Transform::xform(const PoolVector<Vector3> &p_array) const {
+	PoolVector<Vector3> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector3>::Read r = p_array.read();
+	PoolVector<Vector3>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform(r[i]);
+	}
+	return array;
+}
+
+PoolVector<Vector3i> Transform::xform(const PoolVector<Vector3i> &p_array) const {
+	PoolVector<Vector3i> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector3i>::Read r = p_array.read();
+	PoolVector<Vector3i>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform(r[i]);
+	}
+	return array;
+}
+
+PoolVector<Vector3> Transform::xform_inv(const PoolVector<Vector3> &p_array) const {
+	PoolVector<Vector3> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector3>::Read r = p_array.read();
+	PoolVector<Vector3>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform_inv(r[i]);
+	}
+	return array;
+}
+
+PoolVector<Vector3i> Transform::xform_inv(const PoolVector<Vector3i> &p_array) const {
+	PoolVector<Vector3i> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector3i>::Read r = p_array.read();
+	PoolVector<Vector3i>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform_inv(r[i]);
+	}
+	return array;
+}
+
+_FORCE_INLINE_ Plane Transform::xform_fast(const Plane &p_plane, const Basis &p_basis_inverse_transpose) const {
+	// Transform a single point on the plane.
+	Vector3 point = p_plane.normal * p_plane.d;
+	point = xform(point);
+
+	// Use inverse transpose for correct normals with non-uniform scaling.
+	Vector3 normal = p_basis_inverse_transpose.xform(p_plane.normal);
+	normal.normalize();
+
+	real_t d = normal.dot(point);
+	return Plane(normal, d);
+}
+
+_FORCE_INLINE_ Plane Transform::xform_inv_fast(const Plane &p_plane, const Transform &p_inverse, const Basis &p_basis_transpose) {
+	// Transform a single point on the plane.
+	Vector3 point = p_plane.normal * p_plane.d;
+	point = p_inverse.xform(point);
+
+	// Note that instead of precalculating the transpose, an alternative
+	// would be to use the transpose for the basis transform.
+	// However that would be less SIMD friendly (requiring a swizzle).
+	// So the cost is one extra precalced value in the calling code.
+	// This is probably worth it, as this could be used in bottleneck areas. And
+	// where it is not a bottleneck, the non-fast method is fine.
+
+	// Use transpose for correct normals with non-uniform scaling.
+	Vector3 normal = p_basis_transpose.xform(p_plane.normal);
+	normal.normalize();
+
+	real_t d = normal.dot(point);
+	return Plane(normal, d);
+}
+
+#endif // TRANSFORM_H

core/math/transform_2d.cpp

@@ -0,0 +1,337 @@
+/*************************************************************************/
+/*  transform_2d.cpp                                                     */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "transform_2d.h"
+
+void Transform2D::invert() {
+	// FIXME: this function assumes the basis is a rotation matrix, with no scaling.
+	// Transform2D::affine_inverse can handle matrices with scaling, so GDScript should eventually use that.
+	SWAP(columns[0][1], columns[1][0]);
+	columns[2] = basis_xform(-columns[2]);
+}
+
+Transform2D Transform2D::inverse() const {
+	Transform2D inv = *this;
+	inv.invert();
+	return inv;
+}
+
+void Transform2D::affine_invert() {
+	real_t det = basis_determinant();
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND(det == 0);
+#endif
+	real_t idet = 1 / det;
+
+	SWAP(columns[0][0], columns[1][1]);
+	columns[0] *= Vector2(idet, -idet);
+	columns[1] *= Vector2(-idet, idet);
+
+	columns[2] = basis_xform(-columns[2]);
+}
+
+Transform2D Transform2D::affine_inverse() const {
+	Transform2D inv = *this;
+	inv.affine_invert();
+	return inv;
+}
+
+void Transform2D::rotate(real_t p_phi) {
+	*this = Transform2D(p_phi, Vector2()) * (*this);
+}
+
+real_t Transform2D::get_rotation() const {
+	return Math::atan2(columns[0].y, columns[0].x);
+}
+
+void Transform2D::set_rotation(real_t p_rot) {
+	Size2 scale = get_scale();
+	real_t cr = Math::cos(p_rot);
+	real_t sr = Math::sin(p_rot);
+	columns[0][0] = cr;
+	columns[0][1] = sr;
+	columns[1][0] = -sr;
+	columns[1][1] = cr;
+	set_scale(scale);
+}
+
+real_t Transform2D::get_skew() const {
+	real_t det = basis_determinant();
+	return Math::acos(columns[0].normalized().dot(SGN(det) * columns[1].normalized())) - (real_t)Math_PI * 0.5f;
+}
+
+void Transform2D::set_skew(const real_t p_angle) {
+	real_t det = basis_determinant();
+	columns[1] = SGN(det) * columns[0].rotated(((real_t)Math_PI * 0.5f + p_angle)).normalized() * columns[1].length();
+}
+
+Transform2D::Transform2D(real_t p_rot, const Vector2 &p_pos) {
+	real_t cr = Math::cos(p_rot);
+	real_t sr = Math::sin(p_rot);
+	columns[0][0] = cr;
+	columns[0][1] = sr;
+	columns[1][0] = -sr;
+	columns[1][1] = cr;
+	columns[2] = p_pos;
+}
+
+Transform2D::Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos) {
+	columns[0][0] = Math::cos(p_rot) * p_scale.x;
+	columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
+	columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
+	columns[0][1] = Math::sin(p_rot) * p_scale.x;
+	columns[2] = p_pos;
+}
+
+Size2 Transform2D::get_scale() const {
+	real_t det_sign = SGN(basis_determinant());
+	return Size2(columns[0].length(), det_sign * columns[1].length());
+}
+
+void Transform2D::set_scale(const Size2 &p_scale) {
+	columns[0].normalize();
+	columns[1].normalize();
+	columns[0] *= p_scale.x;
+	columns[1] *= p_scale.y;
+}
+
+void Transform2D::scale(const Size2 &p_scale) {
+	scale_basis(p_scale);
+	columns[2] *= p_scale;
+}
+void Transform2D::scale_basis(const Size2 &p_scale) {
+	columns[0][0] *= p_scale.x;
+	columns[0][1] *= p_scale.y;
+	columns[1][0] *= p_scale.x;
+	columns[1][1] *= p_scale.y;
+}
+
+void Transform2D::translate(real_t p_tx, real_t p_ty) {
+	translate(Vector2(p_tx, p_ty));
+}
+void Transform2D::translate(const Vector2 &p_offset) {
+	columns[2] += p_offset;
+}
+
+void Transform2D::translate_local(real_t p_tx, real_t p_ty) {
+	translate_local(Vector2(p_tx, p_ty));
+}
+void Transform2D::translate_local(const Vector2 &p_translation) {
+	columns[2] += basis_xform(p_translation);
+}
+
+void Transform2D::translater(real_t p_tx, real_t p_ty) {
+	translate(Vector2(p_tx, p_ty));
+}
+void Transform2D::translatev(const Vector2 &p_offset) {
+	columns[2] += p_offset;
+}
+
+void Transform2D::translate_localr(real_t p_tx, real_t p_ty) {
+	translate_local(Vector2(p_tx, p_ty));
+}
+void Transform2D::translate_localv(const Vector2 &p_translation) {
+	columns[2] += basis_xform(p_translation);
+}
+
+void Transform2D::orthonormalize() {
+	// Gram-Schmidt Process
+
+	Vector2 x = columns[0];
+	Vector2 y = columns[1];
+
+	x.normalize();
+	y = (y - x * (x.dot(y)));
+	y.normalize();
+
+	columns[0] = x;
+	columns[1] = y;
+}
+
+Transform2D Transform2D::orthonormalized() const {
+	Transform2D on = *this;
+	on.orthonormalize();
+	return on;
+}
+
+bool Transform2D::is_equal_approx(const Transform2D &p_transform) const {
+	return columns[0].is_equal_approx(p_transform.columns[0]) && columns[1].is_equal_approx(p_transform.columns[1]) && columns[2].is_equal_approx(p_transform.columns[2]);
+}
+
+Transform2D Transform2D::looking_at(const Vector2 &p_target) const {
+	Transform2D return_trans = Transform2D(get_rotation(), get_origin());
+	Vector2 target_position = affine_inverse().xform(p_target);
+	return_trans.set_rotation(return_trans.get_rotation() + (target_position * get_scale()).angle());
+	return return_trans;
+}
+
+bool Transform2D::operator==(const Transform2D &p_transform) const {
+	for (int i = 0; i < 3; i++) {
+		if (columns[i] != p_transform.columns[i]) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool Transform2D::operator!=(const Transform2D &p_transform) const {
+	for (int i = 0; i < 3; i++) {
+		if (columns[i] != p_transform.columns[i]) {
+			return true;
+		}
+	}
+
+	return false;
+}
+
+void Transform2D::operator*=(const Transform2D &p_transform) {
+	columns[2] = xform(p_transform.columns[2]);
+
+	real_t x0, x1, y0, y1;
+
+	x0 = tdotx(p_transform.columns[0]);
+	x1 = tdoty(p_transform.columns[0]);
+	y0 = tdotx(p_transform.columns[1]);
+	y1 = tdoty(p_transform.columns[1]);
+
+	columns[0][0] = x0;
+	columns[0][1] = x1;
+	columns[1][0] = y0;
+	columns[1][1] = y1;
+}
+
+Transform2D Transform2D::operator*(const Transform2D &p_transform) const {
+	Transform2D t = *this;
+	t *= p_transform;
+	return t;
+}
+
+void Transform2D::operator*=(const real_t p_val) {
+	columns[0] *= p_val;
+	columns[1] *= p_val;
+	columns[2] *= p_val;
+}
+
+Transform2D Transform2D::operator*(const real_t p_val) const {
+	Transform2D ret(*this);
+	ret *= p_val;
+	return ret;
+}
+
+Transform2D Transform2D::basis_scaled(const Size2 &p_scale) const {
+	Transform2D copy = *this;
+	copy.scale_basis(p_scale);
+	return copy;
+}
+
+Transform2D Transform2D::scaled(const Size2 &p_scale) const {
+	// Equivalent to left multiplication
+	Transform2D copy = *this;
+	copy.scale(p_scale);
+	return copy;
+}
+
+Transform2D Transform2D::scaled_local(const Size2 &p_scale) const {
+	// Equivalent to right multiplication
+	return Transform2D(columns[0] * p_scale.x, columns[1] * p_scale.y, columns[2]);
+}
+
+Transform2D Transform2D::untranslated() const {
+	Transform2D copy = *this;
+	copy.columns[2] = Vector2();
+	return copy;
+}
+
+Transform2D Transform2D::translated(const Vector2 &p_offset) const {
+	// Equivalent to left multiplication
+	return Transform2D(columns[0], columns[1], columns[2] + p_offset);
+}
+
+Transform2D Transform2D::translated_local(const Vector2 &p_offset) const {
+	// Equivalent to right multiplication
+	return Transform2D(columns[0], columns[1], columns[2] + basis_xform(p_offset));
+}
+
+Transform2D Transform2D::rotated(const real_t p_angle) const {
+	// Equivalent to left multiplication
+	return Transform2D(p_angle, Vector2()) * (*this);
+}
+
+Transform2D Transform2D::rotated_local(const real_t p_angle) const {
+	// Equivalent to right multiplication
+	return (*this) * Transform2D(p_angle, Vector2()); // Could be optimized, because origin transform can be skipped.
+}
+
+real_t Transform2D::basis_determinant() const {
+	return columns[0].x * columns[1].y - columns[0].y * columns[1].x;
+}
+
+Transform2D Transform2D::interpolate_with(const Transform2D &p_transform, real_t p_c) const {
+	//extract parameters
+	Vector2 p1 = get_origin();
+	Vector2 p2 = p_transform.get_origin();
+
+	real_t r1 = get_rotation();
+	real_t r2 = p_transform.get_rotation();
+
+	Size2 s1 = get_scale();
+	Size2 s2 = p_transform.get_scale();
+
+	//slerp rotation
+	Vector2 v1(Math::cos(r1), Math::sin(r1));
+	Vector2 v2(Math::cos(r2), Math::sin(r2));
+
+	real_t dot = v1.dot(v2);
+
+	dot = CLAMP(dot, -1, 1);
+
+	Vector2 v;
+
+	if (dot > 0.9995f) {
+		v = Vector2::linear_interpolate(v1, v2, p_c).normalized(); //linearly interpolate to avoid numerical precision issues
+	} else {
+		real_t angle = p_c * Math::acos(dot);
+		Vector2 v3 = (v2 - v1 * dot).normalized();
+		v = v1 * Math::cos(angle) + v3 * Math::sin(angle);
+	}
+
+	//construct matrix
+	Transform2D res(Math::atan2(v.y, v.x), Vector2::linear_interpolate(p1, p2, p_c));
+	res.scale_basis(Vector2::linear_interpolate(s1, s2, p_c));
+	return res;
+}
+
+Transform2D::operator String() const {
+	return "[X: " + columns[0].operator String() +
+			", Y: " + columns[1].operator String() +
+			", O: " + columns[2].operator String() + "]";
+}

core/math/transform_2d.h

@@ -0,0 +1,329 @@
+#ifndef TRANSFORM_2D_H
+#define TRANSFORM_2D_H
+
+/*************************************************************************/
+/*  transform_2d.h                                                       */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/containers/pool_vector.h"
+#include "core/math/rect2.h" // also includes vector2, math_funcs, and ustring
+#include "core/math/rect2i.h" // also includes vector2i, math_funcs, and ustring
+
+struct _NO_DISCARD_CLASS_ Transform2D {
+	// Warning #1: basis of Transform2D is stored differently from Basis. In terms of columns array, the basis matrix looks like "on paper":
+	// M = (columns[0][0] columns[1][0])
+	//     (columns[0][1] columns[1][1])
+	// This is such that the columns, which can be interpreted as basis vectors of the coordinate system "painted" on the object, can be accessed as columns[i].
+	// Note that this is the opposite of the indices in mathematical texts, meaning: $M_{12}$ in a math book corresponds to columns[1][0] here.
+	// This requires additional care when working with explicit indices.
+	// See https://en.wikipedia.org/wiki/Row-_and_column-major_order for further reading.
+
+	// Warning #2: 2D be aware that unlike 3D code, 2D code uses a left-handed coordinate system: Y-axis points down,
+	// and angle is measure from +X to +Y in a clockwise-fashion.
+
+	Vector2 columns[3];
+
+	_FORCE_INLINE_ real_t tdotx(const Vector2 &v) const { return columns[0][0] * v.x + columns[1][0] * v.y; }
+	_FORCE_INLINE_ real_t tdoty(const Vector2 &v) const { return columns[0][1] * v.x + columns[1][1] * v.y; }
+
+	const Vector2 &operator[](int p_idx) const { return columns[p_idx]; }
+	Vector2 &operator[](int p_idx) { return columns[p_idx]; }
+
+	_FORCE_INLINE_ Vector2 get_axis(int p_axis) const {
+		ERR_FAIL_INDEX_V(p_axis, 3, Vector2());
+		return columns[p_axis];
+	}
+	_FORCE_INLINE_ void set_axis(int p_axis, const Vector2 &p_vec) {
+		ERR_FAIL_INDEX(p_axis, 3);
+		columns[p_axis] = p_vec;
+	}
+
+	_FORCE_INLINE_ Vector2 get_column(int p_colum) const {
+		ERR_FAIL_INDEX_V(p_colum, 3, Vector2());
+		return columns[p_colum];
+	}
+	_FORCE_INLINE_ void set_column(int p_colum, const Vector2 &p_vec) {
+		ERR_FAIL_INDEX(p_colum, 3);
+		columns[p_colum] = p_vec;
+	}
+
+	void invert();
+	Transform2D inverse() const;
+
+	void affine_invert();
+	Transform2D affine_inverse() const;
+
+	void set_rotation(real_t p_rot);
+	real_t get_rotation() const;
+	real_t get_skew() const;
+	void set_skew(const real_t p_angle);
+	_FORCE_INLINE_ void set_rotation_and_scale(real_t p_rot, const Size2 &p_scale);
+	_FORCE_INLINE_ void set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew);
+	void rotate(real_t p_phi);
+
+	void scale(const Size2 &p_scale);
+	void scale_basis(const Size2 &p_scale);
+	void translate(real_t p_tx, real_t p_ty);
+	void translate(const Vector2 &p_offset);
+	void translate_local(real_t p_tx, real_t p_ty);
+	void translate_local(const Vector2 &p_translation);
+
+	void translater(real_t p_tx, real_t p_ty);
+	void translatev(const Vector2 &p_offset);
+	void translate_localr(real_t p_tx, real_t p_ty);
+	void translate_localv(const Vector2 &p_translation);
+
+	real_t basis_determinant() const;
+
+	Size2 get_scale() const;
+	void set_scale(const Size2 &p_scale);
+
+	_FORCE_INLINE_ const Vector2 &get_origin() const { return columns[2]; }
+	_FORCE_INLINE_ void set_origin(const Vector2 &p_origin) { columns[2] = p_origin; }
+
+	Transform2D basis_scaled(const Size2 &p_scale) const;
+	Transform2D scaled(const Size2 &p_scale) const;
+	Transform2D scaled_local(const Size2 &p_scale) const;
+	Transform2D translated(const Vector2 &p_offset) const;
+	Transform2D translated_local(const Vector2 &p_offset) const;
+	Transform2D rotated(const real_t p_angle) const;
+	Transform2D rotated_local(const real_t p_angle) const;
+
+	Transform2D untranslated() const;
+
+	void orthonormalize();
+	Transform2D orthonormalized() const;
+	bool is_equal_approx(const Transform2D &p_transform) const;
+
+	Transform2D looking_at(const Vector2 &p_target) const;
+
+	bool operator==(const Transform2D &p_transform) const;
+	bool operator!=(const Transform2D &p_transform) const;
+
+	void operator*=(const Transform2D &p_transform);
+	Transform2D operator*(const Transform2D &p_transform) const;
+	void operator*=(const real_t p_val);
+	Transform2D operator*(const real_t p_val) const;
+
+	Transform2D interpolate_with(const Transform2D &p_transform, real_t p_c) const;
+
+	_FORCE_INLINE_ Vector2 basis_xform(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Vector2 basis_xform_inv(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Vector2 xform(const Vector2 &p_vec) const;
+	_FORCE_INLINE_ Vector2 xform_inv(const Vector2 &p_vec) const;
+
+	_FORCE_INLINE_ Rect2 xform(const Rect2 &p_rect) const;
+	_FORCE_INLINE_ Rect2 xform_inv(const Rect2 &p_rect) const;
+
+	_FORCE_INLINE_ Vector2i basis_xform(const Vector2i &p_vec) const;
+	_FORCE_INLINE_ Vector2i basis_xform_inv(const Vector2i &p_vec) const;
+	_FORCE_INLINE_ Vector2i xform(const Vector2i &p_vec) const;
+	_FORCE_INLINE_ Vector2i xform_inv(const Vector2i &p_vec) const;
+
+	_FORCE_INLINE_ PoolVector<Vector2> xform(const PoolVector<Vector2> &p_array) const;
+	_FORCE_INLINE_ PoolVector<Vector2> xform_inv(const PoolVector<Vector2> &p_array) const;
+	_FORCE_INLINE_ PoolVector<Vector2i> xform(const PoolVector<Vector2i> &p_array) const;
+	_FORCE_INLINE_ PoolVector<Vector2i> xform_inv(const PoolVector<Vector2i> &p_array) const;
+
+	operator String() const;
+
+	Transform2D(real_t xx, real_t xy, real_t yx, real_t yy, real_t ox, real_t oy) {
+		columns[0][0] = xx;
+		columns[0][1] = xy;
+		columns[1][0] = yx;
+		columns[1][1] = yy;
+		columns[2][0] = ox;
+		columns[2][1] = oy;
+	}
+
+	Transform2D(const Vector2 &p_x, const Vector2 &p_y, const Vector2 &p_origin) {
+		columns[0] = p_x;
+		columns[1] = p_y;
+		columns[2] = p_origin;
+	}
+
+	Transform2D(real_t p_rot, const Vector2 &p_pos);
+
+	Transform2D(const real_t p_rot, const Size2 &p_scale, const real_t p_skew, const Vector2 &p_pos);
+
+	Transform2D() {
+		columns[0][0] = 1.0;
+		columns[1][1] = 1.0;
+	}
+};
+
+Vector2 Transform2D::basis_xform(const Vector2 &p_vec) const {
+	return Vector2(
+			tdotx(p_vec),
+			tdoty(p_vec));
+}
+
+Vector2 Transform2D::basis_xform_inv(const Vector2 &p_vec) const {
+	return Vector2(
+			columns[0].dot(p_vec),
+			columns[1].dot(p_vec));
+}
+
+Vector2 Transform2D::xform(const Vector2 &p_vec) const {
+	return Vector2(
+				   tdotx(p_vec),
+				   tdoty(p_vec)) +
+			columns[2];
+}
+Vector2 Transform2D::xform_inv(const Vector2 &p_vec) const {
+	Vector2 v = p_vec - columns[2];
+
+	return Vector2(
+			columns[0].dot(v),
+			columns[1].dot(v));
+}
+Rect2 Transform2D::xform(const Rect2 &p_rect) const {
+	Vector2 x = columns[0] * p_rect.size.x;
+	Vector2 y = columns[1] * p_rect.size.y;
+	Vector2 pos = xform(p_rect.position);
+
+	Rect2 new_rect;
+	new_rect.position = pos;
+	new_rect.expand_to(pos + x);
+	new_rect.expand_to(pos + y);
+	new_rect.expand_to(pos + x + y);
+	return new_rect;
+}
+
+void Transform2D::set_rotation_and_scale(real_t p_rot, const Size2 &p_scale) {
+	columns[0][0] = Math::cos(p_rot) * p_scale.x;
+	columns[1][1] = Math::cos(p_rot) * p_scale.y;
+	columns[1][0] = -Math::sin(p_rot) * p_scale.y;
+	columns[0][1] = Math::sin(p_rot) * p_scale.x;
+}
+
+void Transform2D::set_rotation_scale_and_skew(const real_t p_rot, const Size2 &p_scale, const real_t p_skew) {
+	columns[0][0] = Math::cos(p_rot) * p_scale.x;
+	columns[1][1] = Math::cos(p_rot + p_skew) * p_scale.y;
+	columns[1][0] = -Math::sin(p_rot + p_skew) * p_scale.y;
+	columns[0][1] = Math::sin(p_rot) * p_scale.x;
+}
+
+Rect2 Transform2D::xform_inv(const Rect2 &p_rect) const {
+	Vector2 ends[4] = {
+		xform_inv(p_rect.position),
+		xform_inv(Vector2(p_rect.position.x, p_rect.position.y + p_rect.size.y)),
+		xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y + p_rect.size.y)),
+		xform_inv(Vector2(p_rect.position.x + p_rect.size.x, p_rect.position.y))
+	};
+
+	Rect2 new_rect;
+	new_rect.position = ends[0];
+	new_rect.expand_to(ends[1]);
+	new_rect.expand_to(ends[2]);
+	new_rect.expand_to(ends[3]);
+
+	return new_rect;
+}
+
+Vector2i Transform2D::basis_xform(const Vector2i &p_vec) const {
+	return Vector2i(
+			tdotx(p_vec),
+			tdoty(p_vec));
+}
+
+Vector2i Transform2D::basis_xform_inv(const Vector2i &p_vec) const {
+	return Vector2i(
+			columns[0].dot(p_vec),
+			columns[1].dot(p_vec));
+}
+
+Vector2i Transform2D::xform(const Vector2i &p_vec) const {
+	return Vector2i(
+				   tdotx(p_vec),
+				   tdoty(p_vec)) +
+			columns[2];
+}
+Vector2i Transform2D::xform_inv(const Vector2i &p_vec) const {
+	Vector2i v = p_vec - columns[2];
+
+	return Vector2i(
+			columns[0].dot(v),
+			columns[1].dot(v));
+}
+
+PoolVector<Vector2> Transform2D::xform(const PoolVector<Vector2> &p_array) const {
+	PoolVector<Vector2> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector2>::Read r = p_array.read();
+	PoolVector<Vector2>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform(r[i]);
+	}
+	return array;
+}
+
+PoolVector<Vector2> Transform2D::xform_inv(const PoolVector<Vector2> &p_array) const {
+	PoolVector<Vector2> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector2>::Read r = p_array.read();
+	PoolVector<Vector2>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform_inv(r[i]);
+	}
+	return array;
+}
+
+PoolVector<Vector2i> Transform2D::xform(const PoolVector<Vector2i> &p_array) const {
+	PoolVector<Vector2i> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector2i>::Read r = p_array.read();
+	PoolVector<Vector2i>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform(r[i]);
+	}
+	return array;
+}
+
+PoolVector<Vector2i> Transform2D::xform_inv(const PoolVector<Vector2i> &p_array) const {
+	PoolVector<Vector2i> array;
+	array.resize(p_array.size());
+
+	PoolVector<Vector2i>::Read r = p_array.read();
+	PoolVector<Vector2i>::Write w = array.write();
+
+	for (int i = 0; i < p_array.size(); ++i) {
+		w[i] = xform_inv(r[i]);
+	}
+	return array;
+}
+
+#endif // TRANSFORM_2D_H

core/math/triangle_mesh.cpp

@@ -0,0 +1,722 @@
+/*************************************************************************/
+/*  triangle_mesh.cpp                                                    */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "triangle_mesh.h"
+
+#include "core/containers/sort_array.h"
+
+int TriangleMesh::_create_bvh(BVH *p_bvh, BVH **p_bb, int p_from, int p_size, int p_depth, int &max_depth, int &max_alloc) {
+	if (p_depth > max_depth) {
+		max_depth = p_depth;
+	}
+
+	if (p_size == 1) {
+		return p_bb[p_from] - p_bvh;
+	} else if (p_size == 0) {
+		return -1;
+	}
+
+	AABB aabb;
+	aabb = p_bb[p_from]->aabb;
+	for (int i = 1; i < p_size; i++) {
+		aabb.merge_with(p_bb[p_from + i]->aabb);
+	}
+
+	int li = aabb.get_longest_axis_index();
+
+	switch (li) {
+		case Vector3::AXIS_X: {
+			SortArray<BVH *, BVHCmpX> sort_x;
+			sort_x.nth_element(0, p_size, p_size / 2, &p_bb[p_from]);
+			//sort_x.sort(&p_bb[p_from],p_size);
+		} break;
+		case Vector3::AXIS_Y: {
+			SortArray<BVH *, BVHCmpY> sort_y;
+			sort_y.nth_element(0, p_size, p_size / 2, &p_bb[p_from]);
+			//sort_y.sort(&p_bb[p_from],p_size);
+		} break;
+		case Vector3::AXIS_Z: {
+			SortArray<BVH *, BVHCmpZ> sort_z;
+			sort_z.nth_element(0, p_size, p_size / 2, &p_bb[p_from]);
+			//sort_z.sort(&p_bb[p_from],p_size);
+
+		} break;
+	}
+
+	int left = _create_bvh(p_bvh, p_bb, p_from, p_size / 2, p_depth + 1, max_depth, max_alloc);
+	int right = _create_bvh(p_bvh, p_bb, p_from + p_size / 2, p_size - p_size / 2, p_depth + 1, max_depth, max_alloc);
+
+	int index = max_alloc++;
+	BVH *_new = &p_bvh[index];
+	_new->aabb = aabb;
+	_new->center = aabb.position + aabb.size * 0.5f;
+	_new->face_index = -1;
+	_new->left = left;
+	_new->right = right;
+
+	return index;
+}
+
+void TriangleMesh::get_indices(PoolVector<int> *r_triangles_indices) const {
+	if (!valid) {
+		return;
+	}
+
+	const int triangles_num = triangles.size();
+
+	// Parse vertices indices
+	PoolVector<Triangle>::Read triangles_read = triangles.read();
+
+	r_triangles_indices->resize(triangles_num * 3);
+	PoolVector<int>::Write r_indices_write = r_triangles_indices->write();
+
+	for (int i = 0; i < triangles_num; ++i) {
+		r_indices_write[3 * i + 0] = triangles_read[i].indices[0];
+		r_indices_write[3 * i + 1] = triangles_read[i].indices[1];
+		r_indices_write[3 * i + 2] = triangles_read[i].indices[2];
+	}
+}
+
+void TriangleMesh::create(const PoolVector<Vector3> &p_faces) {
+	valid = false;
+
+	int fc = p_faces.size();
+	ERR_FAIL_COND(!fc || ((fc % 3) != 0));
+	fc /= 3;
+	triangles.resize(fc);
+
+	bvh.resize(fc * 3); //will never be larger than this (todo make better)
+	PoolVector<BVH>::Write bw = bvh.write();
+
+	{
+		//create faces and indices and base bvh
+		//except for the Set for repeated triangles, everything
+		//goes in-place.
+
+		PoolVector<Vector3>::Read r = p_faces.read();
+		PoolVector<Triangle>::Write w = triangles.write();
+		RBMap<Vector3, int> db;
+
+		for (int i = 0; i < fc; i++) {
+			Triangle &f = w[i];
+			const Vector3 *v = &r[i * 3];
+
+			for (int j = 0; j < 3; j++) {
+				int vidx = -1;
+				Vector3 vs = v[j].snapped(Vector3(0.0001, 0.0001, 0.0001));
+				RBMap<Vector3, int>::Element *E = db.find(vs);
+				if (E) {
+					vidx = E->get();
+				} else {
+					vidx = db.size();
+					db[vs] = vidx;
+				}
+
+				f.indices[j] = vidx;
+				if (j == 0) {
+					bw[i].aabb.position = vs;
+				} else {
+					bw[i].aabb.expand_to(vs);
+				}
+			}
+
+			f.normal = Face3(r[i * 3 + 0], r[i * 3 + 1], r[i * 3 + 2]).get_plane().get_normal();
+
+			bw[i].left = -1;
+			bw[i].right = -1;
+			bw[i].face_index = i;
+			bw[i].center = bw[i].aabb.position + bw[i].aabb.size * 0.5f;
+		}
+
+		vertices.resize(db.size());
+		PoolVector<Vector3>::Write vw = vertices.write();
+		for (RBMap<Vector3, int>::Element *E = db.front(); E; E = E->next()) {
+			vw[E->get()] = E->key();
+		}
+	}
+
+	PoolVector<BVH *> bwptrs;
+	bwptrs.resize(fc);
+	PoolVector<BVH *>::Write bwp = bwptrs.write();
+	for (int i = 0; i < fc; i++) {
+		bwp[i] = &bw[i];
+	}
+
+	max_depth = 0;
+	int max_alloc = fc;
+	_create_bvh(bw.ptr(), bwp.ptr(), 0, fc, 1, max_depth, max_alloc);
+
+	bw.release(); //clearup
+	bvh.resize(max_alloc); //resize back
+
+	valid = true;
+}
+
+Vector3 TriangleMesh::get_area_normal(const AABB &p_aabb) const {
+	uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
+
+	enum {
+		TEST_AABB_BIT = 0,
+		VISIT_LEFT_BIT = 1,
+		VISIT_RIGHT_BIT = 2,
+		VISIT_DONE_BIT = 3,
+		VISITED_BIT_SHIFT = 29,
+		NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
+		VISITED_BIT_MASK = ~NODE_IDX_MASK,
+
+	};
+
+	int n_count = 0;
+	Vector3 n;
+
+	int level = 0;
+
+	PoolVector<Triangle>::Read trianglesr = triangles.read();
+	PoolVector<Vector3>::Read verticesr = vertices.read();
+	PoolVector<BVH>::Read bvhr = bvh.read();
+
+	const Triangle *triangleptr = trianglesr.ptr();
+	int pos = bvh.size() - 1;
+	const BVH *bvhptr = bvhr.ptr();
+
+	stack[0] = pos;
+	while (true) {
+		uint32_t node = stack[level] & NODE_IDX_MASK;
+		const BVH &b = bvhptr[node];
+		bool done = false;
+
+		switch (stack[level] >> VISITED_BIT_SHIFT) {
+			case TEST_AABB_BIT: {
+				bool valid = b.aabb.intersects(p_aabb);
+				if (!valid) {
+					stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+				} else {
+					if (b.face_index >= 0) {
+						const Triangle &s = triangleptr[b.face_index];
+						n += s.normal;
+						n_count++;
+
+						stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+					} else {
+						stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
+					}
+				}
+				continue;
+			}
+			case VISIT_LEFT_BIT: {
+				stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.left | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_RIGHT_BIT: {
+				stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.right | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_DONE_BIT: {
+				if (level == 0) {
+					done = true;
+					break;
+				} else {
+					level--;
+				}
+				continue;
+			}
+		}
+
+		if (done) {
+			break;
+		}
+	}
+
+	if (n_count > 0) {
+		n /= n_count;
+	}
+
+	return n;
+}
+
+bool TriangleMesh::intersect_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 &r_point, Vector3 &r_normal) const {
+	uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
+
+	enum {
+		TEST_AABB_BIT = 0,
+		VISIT_LEFT_BIT = 1,
+		VISIT_RIGHT_BIT = 2,
+		VISIT_DONE_BIT = 3,
+		VISITED_BIT_SHIFT = 29,
+		NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
+		VISITED_BIT_MASK = ~NODE_IDX_MASK,
+
+	};
+
+	Vector3 n = (p_end - p_begin).normalized();
+	real_t d = 1e10;
+	bool inters = false;
+
+	int level = 0;
+
+	PoolVector<Triangle>::Read trianglesr = triangles.read();
+	PoolVector<Vector3>::Read verticesr = vertices.read();
+	PoolVector<BVH>::Read bvhr = bvh.read();
+
+	const Triangle *triangleptr = trianglesr.ptr();
+	const Vector3 *vertexptr = verticesr.ptr();
+	int pos = bvh.size() - 1;
+	const BVH *bvhptr = bvhr.ptr();
+
+	stack[0] = pos;
+	while (true) {
+		uint32_t node = stack[level] & NODE_IDX_MASK;
+		const BVH &b = bvhptr[node];
+		bool done = false;
+
+		switch (stack[level] >> VISITED_BIT_SHIFT) {
+			case TEST_AABB_BIT: {
+				bool valid = b.aabb.intersects_segment(p_begin, p_end);
+				//bool valid = b.aabb.intersects(ray_aabb);
+
+				if (!valid) {
+					stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+				} else {
+					if (b.face_index >= 0) {
+						const Triangle &s = triangleptr[b.face_index];
+						Face3 f3(vertexptr[s.indices[0]], vertexptr[s.indices[1]], vertexptr[s.indices[2]]);
+
+						Vector3 res;
+
+						if (f3.intersects_segment(p_begin, p_end, &res)) {
+							real_t nd = n.dot(res);
+							if (nd < d) {
+								d = nd;
+								r_point = res;
+								r_normal = f3.get_plane().get_normal();
+								inters = true;
+							}
+						}
+
+						stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+					} else {
+						stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
+					}
+				}
+				continue;
+			}
+			case VISIT_LEFT_BIT: {
+				stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.left | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_RIGHT_BIT: {
+				stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.right | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_DONE_BIT: {
+				if (level == 0) {
+					done = true;
+					break;
+				} else {
+					level--;
+				}
+				continue;
+			}
+		}
+
+		if (done) {
+			break;
+		}
+	}
+
+	if (inters) {
+		if (n.dot(r_normal) > 0) {
+			r_normal = -r_normal;
+		}
+	}
+
+	return inters;
+}
+
+bool TriangleMesh::intersect_ray(const Vector3 &p_begin, const Vector3 &p_dir, Vector3 &r_point, Vector3 &r_normal) const {
+	uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
+
+	enum {
+		TEST_AABB_BIT = 0,
+		VISIT_LEFT_BIT = 1,
+		VISIT_RIGHT_BIT = 2,
+		VISIT_DONE_BIT = 3,
+		VISITED_BIT_SHIFT = 29,
+		NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
+		VISITED_BIT_MASK = ~NODE_IDX_MASK,
+
+	};
+
+	Vector3 n = p_dir;
+	real_t d = 1e20;
+	bool inters = false;
+
+	int level = 0;
+
+	PoolVector<Triangle>::Read trianglesr = triangles.read();
+	PoolVector<Vector3>::Read verticesr = vertices.read();
+	PoolVector<BVH>::Read bvhr = bvh.read();
+
+	const Triangle *triangleptr = trianglesr.ptr();
+	const Vector3 *vertexptr = verticesr.ptr();
+	int pos = bvh.size() - 1;
+	const BVH *bvhptr = bvhr.ptr();
+
+	stack[0] = pos;
+	while (true) {
+		uint32_t node = stack[level] & NODE_IDX_MASK;
+		const BVH &b = bvhptr[node];
+		bool done = false;
+
+		switch (stack[level] >> VISITED_BIT_SHIFT) {
+			case TEST_AABB_BIT: {
+				bool valid = b.aabb.intersects_ray(p_begin, p_dir);
+				if (!valid) {
+					stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+				} else {
+					if (b.face_index >= 0) {
+						const Triangle &s = triangleptr[b.face_index];
+						Face3 f3(vertexptr[s.indices[0]], vertexptr[s.indices[1]], vertexptr[s.indices[2]]);
+
+						Vector3 res;
+
+						if (f3.intersects_ray(p_begin, p_dir, &res)) {
+							real_t nd = n.dot(res);
+							if (nd < d) {
+								d = nd;
+								r_point = res;
+								r_normal = f3.get_plane().get_normal();
+								inters = true;
+							}
+						}
+
+						stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+					} else {
+						stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
+					}
+				}
+				continue;
+			}
+			case VISIT_LEFT_BIT: {
+				stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.left | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_RIGHT_BIT: {
+				stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.right | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_DONE_BIT: {
+				if (level == 0) {
+					done = true;
+					break;
+				} else {
+					level--;
+				}
+				continue;
+			}
+		}
+
+		if (done) {
+			break;
+		}
+	}
+
+	if (inters) {
+		if (n.dot(r_normal) > 0) {
+			r_normal = -r_normal;
+		}
+	}
+
+	return inters;
+}
+
+bool TriangleMesh::intersect_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const {
+	uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
+
+	//p_fully_inside = true;
+
+	enum {
+		TEST_AABB_BIT = 0,
+		VISIT_LEFT_BIT = 1,
+		VISIT_RIGHT_BIT = 2,
+		VISIT_DONE_BIT = 3,
+		VISITED_BIT_SHIFT = 29,
+		NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
+		VISITED_BIT_MASK = ~NODE_IDX_MASK,
+
+	};
+
+	int level = 0;
+
+	PoolVector<Triangle>::Read trianglesr = triangles.read();
+	PoolVector<Vector3>::Read verticesr = vertices.read();
+	PoolVector<BVH>::Read bvhr = bvh.read();
+
+	const Triangle *triangleptr = trianglesr.ptr();
+	const Vector3 *vertexptr = verticesr.ptr();
+	int pos = bvh.size() - 1;
+	const BVH *bvhptr = bvhr.ptr();
+
+	stack[0] = pos;
+	while (true) {
+		uint32_t node = stack[level] & NODE_IDX_MASK;
+		const BVH &b = bvhptr[node];
+		bool done = false;
+
+		switch (stack[level] >> VISITED_BIT_SHIFT) {
+			case TEST_AABB_BIT: {
+				bool valid = b.aabb.intersects_convex_shape(p_planes, p_plane_count, p_points, p_point_count);
+				if (!valid) {
+					stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+				} else {
+					if (b.face_index >= 0) {
+						const Triangle &s = triangleptr[b.face_index];
+
+						for (int j = 0; j < 3; ++j) {
+							const Vector3 &point = vertexptr[s.indices[j]];
+							const Vector3 &next_point = vertexptr[s.indices[(j + 1) % 3]];
+							Vector3 res;
+							bool over = true;
+							for (int i = 0; i < p_plane_count; i++) {
+								const Plane &p = p_planes[i];
+
+								if (p.intersects_segment(point, next_point, &res)) {
+									bool inisde = true;
+									for (int k = 0; k < p_plane_count; k++) {
+										if (k == i) {
+											continue;
+										}
+										const Plane &pp = p_planes[k];
+										if (pp.is_point_over(res)) {
+											inisde = false;
+											break;
+										}
+									}
+									if (inisde) {
+										return true;
+									}
+								}
+
+								if (p.is_point_over(point)) {
+									over = false;
+									break;
+								}
+							}
+							if (over) {
+								return true;
+							}
+						}
+
+						stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+					} else {
+						stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
+					}
+				}
+				continue;
+			}
+			case VISIT_LEFT_BIT: {
+				stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.left | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_RIGHT_BIT: {
+				stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.right | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_DONE_BIT: {
+				if (level == 0) {
+					done = true;
+					break;
+				} else {
+					level--;
+				}
+				continue;
+			}
+		}
+
+		if (done) {
+			break;
+		}
+	}
+
+	return false;
+}
+
+bool TriangleMesh::inside_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count, Vector3 p_scale) const {
+	uint32_t *stack = (uint32_t *)alloca(sizeof(int) * max_depth);
+
+	enum {
+		TEST_AABB_BIT = 0,
+		VISIT_LEFT_BIT = 1,
+		VISIT_RIGHT_BIT = 2,
+		VISIT_DONE_BIT = 3,
+		VISITED_BIT_SHIFT = 29,
+		NODE_IDX_MASK = (1 << VISITED_BIT_SHIFT) - 1,
+		VISITED_BIT_MASK = ~NODE_IDX_MASK,
+
+	};
+
+	int level = 0;
+
+	PoolVector<Triangle>::Read trianglesr = triangles.read();
+	PoolVector<Vector3>::Read verticesr = vertices.read();
+	PoolVector<BVH>::Read bvhr = bvh.read();
+
+	Transform scale(Basis().scaled(p_scale));
+
+	const Triangle *triangleptr = trianglesr.ptr();
+	const Vector3 *vertexptr = verticesr.ptr();
+	int pos = bvh.size() - 1;
+	const BVH *bvhptr = bvhr.ptr();
+
+	stack[0] = pos;
+	while (true) {
+		uint32_t node = stack[level] & NODE_IDX_MASK;
+		const BVH &b = bvhptr[node];
+		bool done = false;
+
+		switch (stack[level] >> VISITED_BIT_SHIFT) {
+			case TEST_AABB_BIT: {
+				bool intersects = scale.xform(b.aabb).intersects_convex_shape(p_planes, p_plane_count, p_points, p_point_count);
+				if (!intersects) {
+					return false;
+				}
+
+				bool inside = scale.xform(b.aabb).inside_convex_shape(p_planes, p_plane_count);
+				if (inside) {
+					stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+				} else {
+					if (b.face_index >= 0) {
+						const Triangle &s = triangleptr[b.face_index];
+						for (int j = 0; j < 3; ++j) {
+							Vector3 point = scale.xform(vertexptr[s.indices[j]]);
+							for (int i = 0; i < p_plane_count; i++) {
+								const Plane &p = p_planes[i];
+								if (p.is_point_over(point)) {
+									return false;
+								}
+							}
+						}
+
+						stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+
+					} else {
+						stack[level] = (VISIT_LEFT_BIT << VISITED_BIT_SHIFT) | node;
+					}
+				}
+				continue;
+			}
+			case VISIT_LEFT_BIT: {
+				stack[level] = (VISIT_RIGHT_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.left | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_RIGHT_BIT: {
+				stack[level] = (VISIT_DONE_BIT << VISITED_BIT_SHIFT) | node;
+				stack[level + 1] = b.right | TEST_AABB_BIT;
+				level++;
+				continue;
+			}
+			case VISIT_DONE_BIT: {
+				if (level == 0) {
+					done = true;
+					break;
+				} else {
+					level--;
+				}
+				continue;
+			}
+		}
+
+		if (done) {
+			break;
+		}
+	}
+
+	return true;
+}
+
+bool TriangleMesh::is_valid() const {
+	return valid;
+}
+
+PoolVector<Face3> TriangleMesh::get_faces() const {
+	if (!valid) {
+		return PoolVector<Face3>();
+	}
+
+	PoolVector<Face3> faces;
+	int ts = triangles.size();
+	faces.resize(triangles.size());
+
+	PoolVector<Face3>::Write w = faces.write();
+	PoolVector<Triangle>::Read r = triangles.read();
+	PoolVector<Vector3>::Read rv = vertices.read();
+
+	for (int i = 0; i < ts; i++) {
+		for (int j = 0; j < 3; j++) {
+			w[i].vertex[j] = rv[r[i].indices[j]];
+		}
+	}
+
+	w.release();
+	return faces;
+}
+
+TriangleMesh::TriangleMesh() {
+	valid = false;
+	max_depth = 0;
+}

core/math/triangle_mesh.h

@@ -0,0 +1,100 @@
+#ifndef TRIANGLE_MESH_H
+#define TRIANGLE_MESH_H
+
+/*************************************************************************/
+/*  triangle_mesh.h                                                      */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/face3.h"
+#include "core/object/reference.h"
+
+class TriangleMesh : public Reference {
+	GDCLASS(TriangleMesh, Reference);
+
+public:
+	struct Triangle {
+		Vector3 normal;
+		int indices[3];
+	};
+
+private:
+	PoolVector<Triangle> triangles;
+	PoolVector<Vector3> vertices;
+
+	struct BVH {
+		AABB aabb;
+		Vector3 center; //used for sorting
+		int left;
+		int right;
+
+		int face_index;
+	};
+
+	struct BVHCmpX {
+		bool operator()(const BVH *p_left, const BVH *p_right) const {
+			return p_left->center.x < p_right->center.x;
+		}
+	};
+
+	struct BVHCmpY {
+		bool operator()(const BVH *p_left, const BVH *p_right) const {
+			return p_left->center.y < p_right->center.y;
+		}
+	};
+	struct BVHCmpZ {
+		bool operator()(const BVH *p_left, const BVH *p_right) const {
+			return p_left->center.z < p_right->center.z;
+		}
+	};
+
+	int _create_bvh(BVH *p_bvh, BVH **p_bb, int p_from, int p_size, int p_depth, int &max_depth, int &max_alloc);
+
+	PoolVector<BVH> bvh;
+	int max_depth;
+	bool valid;
+
+public:
+	bool is_valid() const;
+	bool intersect_segment(const Vector3 &p_begin, const Vector3 &p_end, Vector3 &r_point, Vector3 &r_normal) const;
+	bool intersect_ray(const Vector3 &p_begin, const Vector3 &p_dir, Vector3 &r_point, Vector3 &r_normal) const;
+	bool intersect_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count) const;
+	bool inside_convex_shape(const Plane *p_planes, int p_plane_count, const Vector3 *p_points, int p_point_count, Vector3 p_scale = Vector3(1, 1, 1)) const;
+	Vector3 get_area_normal(const AABB &p_aabb) const;
+	PoolVector<Face3> get_faces() const;
+
+	const PoolVector<Triangle> &get_triangles() const { return triangles; }
+	const PoolVector<Vector3> &get_vertices() const { return vertices; }
+	void get_indices(PoolVector<int> *r_triangles_indices) const;
+
+	void create(const PoolVector<Vector3> &p_faces);
+	TriangleMesh();
+};
+
+#endif // TRIANGLE_MESH_H

core/math/triangulate.cpp

@@ -0,0 +1,210 @@
+/*************************************************************************/
+/*  triangulate.cpp                                                      */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "triangulate.h"
+
+real_t Triangulate::get_area(const Vector<Vector2> &contour) {
+	int n = contour.size();
+	const Vector2 *c = &contour[0];
+
+	real_t A = 0.0;
+
+	for (int p = n - 1, q = 0; q < n; p = q++) {
+		A += c[p].cross(c[q]);
+	}
+	return A * 0.5f;
+}
+
+/*
+ * `is_inside_triangle` decides if a point P is inside the triangle
+ * defined by A, B, C.
+ */
+bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
+		real_t Bx, real_t By,
+		real_t Cx, real_t Cy,
+		real_t Px, real_t Py,
+		bool include_edges) {
+	real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
+	real_t cCROSSap, bCROSScp, aCROSSbp;
+
+	ax = Cx - Bx;
+	ay = Cy - By;
+	bx = Ax - Cx;
+	by = Ay - Cy;
+	cx = Bx - Ax;
+	cy = By - Ay;
+	apx = Px - Ax;
+	apy = Py - Ay;
+	bpx = Px - Bx;
+	bpy = Py - By;
+	cpx = Px - Cx;
+	cpy = Py - Cy;
+
+	aCROSSbp = ax * bpy - ay * bpx;
+	cCROSSap = cx * apy - cy * apx;
+	bCROSScp = bx * cpy - by * cpx;
+
+	if (include_edges) {
+		return ((aCROSSbp > 0) && (bCROSScp > 0) && (cCROSSap > 0));
+	} else {
+		return ((aCROSSbp >= 0) && (bCROSScp >= 0) && (cCROSSap >= 0));
+	}
+}
+
+bool Triangulate::snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed) {
+	int p;
+	real_t Ax, Ay, Bx, By, Cx, Cy, Px, Py;
+	const Vector2 *contour = &p_contour[0];
+
+	Ax = contour[V[u]].x;
+	Ay = contour[V[u]].y;
+
+	Bx = contour[V[v]].x;
+	By = contour[V[v]].y;
+
+	Cx = contour[V[w]].x;
+	Cy = contour[V[w]].y;
+
+	// It can happen that the triangulation ends up with three aligned vertices to deal with.
+	// In this scenario, making the check below strict may reject the possibility of
+	// forming a last triangle with these aligned vertices, preventing the triangulatiom
+	// from completing.
+	// To avoid that we allow zero-area triangles if all else failed.
+	float threshold = relaxed ? -CMP_EPSILON : CMP_EPSILON;
+
+	if (threshold > (((Bx - Ax) * (Cy - Ay)) - ((By - Ay) * (Cx - Ax)))) {
+		return false;
+	}
+
+	for (p = 0; p < n; p++) {
+		if ((p == u) || (p == v) || (p == w)) {
+			continue;
+		}
+		Px = contour[V[p]].x;
+		Py = contour[V[p]].y;
+		if (is_inside_triangle(Ax, Ay, Bx, By, Cx, Cy, Px, Py, relaxed)) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+bool Triangulate::triangulate(const Vector<Vector2> &contour, Vector<int> &result) {
+	/* allocate and initialize list of Vertices in polygon */
+
+	int n = contour.size();
+	if (n < 3) {
+		return false;
+	}
+
+	Vector<int> V;
+	V.resize(n);
+
+	/* we want a counter-clockwise polygon in V */
+
+	if (0 < get_area(contour)) {
+		for (int v = 0; v < n; v++) {
+			V.write[v] = v;
+		}
+	} else {
+		for (int v = 0; v < n; v++) {
+			V.write[v] = (n - 1) - v;
+		}
+	}
+
+	bool relaxed = false;
+
+	int nv = n;
+
+	/*  remove nv-2 Vertices, creating 1 triangle every time */
+	int count = 2 * nv; /* error detection */
+
+	for (int v = nv - 1; nv > 2;) {
+		/* if we loop, it is probably a non-simple polygon */
+		if (0 >= (count--)) {
+			if (relaxed) {
+				//** Triangulate: ERROR - probable bad polygon!
+				return false;
+			} else {
+				// There may be aligned vertices that the strict
+				// checks prevent from triangulating. In this situation
+				// we are better off adding flat triangles than
+				// failing, so we relax the checks and try one last
+				// round.
+				// Only relaxing the constraints as a last resort avoids
+				// degenerate triangles when they aren't necessary.
+				count = 2 * nv;
+				relaxed = true;
+			}
+		}
+
+		/* three consecutive vertices in current polygon, <u,v,w> */
+		int u = v;
+		if (nv <= u) {
+			u = 0; /* previous */
+		}
+		v = u + 1;
+		if (nv <= v) {
+			v = 0; /* new v    */
+		}
+		int w = v + 1;
+		if (nv <= w) {
+			w = 0; /* next     */
+		}
+
+		if (snip(contour, u, v, w, nv, V, relaxed)) {
+			int a, b, c, s, t;
+
+			/* true names of the vertices */
+			a = V[u];
+			b = V[v];
+			c = V[w];
+
+			/* output Triangle */
+			result.push_back(a);
+			result.push_back(b);
+			result.push_back(c);
+
+			/* remove v from remaining polygon */
+			for (s = v, t = v + 1; t < nv; s++, t++) {
+				V.write[s] = V[t];
+			}
+
+			nv--;
+
+			/* reset error detection counter */
+			count = 2 * nv;
+		}
+	}
+
+	return true;
+}

core/math/triangulate.h

@@ -0,0 +1,64 @@
+#ifndef TRIANGULATE_H
+#define TRIANGULATE_H
+
+/*************************************************************************/
+/*  triangulate.h                                                        */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/vector2.h"
+
+#include "core/containers/vector.h"
+
+/*
+http://www.flipcode.com/archives/Efficient_Polygon_Triangulation.shtml
+*/
+
+class Triangulate {
+public:
+	// triangulate a contour/polygon, places results in STL vector
+	// as series of triangles.
+	static bool triangulate(const Vector<Vector2> &contour, Vector<int> &result);
+
+	// compute area of a contour/polygon
+	static real_t get_area(const Vector<Vector2> &contour);
+
+	// decide if point Px/Py is inside triangle defined by
+	// (Ax,Ay) (Bx,By) (Cx,Cy)
+	static bool is_inside_triangle(real_t Ax, real_t Ay,
+			real_t Bx, real_t By,
+			real_t Cx, real_t Cy,
+			real_t Px, real_t Py,
+			bool include_edges);
+
+private:
+	static bool snip(const Vector<Vector2> &p_contour, int u, int v, int w, int n, const Vector<int> &V, bool relaxed);
+};
+
+#endif

core/math/vector2.cpp

@@ -0,0 +1,176 @@
+/*************************************************************************/
+/*  vector2.cpp                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "vector2.h"
+
+#include "core/string/ustring.h"
+
+real_t Vector2::angle() const {
+	return Math::atan2(y, x);
+}
+
+real_t Vector2::length() const {
+	return Math::sqrt(x * x + y * y);
+}
+
+real_t Vector2::length_squared() const {
+	return x * x + y * y;
+}
+
+void Vector2::normalize() {
+	real_t l = x * x + y * y;
+	if (l != 0) {
+		l = Math::sqrt(l);
+		x /= l;
+		y /= l;
+	}
+}
+
+Vector2 Vector2::normalized() const {
+	Vector2 v = *this;
+	v.normalize();
+	return v;
+}
+
+bool Vector2::is_normalized() const {
+	// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
+	return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON);
+}
+
+real_t Vector2::distance_to(const Vector2 &p_vector2) const {
+	return Math::sqrt((x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y));
+}
+
+real_t Vector2::distance_squared_to(const Vector2 &p_vector2) const {
+	return (x - p_vector2.x) * (x - p_vector2.x) + (y - p_vector2.y) * (y - p_vector2.y);
+}
+
+real_t Vector2::angle_to(const Vector2 &p_vector2) const {
+	return Math::atan2(cross(p_vector2), dot(p_vector2));
+}
+
+real_t Vector2::angle_to_point(const Vector2 &p_vector2) const {
+	return Math::atan2(y - p_vector2.y, x - p_vector2.x);
+}
+
+real_t Vector2::dot(const Vector2 &p_other) const {
+	return x * p_other.x + y * p_other.y;
+}
+
+real_t Vector2::cross(const Vector2 &p_other) const {
+	return x * p_other.y - y * p_other.x;
+}
+
+Vector2 Vector2::sign() const {
+	return Vector2(SGN(x), SGN(y));
+}
+
+Vector2 Vector2::floor() const {
+	return Vector2(Math::floor(x), Math::floor(y));
+}
+
+Vector2 Vector2::ceil() const {
+	return Vector2(Math::ceil(x), Math::ceil(y));
+}
+
+Vector2 Vector2::round() const {
+	return Vector2(Math::round(x), Math::round(y));
+}
+
+Vector2 Vector2::rotated(real_t p_by) const {
+	Vector2 v;
+	v.set_rotation(angle() + p_by);
+	v *= length();
+	return v;
+}
+
+Vector2 Vector2::posmod(const real_t p_mod) const {
+	return Vector2(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod));
+}
+
+Vector2 Vector2::posmodv(const Vector2 &p_modv) const {
+	return Vector2(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y));
+}
+
+Vector2 Vector2::project(const Vector2 &p_to) const {
+	return p_to * (dot(p_to) / p_to.length_squared());
+}
+
+Vector2 Vector2::snapped(const Vector2 &p_by) const {
+	return Vector2(
+			Math::stepify(x, p_by.x),
+			Math::stepify(y, p_by.y));
+}
+
+Vector2 Vector2::limit_length(const real_t p_len) const {
+	const real_t l = length();
+	Vector2 v = *this;
+	if (l > 0 && p_len < l) {
+		v /= l;
+		v *= p_len;
+	}
+
+	return v;
+}
+
+Vector2 Vector2::move_toward(const Vector2 &p_to, const real_t p_delta) const {
+	Vector2 v = *this;
+	Vector2 vd = p_to - v;
+	real_t len = vd.length();
+	return len <= p_delta || len < (real_t)CMP_EPSILON ? p_to : v + vd / len * p_delta;
+}
+
+// slide returns the component of the vector along the given plane, specified by its normal vector.
+Vector2 Vector2::slide(const Vector2 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector2(), "The normal Vector2 must be normalized.");
+#endif
+	return *this - p_normal * this->dot(p_normal);
+}
+
+Vector2 Vector2::bounce(const Vector2 &p_normal) const {
+	return -reflect(p_normal);
+}
+
+Vector2 Vector2::reflect(const Vector2 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector2(), "The normal Vector2 must be normalized.");
+#endif
+	return 2 * p_normal * this->dot(p_normal) - *this;
+}
+
+bool Vector2::is_equal_approx(const Vector2 &p_v) const {
+	return Math::is_equal_approx(x, p_v.x) && Math::is_equal_approx(y, p_v.y);
+}
+
+Vector2::operator String() const {
+	return "(" + String::num_real(x) + ", " + String::num_real(y) + ")";
+}

core/math/vector2.h

@@ -0,0 +1,305 @@
+#ifndef VECTOR2_H
+#define VECTOR2_H
+
+/*************************************************************************/
+/*  vector2.h                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/math_funcs.h"
+
+#include "core/error/error_macros.h"
+
+class String;
+
+struct _NO_DISCARD_CLASS_ Vector2 {
+	static const int AXIS_COUNT = 2;
+
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+	};
+
+	union {
+		struct {
+			union {
+				real_t x;
+				real_t width;
+			};
+			union {
+				real_t y;
+				real_t height;
+			};
+		};
+
+		real_t coord[2];
+	};
+
+	_FORCE_INLINE_ real_t &operator[](int p_idx) {
+		DEV_ASSERT((unsigned int)p_idx < 2);
+		return coord[p_idx];
+	}
+	_FORCE_INLINE_ const real_t &operator[](int p_idx) const {
+		DEV_ASSERT((unsigned int)p_idx < 2);
+		return coord[p_idx];
+	}
+
+	_FORCE_INLINE_ void set_all(real_t p_value) {
+		x = y = p_value;
+	}
+
+	_FORCE_INLINE_ int min_axis() const {
+		return x < y ? 0 : 1;
+	}
+
+	_FORCE_INLINE_ int max_axis() const {
+		return x < y ? 1 : 0;
+	}
+
+	void normalize();
+	Vector2 normalized() const;
+	bool is_normalized() const;
+
+	real_t length() const;
+	real_t length_squared() const;
+	Vector2 limit_length(const real_t p_len = 1.0) const;
+
+	Vector2 min(const Vector2 &p_vector2) const {
+		return Vector2(MIN(x, p_vector2.x), MIN(y, p_vector2.y));
+	}
+
+	Vector2 max(const Vector2 &p_vector2) const {
+		return Vector2(MAX(x, p_vector2.x), MAX(y, p_vector2.y));
+	}
+
+	real_t distance_to(const Vector2 &p_vector2) const;
+	real_t distance_squared_to(const Vector2 &p_vector2) const;
+	real_t angle_to(const Vector2 &p_vector2) const;
+	real_t angle_to_point(const Vector2 &p_vector2) const;
+	_FORCE_INLINE_ Vector2 direction_to(const Vector2 &p_to) const;
+
+	real_t dot(const Vector2 &p_other) const;
+	real_t cross(const Vector2 &p_other) const;
+	Vector2 posmod(const real_t p_mod) const;
+	Vector2 posmodv(const Vector2 &p_modv) const;
+	Vector2 project(const Vector2 &p_to) const;
+
+	Vector2 plane_project(real_t p_d, const Vector2 &p_vec) const;
+
+	_FORCE_INLINE_ static Vector2 linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_weight);
+	_FORCE_INLINE_ Vector2 linear_interpolate(const Vector2 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 slerp(const Vector2 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, real_t p_weight) const;
+	_FORCE_INLINE_ Vector2 bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const;
+
+	Vector2 move_toward(const Vector2 &p_to, const real_t p_delta) const;
+
+	Vector2 slide(const Vector2 &p_normal) const;
+	Vector2 bounce(const Vector2 &p_normal) const;
+	Vector2 reflect(const Vector2 &p_normal) const;
+
+	bool is_equal_approx(const Vector2 &p_v) const;
+
+	Vector2 operator+(const Vector2 &p_v) const;
+	void operator+=(const Vector2 &p_v);
+	Vector2 operator-(const Vector2 &p_v) const;
+	void operator-=(const Vector2 &p_v);
+	Vector2 operator*(const Vector2 &p_v1) const;
+
+	Vector2 operator*(const real_t &rvalue) const;
+	void operator*=(const real_t &rvalue);
+	void operator*=(const Vector2 &rvalue) { *this = *this * rvalue; }
+
+	Vector2 operator/(const Vector2 &p_v1) const;
+
+	Vector2 operator/(const real_t &rvalue) const;
+
+	void operator/=(const real_t &rvalue);
+	void operator/=(const Vector2 &rvalue) { *this = *this / rvalue; }
+
+	Vector2 operator-() const;
+
+	bool operator==(const Vector2 &p_vec2) const;
+	bool operator!=(const Vector2 &p_vec2) const;
+
+	bool operator<(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y < p_vec2.y) : (x < p_vec2.x); }
+	bool operator>(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y > p_vec2.y) : (x > p_vec2.x); }
+	bool operator<=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y <= p_vec2.y) : (x < p_vec2.x); }
+	bool operator>=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y >= p_vec2.y) : (x > p_vec2.x); }
+
+	real_t angle() const;
+
+	void set_rotation(real_t p_radians) {
+		x = Math::cos(p_radians);
+		y = Math::sin(p_radians);
+	}
+
+	_FORCE_INLINE_ Vector2 abs() const {
+		return Vector2(Math::abs(x), Math::abs(y));
+	}
+
+	Vector2 rotated(real_t p_by) const;
+	_FORCE_INLINE_ Vector2 tangent() const {
+		return Vector2(y, -x);
+	}
+	_FORCE_INLINE_ Vector2 orthogonal() const {
+		return Vector2(y, -x);
+	}
+
+	Vector2 sign() const;
+	Vector2 floor() const;
+	Vector2 ceil() const;
+	Vector2 round() const;
+	Vector2 snapped(const Vector2 &p_by) const;
+	real_t aspect() const { return width / height; }
+
+	operator String() const;
+
+	_FORCE_INLINE_ Vector2(real_t p_x, real_t p_y) {
+		x = p_x;
+		y = p_y;
+	}
+	_FORCE_INLINE_ Vector2() { x = y = 0; }
+};
+
+_FORCE_INLINE_ Vector2 Vector2::plane_project(real_t p_d, const Vector2 &p_vec) const {
+	return p_vec - *this * (dot(p_vec) - p_d);
+}
+
+_FORCE_INLINE_ Vector2 operator*(real_t p_scalar, const Vector2 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+_FORCE_INLINE_ Vector2 Vector2::operator+(const Vector2 &p_v) const {
+	return Vector2(x + p_v.x, y + p_v.y);
+}
+_FORCE_INLINE_ void Vector2::operator+=(const Vector2 &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+}
+_FORCE_INLINE_ Vector2 Vector2::operator-(const Vector2 &p_v) const {
+	return Vector2(x - p_v.x, y - p_v.y);
+}
+_FORCE_INLINE_ void Vector2::operator-=(const Vector2 &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+}
+
+_FORCE_INLINE_ Vector2 Vector2::operator*(const Vector2 &p_v1) const {
+	return Vector2(x * p_v1.x, y * p_v1.y);
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator*(const real_t &rvalue) const {
+	return Vector2(x * rvalue, y * rvalue);
+};
+_FORCE_INLINE_ void Vector2::operator*=(const real_t &rvalue) {
+	x *= rvalue;
+	y *= rvalue;
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator/(const Vector2 &p_v1) const {
+	return Vector2(x / p_v1.x, y / p_v1.y);
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator/(const real_t &rvalue) const {
+	return Vector2(x / rvalue, y / rvalue);
+};
+
+_FORCE_INLINE_ void Vector2::operator/=(const real_t &rvalue) {
+	x /= rvalue;
+	y /= rvalue;
+};
+
+_FORCE_INLINE_ Vector2 Vector2::operator-() const {
+	return Vector2(-x, -y);
+}
+
+_FORCE_INLINE_ bool Vector2::operator==(const Vector2 &p_vec2) const {
+	return x == p_vec2.x && y == p_vec2.y;
+}
+_FORCE_INLINE_ bool Vector2::operator!=(const Vector2 &p_vec2) const {
+	return x != p_vec2.x || y != p_vec2.y;
+}
+
+Vector2 Vector2::linear_interpolate(const Vector2 &p_to, real_t p_weight) const {
+	Vector2 res = *this;
+
+	res.x += (p_weight * (p_to.x - x));
+	res.y += (p_weight * (p_to.y - y));
+
+	return res;
+}
+
+Vector2 Vector2::slerp(const Vector2 &p_to, real_t p_weight) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!is_normalized(), Vector2(), "The start Vector2 must be normalized.");
+#endif
+	real_t theta = angle_to(p_to);
+	return rotated(theta * p_weight);
+}
+
+Vector2 Vector2::bezier_interpolate(const Vector2 &p_control_1, const Vector2 &p_control_2, const Vector2 &p_end, const real_t p_t) const {
+	Vector2 res = *this;
+
+	/* Formula from Wikipedia article on Bezier curves. */
+	real_t omt = (1.0 - p_t);
+	real_t omt2 = omt * omt;
+	real_t omt3 = omt2 * omt;
+	real_t t2 = p_t * p_t;
+	real_t t3 = t2 * p_t;
+
+	return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+}
+
+Vector2 Vector2::cubic_interpolate(const Vector2 &p_b, const Vector2 &p_pre_a, const Vector2 &p_post_b, const real_t p_weight) const {
+	Vector2 res = *this;
+	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
+	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
+	return res;
+}
+
+Vector2 Vector2::direction_to(const Vector2 &p_to) const {
+	Vector2 ret(p_to.x - x, p_to.y - y);
+	ret.normalize();
+	return ret;
+}
+
+Vector2 Vector2::linear_interpolate(const Vector2 &p_a, const Vector2 &p_b, real_t p_weight) {
+	Vector2 res = p_a;
+
+	res.x += (p_weight * (p_b.x - p_a.x));
+	res.y += (p_weight * (p_b.y - p_a.y));
+
+	return res;
+}
+
+typedef Vector2 Size2;
+typedef Vector2 Point2;
+
+#endif // VECTOR2_H

core/math/vector2i.cpp

@@ -0,0 +1,103 @@
+/*************************************************************************/
+/*  vector2i.cpp                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "vector2i.h"
+
+#include "core/string/ustring.h"
+
+Vector2i Vector2i::clamp(const Vector2i &p_min, const Vector2i &p_max) const {
+	return Vector2i(
+			CLAMP(x, p_min.x, p_max.x),
+			CLAMP(y, p_min.y, p_max.y));
+}
+
+int64_t Vector2i::length_squared() const {
+	return x * (int64_t)x + y * (int64_t)y;
+}
+
+double Vector2i::length() const {
+	return Math::sqrt((double)length_squared());
+}
+
+Vector2i Vector2i::operator+(const Vector2i &p_v) const {
+	return Vector2i(x + p_v.x, y + p_v.y);
+}
+void Vector2i::operator+=(const Vector2i &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+}
+Vector2i Vector2i::operator-(const Vector2i &p_v) const {
+	return Vector2i(x - p_v.x, y - p_v.y);
+}
+void Vector2i::operator-=(const Vector2i &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+}
+
+Vector2i Vector2i::operator*(const Vector2i &p_v1) const {
+	return Vector2i(x * p_v1.x, y * p_v1.y);
+};
+
+Vector2i Vector2i::operator*(const int &rvalue) const {
+	return Vector2i(x * rvalue, y * rvalue);
+};
+void Vector2i::operator*=(const int &rvalue) {
+	x *= rvalue;
+	y *= rvalue;
+};
+
+Vector2i Vector2i::operator/(const Vector2i &p_v1) const {
+	return Vector2i(x / p_v1.x, y / p_v1.y);
+};
+
+Vector2i Vector2i::operator/(const int &rvalue) const {
+	return Vector2i(x / rvalue, y / rvalue);
+};
+
+void Vector2i::operator/=(const int &rvalue) {
+	x /= rvalue;
+	y /= rvalue;
+};
+
+Vector2i Vector2i::operator-() const {
+	return Vector2i(-x, -y);
+}
+
+bool Vector2i::operator==(const Vector2i &p_vec2) const {
+	return x == p_vec2.x && y == p_vec2.y;
+}
+bool Vector2i::operator!=(const Vector2i &p_vec2) const {
+	return x != p_vec2.x || y != p_vec2.y;
+}
+
+Vector2i::operator String() const {
+	return "(" + itos(x) + ", " + itos(y) + ")";
+}

core/math/vector2i.h

@@ -0,0 +1,167 @@
+#ifndef VECTOR2I_H
+#define VECTOR2I_H
+
+/*************************************************************************/
+/*  vector2i.h                                                           */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/error/error_macros.h"
+#include "core/math/math_funcs.h"
+
+#include "vector2.h"
+
+class String;
+
+struct _NO_DISCARD_CLASS_ Vector2i {
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+	};
+
+	union {
+		struct {
+			union {
+				int x;
+				int width;
+			};
+			union {
+				int y;
+				int height;
+			};
+		};
+
+		int coord[2];
+	};
+
+	_FORCE_INLINE_ int &operator[](int p_idx) {
+		DEV_ASSERT((unsigned int)p_idx < 2);
+		return coord[p_idx];
+	}
+	_FORCE_INLINE_ const int &operator[](int p_idx) const {
+		DEV_ASSERT((unsigned int)p_idx < 2);
+		return coord[p_idx];
+	}
+
+	_FORCE_INLINE_ void set_all(int p_value) {
+		x = y = p_value;
+	}
+
+	_FORCE_INLINE_ int min_axis() const {
+		return x < y ? 0 : 1;
+	}
+
+	_FORCE_INLINE_ int max_axis() const {
+		return x < y ? 1 : 0;
+	}
+
+	Vector2i min(const Vector2i &p_vector2i) const {
+		return Vector2i(MIN(x, p_vector2i.x), MIN(y, p_vector2i.y));
+	}
+
+	Vector2i max(const Vector2i &p_vector2i) const {
+		return Vector2i(MAX(x, p_vector2i.x), MAX(y, p_vector2i.y));
+	}
+
+	_FORCE_INLINE_ static Vector2i linear_interpolate(const Vector2i &p_a, const Vector2i &p_b, real_t p_weight);
+	_FORCE_INLINE_ Vector2i linear_interpolate(const Vector2i &p_to, real_t p_weight) const;
+
+	Vector2i operator+(const Vector2i &p_v) const;
+	void operator+=(const Vector2i &p_v);
+	Vector2i operator-(const Vector2i &p_v) const;
+	void operator-=(const Vector2i &p_v);
+	Vector2i operator*(const Vector2i &p_v1) const;
+
+	Vector2i operator*(const int &rvalue) const;
+	void operator*=(const int &rvalue);
+
+	Vector2i operator/(const Vector2i &p_v1) const;
+
+	Vector2i operator/(const int &rvalue) const;
+
+	void operator/=(const int &rvalue);
+
+	Vector2i operator-() const;
+	bool operator<(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y < p_vec2.y) : (x < p_vec2.x); }
+	bool operator>(const Vector2i &p_vec2) const { return (x == p_vec2.x) ? (y > p_vec2.y) : (x > p_vec2.x); }
+	bool operator<=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y <= p_vec2.y) : (x < p_vec2.x); }
+	bool operator>=(const Vector2 &p_vec2) const { return x == p_vec2.x ? (y >= p_vec2.y) : (x > p_vec2.x); }
+
+	bool operator==(const Vector2i &p_vec2) const;
+	bool operator!=(const Vector2i &p_vec2) const;
+
+	int64_t length_squared() const;
+	double length() const;
+
+	real_t aspect() const { return width / (real_t)height; }
+	Vector2i sign() const { return Vector2i(SGN(x), SGN(y)); }
+	Vector2i abs() const { return Vector2i(ABS(x), ABS(y)); }
+	Vector2i clamp(const Vector2i &p_min, const Vector2i &p_max) const;
+
+	Vector2 to_vector2() const { return Vector2(x, y); }
+
+	operator String() const;
+	operator Vector2() const { return Vector2(x, y); }
+
+	inline Vector2i(const Vector2 &p_vec2) {
+		x = (int)p_vec2.x;
+		y = (int)p_vec2.y;
+	}
+	inline Vector2i(int p_x, int p_y) {
+		x = p_x;
+		y = p_y;
+	}
+	inline Vector2i() {
+		x = 0;
+		y = 0;
+	}
+};
+
+Vector2i Vector2i::linear_interpolate(const Vector2i &p_a, const Vector2i &p_b, real_t p_weight) {
+	Vector2i res = p_a;
+
+	res.x += (p_weight * (p_b.x - p_a.x));
+	res.y += (p_weight * (p_b.y - p_a.y));
+
+	return res;
+}
+
+Vector2i Vector2i::linear_interpolate(const Vector2i &p_to, real_t p_weight) const {
+	Vector2 res = *this;
+
+	res.x += (p_weight * (p_to.x - x));
+	res.y += (p_weight * (p_to.y - y));
+
+	return res;
+}
+
+typedef Vector2i Size2i;
+typedef Vector2i Point2i;
+
+#endif // VECTOR2_H

core/math/vector3.cpp

@@ -0,0 +1,111 @@
+/*************************************************************************/
+/*  vector3.cpp                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "vector3.h"
+
+#include "core/math/basis.h"
+
+void Vector3::rotate(const Vector3 &p_axis, real_t p_phi) {
+	*this = Basis(p_axis, p_phi).xform(*this);
+}
+
+Vector3 Vector3::rotated(const Vector3 &p_axis, real_t p_phi) const {
+	Vector3 r = *this;
+	r.rotate(p_axis, p_phi);
+	return r;
+}
+
+void Vector3::set_axis(int p_axis, real_t p_value) {
+	ERR_FAIL_INDEX(p_axis, 3);
+	coord[p_axis] = p_value;
+}
+real_t Vector3::get_axis(int p_axis) const {
+	ERR_FAIL_INDEX_V(p_axis, 3, 0);
+	return operator[](p_axis);
+}
+
+void Vector3::snap(const Vector3 &p_val) {
+	x = Math::stepify(x, p_val.x);
+	y = Math::stepify(y, p_val.y);
+	z = Math::stepify(z, p_val.z);
+}
+Vector3 Vector3::snapped(const Vector3 &p_val) const {
+	Vector3 v = *this;
+	v.snap(p_val);
+	return v;
+}
+
+Vector3 Vector3::limit_length(const real_t p_len) const {
+	const real_t l = length();
+	Vector3 v = *this;
+	if (l > 0 && p_len < l) {
+		v /= l;
+		v *= p_len;
+	}
+
+	return v;
+}
+
+Vector3 Vector3::move_toward(const Vector3 &p_to, const real_t p_delta) const {
+	Vector3 v = *this;
+	Vector3 vd = p_to - v;
+	real_t len = vd.length();
+	return len <= p_delta || len < (real_t)CMP_EPSILON ? p_to : v + vd / len * p_delta;
+}
+
+Basis Vector3::outer(const Vector3 &p_b) const {
+	Vector3 row0(x * p_b.x, x * p_b.y, x * p_b.z);
+	Vector3 row1(y * p_b.x, y * p_b.y, y * p_b.z);
+	Vector3 row2(z * p_b.x, z * p_b.y, z * p_b.z);
+
+	return Basis(row0, row1, row2);
+}
+
+Basis Vector3::to_diagonal_matrix() const {
+	return Basis(x, 0, 0,
+			0, y, 0,
+			0, 0, z);
+}
+
+Vector3 Vector3::clamp(const Vector3 &p_min, const Vector3 &p_max) const {
+	return Vector3(
+			CLAMP(x, p_min.x, p_max.x),
+			CLAMP(y, p_min.y, p_max.y),
+			CLAMP(z, p_min.z, p_max.z));
+}
+
+bool Vector3::is_equal_approx(const Vector3 &p_v) const {
+	return Math::is_equal_approx(x, p_v.x) && Math::is_equal_approx(y, p_v.y) && Math::is_equal_approx(z, p_v.z);
+}
+
+Vector3::operator String() const {
+	return "(" + String::num_real(x) + ", " + String::num_real(y) + ", " + String::num_real(z) + ")";
+}

core/math/vector3.h

@@ -0,0 +1,508 @@
+#ifndef VECTOR3_H
+#define VECTOR3_H
+
+/*************************************************************************/
+/*  vector3.h                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/math/math_funcs.h"
+#include "core/string/ustring.h"
+
+struct Basis;
+
+struct _NO_DISCARD_CLASS_ Vector3 {
+	static const int AXIS_COUNT = 3;
+
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+		AXIS_Z,
+	};
+
+	union {
+		struct {
+			real_t x;
+			real_t y;
+			real_t z;
+		};
+
+		real_t coord[3];
+	};
+
+	_FORCE_INLINE_ const real_t &operator[](int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 3);
+		return coord[p_axis];
+	}
+
+	_FORCE_INLINE_ real_t &operator[](int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 3);
+		return coord[p_axis];
+	}
+
+	void set_axis(int p_axis, real_t p_value);
+	real_t get_axis(int p_axis) const;
+
+	_FORCE_INLINE_ void set_all(real_t p_value) {
+		x = y = z = p_value;
+	}
+
+	_FORCE_INLINE_ int min_axis() const {
+		return x < y ? (x < z ? 0 : 2) : (y < z ? 1 : 2);
+	}
+
+	_FORCE_INLINE_ int max_axis() const {
+		return x < y ? (y < z ? 2 : 1) : (x < z ? 2 : 0);
+	}
+
+	_FORCE_INLINE_ real_t length() const;
+	_FORCE_INLINE_ real_t length_squared() const;
+
+	_FORCE_INLINE_ void normalize();
+	_FORCE_INLINE_ Vector3 normalized() const;
+	_FORCE_INLINE_ bool is_normalized() const;
+	_FORCE_INLINE_ Vector3 inverse() const;
+	Vector3 limit_length(const real_t p_len = 1.0) const;
+
+	_FORCE_INLINE_ void zero();
+
+	void snap(const Vector3 &p_val);
+	Vector3 snapped(const Vector3 &p_val) const;
+
+	void rotate(const Vector3 &p_axis, real_t p_phi);
+	Vector3 rotated(const Vector3 &p_axis, real_t p_phi) const;
+
+	/* Static Methods between 2 vector3s */
+
+	_FORCE_INLINE_ Vector3 linear_interpolate(const Vector3 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 slerp(const Vector3 &p_to, real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, real_t p_weight) const;
+	_FORCE_INLINE_ Vector3 bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const;
+
+	Vector3 move_toward(const Vector3 &p_to, const real_t p_delta) const;
+
+	_FORCE_INLINE_ Vector3 cross(const Vector3 &p_b) const;
+	_FORCE_INLINE_ real_t dot(const Vector3 &p_b) const;
+	Basis outer(const Vector3 &p_b) const;
+	Basis to_diagonal_matrix() const;
+
+	_FORCE_INLINE_ Vector3 abs() const;
+	_FORCE_INLINE_ Vector3 floor() const;
+	_FORCE_INLINE_ Vector3 sign() const;
+	_FORCE_INLINE_ Vector3 ceil() const;
+	_FORCE_INLINE_ Vector3 round() const;
+	Vector3 clamp(const Vector3 &p_min, const Vector3 &p_max) const;
+
+	_FORCE_INLINE_ real_t distance_to(const Vector3 &p_to) const;
+	_FORCE_INLINE_ real_t distance_squared_to(const Vector3 &p_to) const;
+
+	_FORCE_INLINE_ Vector3 posmod(const real_t p_mod) const;
+	_FORCE_INLINE_ Vector3 posmodv(const Vector3 &p_modv) const;
+	_FORCE_INLINE_ Vector3 project(const Vector3 &p_to) const;
+
+	_FORCE_INLINE_ real_t angle_to(const Vector3 &p_to) const;
+	_FORCE_INLINE_ real_t signed_angle_to(const Vector3 &p_to, const Vector3 &p_axis) const;
+	_FORCE_INLINE_ Vector3 direction_to(const Vector3 &p_to) const;
+
+	_FORCE_INLINE_ Vector3 slide(const Vector3 &p_normal) const;
+	_FORCE_INLINE_ Vector3 bounce(const Vector3 &p_normal) const;
+	_FORCE_INLINE_ Vector3 reflect(const Vector3 &p_normal) const;
+
+	bool is_equal_approx(const Vector3 &p_v) const;
+	inline bool is_equal_approx(const Vector3 &p_v, real_t p_tolerance) const;
+	inline bool is_equal_approxt(const Vector3 &p_v, real_t p_tolerance) const;
+
+	/* Operators */
+
+	_FORCE_INLINE_ Vector3 &operator+=(const Vector3 &p_v);
+	_FORCE_INLINE_ Vector3 operator+(const Vector3 &p_v) const;
+	_FORCE_INLINE_ Vector3 &operator-=(const Vector3 &p_v);
+	_FORCE_INLINE_ Vector3 operator-(const Vector3 &p_v) const;
+	_FORCE_INLINE_ Vector3 &operator*=(const Vector3 &p_v);
+	_FORCE_INLINE_ Vector3 operator*(const Vector3 &p_v) const;
+	_FORCE_INLINE_ Vector3 &operator/=(const Vector3 &p_v);
+	_FORCE_INLINE_ Vector3 operator/(const Vector3 &p_v) const;
+
+	_FORCE_INLINE_ Vector3 &operator*=(real_t p_scalar);
+	_FORCE_INLINE_ Vector3 operator*(real_t p_scalar) const;
+	_FORCE_INLINE_ Vector3 &operator/=(real_t p_scalar);
+	_FORCE_INLINE_ Vector3 operator/(real_t p_scalar) const;
+
+	_FORCE_INLINE_ Vector3 operator-() const;
+
+	_FORCE_INLINE_ bool operator==(const Vector3 &p_v) const;
+	_FORCE_INLINE_ bool operator!=(const Vector3 &p_v) const;
+	_FORCE_INLINE_ bool operator<(const Vector3 &p_v) const;
+	_FORCE_INLINE_ bool operator<=(const Vector3 &p_v) const;
+	_FORCE_INLINE_ bool operator>(const Vector3 &p_v) const;
+	_FORCE_INLINE_ bool operator>=(const Vector3 &p_v) const;
+
+	operator String() const;
+
+	_FORCE_INLINE_ Vector3(real_t p_x, real_t p_y, real_t p_z) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+	}
+	_FORCE_INLINE_ Vector3() { x = y = z = 0; }
+};
+
+Vector3 Vector3::cross(const Vector3 &p_b) const {
+	Vector3 ret(
+			(y * p_b.z) - (z * p_b.y),
+			(z * p_b.x) - (x * p_b.z),
+			(x * p_b.y) - (y * p_b.x));
+
+	return ret;
+}
+
+real_t Vector3::dot(const Vector3 &p_b) const {
+	return x * p_b.x + y * p_b.y + z * p_b.z;
+}
+
+Vector3 Vector3::abs() const {
+	return Vector3(Math::abs(x), Math::abs(y), Math::abs(z));
+}
+
+Vector3 Vector3::sign() const {
+	return Vector3(SGN(x), SGN(y), SGN(z));
+}
+
+Vector3 Vector3::floor() const {
+	return Vector3(Math::floor(x), Math::floor(y), Math::floor(z));
+}
+
+Vector3 Vector3::ceil() const {
+	return Vector3(Math::ceil(x), Math::ceil(y), Math::ceil(z));
+}
+
+Vector3 Vector3::round() const {
+	return Vector3(Math::round(x), Math::round(y), Math::round(z));
+}
+
+Vector3 Vector3::linear_interpolate(const Vector3 &p_to, real_t p_weight) const {
+	return Vector3(
+			x + (p_weight * (p_to.x - x)),
+			y + (p_weight * (p_to.y - y)),
+			z + (p_weight * (p_to.z - z)));
+}
+
+Vector3 Vector3::slerp(const Vector3 &p_to, const real_t p_weight) const {
+	// This method seems more complicated than it really is, since we write out
+	// the internals of some methods for efficiency (mainly, checking length).
+	real_t start_length_sq = length_squared();
+	real_t end_length_sq = p_to.length_squared();
+	if (unlikely(start_length_sq == 0.0f || end_length_sq == 0.0f)) {
+		// Zero length vectors have no angle, so the best we can do is either lerp or throw an error.
+		return linear_interpolate(p_to, p_weight);
+	}
+	Vector3 axis = cross(p_to);
+	real_t axis_length_sq = axis.length_squared();
+	if (unlikely(axis_length_sq == 0.0f)) {
+		// Colinear vectors have no rotation axis or angle between them, so the best we can do is lerp.
+		return linear_interpolate(p_to, p_weight);
+	}
+	axis /= Math::sqrt(axis_length_sq);
+	real_t start_length = Math::sqrt(start_length_sq);
+	real_t result_length = Math::lerp(start_length, Math::sqrt(end_length_sq), p_weight);
+	real_t angle = angle_to(p_to);
+	return rotated(axis, angle * p_weight) * (result_length / start_length);
+}
+
+Vector3 Vector3::cubic_interpolate(const Vector3 &p_b, const Vector3 &p_pre_a, const Vector3 &p_post_b, const real_t p_weight) const {
+	Vector3 res = *this;
+	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
+	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
+	res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
+	return res;
+}
+
+Vector3 Vector3::bezier_interpolate(const Vector3 &p_control_1, const Vector3 &p_control_2, const Vector3 &p_end, const real_t p_t) const {
+	Vector3 res = *this;
+
+	/* Formula from Wikipedia article on Bezier curves. */
+	real_t omt = (1.0 - p_t);
+	real_t omt2 = omt * omt;
+	real_t omt3 = omt2 * omt;
+	real_t t2 = p_t * p_t;
+	real_t t3 = t2 * p_t;
+
+	return res * omt3 + p_control_1 * omt2 * p_t * 3.0 + p_control_2 * omt * t2 * 3.0 + p_end * t3;
+}
+
+real_t Vector3::distance_to(const Vector3 &p_to) const {
+	return (p_to - *this).length();
+}
+
+real_t Vector3::distance_squared_to(const Vector3 &p_to) const {
+	return (p_to - *this).length_squared();
+}
+
+Vector3 Vector3::posmod(const real_t p_mod) const {
+	return Vector3(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod));
+}
+
+Vector3 Vector3::posmodv(const Vector3 &p_modv) const {
+	return Vector3(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y), Math::fposmod(z, p_modv.z));
+}
+
+Vector3 Vector3::project(const Vector3 &p_to) const {
+	return p_to * (dot(p_to) / p_to.length_squared());
+}
+
+real_t Vector3::angle_to(const Vector3 &p_to) const {
+	return Math::atan2(cross(p_to).length(), dot(p_to));
+}
+
+real_t Vector3::signed_angle_to(const Vector3 &p_to, const Vector3 &p_axis) const {
+	Vector3 cross_to = cross(p_to);
+	real_t unsigned_angle = Math::atan2(cross_to.length(), dot(p_to));
+	real_t sign = cross_to.dot(p_axis);
+	return (sign < 0) ? -unsigned_angle : unsigned_angle;
+}
+
+Vector3 Vector3::direction_to(const Vector3 &p_to) const {
+	Vector3 ret(p_to.x - x, p_to.y - y, p_to.z - z);
+	ret.normalize();
+	return ret;
+}
+
+/* Operators */
+
+Vector3 &Vector3::operator+=(const Vector3 &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+	z += p_v.z;
+	return *this;
+}
+
+Vector3 Vector3::operator+(const Vector3 &p_v) const {
+	return Vector3(x + p_v.x, y + p_v.y, z + p_v.z);
+}
+
+Vector3 &Vector3::operator-=(const Vector3 &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+	z -= p_v.z;
+	return *this;
+}
+Vector3 Vector3::operator-(const Vector3 &p_v) const {
+	return Vector3(x - p_v.x, y - p_v.y, z - p_v.z);
+}
+
+Vector3 &Vector3::operator*=(const Vector3 &p_v) {
+	x *= p_v.x;
+	y *= p_v.y;
+	z *= p_v.z;
+	return *this;
+}
+Vector3 Vector3::operator*(const Vector3 &p_v) const {
+	return Vector3(x * p_v.x, y * p_v.y, z * p_v.z);
+}
+
+Vector3 &Vector3::operator/=(const Vector3 &p_v) {
+	x /= p_v.x;
+	y /= p_v.y;
+	z /= p_v.z;
+	return *this;
+}
+
+Vector3 Vector3::operator/(const Vector3 &p_v) const {
+	return Vector3(x / p_v.x, y / p_v.y, z / p_v.z);
+}
+
+Vector3 &Vector3::operator*=(real_t p_scalar) {
+	x *= p_scalar;
+	y *= p_scalar;
+	z *= p_scalar;
+	return *this;
+}
+
+_FORCE_INLINE_ Vector3 operator*(real_t p_scalar, const Vector3 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+Vector3 Vector3::operator*(real_t p_scalar) const {
+	return Vector3(x * p_scalar, y * p_scalar, z * p_scalar);
+}
+
+Vector3 &Vector3::operator/=(real_t p_scalar) {
+	x /= p_scalar;
+	y /= p_scalar;
+	z /= p_scalar;
+	return *this;
+}
+
+Vector3 Vector3::operator/(real_t p_scalar) const {
+	return Vector3(x / p_scalar, y / p_scalar, z / p_scalar);
+}
+
+Vector3 Vector3::operator-() const {
+	return Vector3(-x, -y, -z);
+}
+
+bool Vector3::operator==(const Vector3 &p_v) const {
+	return x == p_v.x && y == p_v.y && z == p_v.z;
+}
+
+bool Vector3::operator!=(const Vector3 &p_v) const {
+	return x != p_v.x || y != p_v.y || z != p_v.z;
+}
+
+bool Vector3::operator<(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z < p_v.z;
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector3::operator>(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z > p_v.z;
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+bool Vector3::operator<=(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z <= p_v.z;
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector3::operator>=(const Vector3 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z >= p_v.z;
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+_FORCE_INLINE_ Vector3 vec3_cross(const Vector3 &p_a, const Vector3 &p_b) {
+	return p_a.cross(p_b);
+}
+
+_FORCE_INLINE_ real_t vec3_dot(const Vector3 &p_a, const Vector3 &p_b) {
+	return p_a.dot(p_b);
+}
+
+real_t Vector3::length() const {
+	real_t x2 = x * x;
+	real_t y2 = y * y;
+	real_t z2 = z * z;
+
+	return Math::sqrt(x2 + y2 + z2);
+}
+
+real_t Vector3::length_squared() const {
+	real_t x2 = x * x;
+	real_t y2 = y * y;
+	real_t z2 = z * z;
+
+	return x2 + y2 + z2;
+}
+
+void Vector3::normalize() {
+	real_t lengthsq = length_squared();
+	if (lengthsq == 0) {
+		x = y = z = 0;
+	} else {
+		real_t length = Math::sqrt(lengthsq);
+		x /= length;
+		y /= length;
+		z /= length;
+	}
+}
+
+Vector3 Vector3::normalized() const {
+	Vector3 v = *this;
+	v.normalize();
+	return v;
+}
+
+bool Vector3::is_normalized() const {
+	// use length_squared() instead of length() to avoid sqrt(), makes it more stringent.
+	return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON);
+}
+
+Vector3 Vector3::inverse() const {
+	return Vector3(1 / x, 1 / y, 1 / z);
+}
+
+void Vector3::zero() {
+	x = y = z = 0;
+}
+
+// slide returns the component of the vector along the given plane, specified by its normal vector.
+Vector3 Vector3::slide(const Vector3 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 must be normalized.");
+#endif
+	return *this - p_normal * this->dot(p_normal);
+}
+
+Vector3 Vector3::bounce(const Vector3 &p_normal) const {
+	return -reflect(p_normal);
+}
+
+Vector3 Vector3::reflect(const Vector3 &p_normal) const {
+#ifdef MATH_CHECKS
+	ERR_FAIL_COND_V_MSG(!p_normal.is_normalized(), Vector3(), "The normal Vector3 must be normalized.");
+#endif
+	return 2 * p_normal * this->dot(p_normal) - *this;
+}
+
+bool Vector3::is_equal_approx(const Vector3 &p_v, real_t p_tolerance) const {
+	return Math::is_equal_approx(x, p_v.x, p_tolerance) && Math::is_equal_approx(y, p_v.y, p_tolerance) && Math::is_equal_approx(z, p_v.z, p_tolerance);
+}
+
+bool Vector3::is_equal_approxt(const Vector3 &p_v, real_t p_tolerance) const {
+	return Math::is_equal_approx(x, p_v.x, p_tolerance) && Math::is_equal_approx(y, p_v.y, p_tolerance) && Math::is_equal_approx(z, p_v.z, p_tolerance);
+}
+
+#endif // VECTOR3_H

core/math/vector3i.cpp

@@ -0,0 +1,72 @@
+/*************************************************************************/
+/*  vector3i.cpp                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "vector3i.h"
+
+#include "core/math/vector3.h"
+#include "core/string/ustring.h"
+
+void Vector3i::set_axis(const int p_axis, const int32_t p_value) {
+	ERR_FAIL_INDEX(p_axis, 3);
+	coord[p_axis] = p_value;
+}
+
+int32_t Vector3i::get_axis(const int p_axis) const {
+	ERR_FAIL_INDEX_V(p_axis, 3, 0);
+	return operator[](p_axis);
+}
+
+Vector3i::Axis Vector3i::min_axis() const {
+	return x < y ? (x < z ? Vector3i::AXIS_X : Vector3i::AXIS_Z) : (y < z ? Vector3i::AXIS_Y : Vector3i::AXIS_Z);
+}
+
+Vector3i::Axis Vector3i::max_axis() const {
+	return x < y ? (y < z ? Vector3i::AXIS_Z : Vector3i::AXIS_Y) : (x < z ? Vector3i::AXIS_Z : Vector3i::AXIS_X);
+}
+
+Vector3i Vector3i::clamp(const Vector3i &p_min, const Vector3i &p_max) const {
+	return Vector3i(
+			CLAMP(x, p_min.x, p_max.x),
+			CLAMP(y, p_min.y, p_max.y),
+			CLAMP(z, p_min.z, p_max.z));
+}
+
+Vector3 Vector3i::to_vector3() const {
+	return Vector3(x, y, z);
+}
+
+Vector3i::operator String() const {
+	return "(" + itos(x) + ", " + itos(y) + ", " + itos(z) + ")";
+}
+
+Vector3i::operator Vector3() const {
+	return Vector3(x, y, z);
+}

core/math/vector3i.h

@@ -0,0 +1,333 @@
+/*************************************************************************/
+/*  vector3i.h                                                           */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef VECTOR3I_H
+#define VECTOR3I_H
+
+#include "core/error/error_macros.h"
+#include "core/math/math_funcs.h"
+
+class String;
+struct Vector3;
+
+struct _NO_DISCARD_CLASS_ Vector3i {
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+		AXIS_Z,
+	};
+
+	union {
+		struct {
+			int32_t x;
+			int32_t y;
+			int32_t z;
+		};
+
+		int32_t coord[3];
+	};
+
+	_FORCE_INLINE_ const int32_t &operator[](const int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 3);
+		return coord[p_axis];
+	}
+
+	_FORCE_INLINE_ int32_t &operator[](const int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 3);
+		return coord[p_axis];
+	}
+
+	void set_axis(const int p_axis, const int32_t p_value);
+	int32_t get_axis(const int p_axis) const;
+
+	_FORCE_INLINE_ void set_all(int32_t p_value) {
+		x = y = z = p_value;
+	}
+
+	Vector3i::Axis min_axis() const;
+	Vector3i::Axis max_axis() const;
+
+	_FORCE_INLINE_ int64_t length_squared() const;
+	_FORCE_INLINE_ double length() const;
+
+	_FORCE_INLINE_ void zero();
+
+	_FORCE_INLINE_ Vector3i abs() const;
+	_FORCE_INLINE_ Vector3i sign() const;
+	Vector3i clamp(const Vector3i &p_min, const Vector3i &p_max) const;
+
+	_FORCE_INLINE_ Vector3i linear_interpolate(const Vector3i &p_to, real_t p_weight) const;
+
+	/* Operators */
+
+	_FORCE_INLINE_ Vector3i &operator+=(const Vector3i &p_v);
+	_FORCE_INLINE_ Vector3i operator+(const Vector3i &p_v) const;
+	_FORCE_INLINE_ Vector3i &operator-=(const Vector3i &p_v);
+	_FORCE_INLINE_ Vector3i operator-(const Vector3i &p_v) const;
+	_FORCE_INLINE_ Vector3i &operator*=(const Vector3i &p_v);
+	_FORCE_INLINE_ Vector3i operator*(const Vector3i &p_v) const;
+	_FORCE_INLINE_ Vector3i &operator/=(const Vector3i &p_v);
+	_FORCE_INLINE_ Vector3i operator/(const Vector3i &p_v) const;
+	_FORCE_INLINE_ Vector3i &operator%=(const Vector3i &p_v);
+	_FORCE_INLINE_ Vector3i operator%(const Vector3i &p_v) const;
+
+	_FORCE_INLINE_ Vector3i &operator*=(const int32_t p_scalar);
+	_FORCE_INLINE_ Vector3i operator*(const int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector3i &operator/=(const int32_t p_scalar);
+	_FORCE_INLINE_ Vector3i operator/(const int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector3i &operator%=(const int32_t p_scalar);
+	_FORCE_INLINE_ Vector3i operator%(const int32_t p_scalar) const;
+
+	_FORCE_INLINE_ Vector3i operator-() const;
+
+	_FORCE_INLINE_ bool operator==(const Vector3i &p_v) const;
+	_FORCE_INLINE_ bool operator!=(const Vector3i &p_v) const;
+	_FORCE_INLINE_ bool operator<(const Vector3i &p_v) const;
+	_FORCE_INLINE_ bool operator<=(const Vector3i &p_v) const;
+	_FORCE_INLINE_ bool operator>(const Vector3i &p_v) const;
+	_FORCE_INLINE_ bool operator>=(const Vector3i &p_v) const;
+
+	Vector3 to_vector3() const;
+
+	operator String() const;
+	operator Vector3() const;
+
+	_FORCE_INLINE_ Vector3i() {
+		x = 0;
+		y = 0;
+		z = 0;
+	}
+	_FORCE_INLINE_ Vector3i(const int32_t p_x, const int32_t p_y, const int32_t p_z) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+	}
+};
+
+int64_t Vector3i::length_squared() const {
+	return x * (int64_t)x + y * (int64_t)y + z * (int64_t)z;
+}
+
+double Vector3i::length() const {
+	return Math::sqrt((double)length_squared());
+}
+
+Vector3i Vector3i::abs() const {
+	return Vector3i(ABS(x), ABS(y), ABS(z));
+}
+
+Vector3i Vector3i::sign() const {
+	return Vector3i(SGN(x), SGN(y), SGN(z));
+}
+
+Vector3i Vector3i::linear_interpolate(const Vector3i &p_to, real_t p_weight) const {
+	return Vector3i(
+			x + (p_weight * (p_to.x - x)),
+			y + (p_weight * (p_to.y - y)),
+			z + (p_weight * (p_to.z - z)));
+}
+
+/* Operators */
+
+Vector3i &Vector3i::operator+=(const Vector3i &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+	z += p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator+(const Vector3i &p_v) const {
+	return Vector3i(x + p_v.x, y + p_v.y, z + p_v.z);
+}
+
+Vector3i &Vector3i::operator-=(const Vector3i &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+	z -= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator-(const Vector3i &p_v) const {
+	return Vector3i(x - p_v.x, y - p_v.y, z - p_v.z);
+}
+
+Vector3i &Vector3i::operator*=(const Vector3i &p_v) {
+	x *= p_v.x;
+	y *= p_v.y;
+	z *= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator*(const Vector3i &p_v) const {
+	return Vector3i(x * p_v.x, y * p_v.y, z * p_v.z);
+}
+
+Vector3i &Vector3i::operator/=(const Vector3i &p_v) {
+	x /= p_v.x;
+	y /= p_v.y;
+	z /= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator/(const Vector3i &p_v) const {
+	return Vector3i(x / p_v.x, y / p_v.y, z / p_v.z);
+}
+
+Vector3i &Vector3i::operator%=(const Vector3i &p_v) {
+	x %= p_v.x;
+	y %= p_v.y;
+	z %= p_v.z;
+	return *this;
+}
+
+Vector3i Vector3i::operator%(const Vector3i &p_v) const {
+	return Vector3i(x % p_v.x, y % p_v.y, z % p_v.z);
+}
+
+Vector3i &Vector3i::operator*=(const int32_t p_scalar) {
+	x *= p_scalar;
+	y *= p_scalar;
+	z *= p_scalar;
+	return *this;
+}
+
+Vector3i Vector3i::operator*(const int32_t p_scalar) const {
+	return Vector3i(x * p_scalar, y * p_scalar, z * p_scalar);
+}
+
+// Multiplication operators required to workaround issues with LLVM using implicit conversion.
+
+_FORCE_INLINE_ Vector3i operator*(const int32_t p_scalar, const Vector3i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+_FORCE_INLINE_ Vector3i operator*(const int64_t p_scalar, const Vector3i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+_FORCE_INLINE_ Vector3i operator*(const float p_scalar, const Vector3i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+_FORCE_INLINE_ Vector3i operator*(const double p_scalar, const Vector3i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+Vector3i &Vector3i::operator/=(const int32_t p_scalar) {
+	x /= p_scalar;
+	y /= p_scalar;
+	z /= p_scalar;
+	return *this;
+}
+
+Vector3i Vector3i::operator/(const int32_t p_scalar) const {
+	return Vector3i(x / p_scalar, y / p_scalar, z / p_scalar);
+}
+
+Vector3i &Vector3i::operator%=(const int32_t p_scalar) {
+	x %= p_scalar;
+	y %= p_scalar;
+	z %= p_scalar;
+	return *this;
+}
+
+Vector3i Vector3i::operator%(const int32_t p_scalar) const {
+	return Vector3i(x % p_scalar, y % p_scalar, z % p_scalar);
+}
+
+Vector3i Vector3i::operator-() const {
+	return Vector3i(-x, -y, -z);
+}
+
+bool Vector3i::operator==(const Vector3i &p_v) const {
+	return (x == p_v.x && y == p_v.y && z == p_v.z);
+}
+
+bool Vector3i::operator!=(const Vector3i &p_v) const {
+	return (x != p_v.x || y != p_v.y || z != p_v.z);
+}
+
+bool Vector3i::operator<(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z < p_v.z;
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector3i::operator>(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z > p_v.z;
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+bool Vector3i::operator<=(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z <= p_v.z;
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector3i::operator>=(const Vector3i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			return z >= p_v.z;
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+void Vector3i::zero() {
+	x = y = z = 0;
+}
+
+typedef Vector3i Size3i;
+typedef Vector3i Point3i;
+
+#endif // VECTOR3I_H

core/math/vector4.cpp

@@ -0,0 +1,188 @@
+/*************************************************************************/
+/*  vector4.cpp                                                          */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "vector4.h"
+
+#include "core/math/basis.h"
+#include "core/string/print_string.h"
+
+void Vector4::set_axis(const int p_axis, const real_t p_value) {
+	ERR_FAIL_INDEX(p_axis, 4);
+	components[p_axis] = p_value;
+}
+
+real_t Vector4::get_axis(const int p_axis) const {
+	ERR_FAIL_INDEX_V(p_axis, 4, 0);
+	return operator[](p_axis);
+}
+
+Vector4::Axis Vector4::min_axis() const {
+	uint32_t min_index = 0;
+	real_t min_value = x;
+	for (uint32_t i = 1; i < 4; i++) {
+		if (operator[](i) <= min_value) {
+			min_index = i;
+			min_value = operator[](i);
+		}
+	}
+	return Vector4::Axis(min_index);
+}
+
+Vector4::Axis Vector4::max_axis() const {
+	uint32_t max_index = 0;
+	real_t max_value = x;
+	for (uint32_t i = 1; i < 4; i++) {
+		if (operator[](i) > max_value) {
+			max_index = i;
+			max_value = operator[](i);
+		}
+	}
+	return Vector4::Axis(max_index);
+}
+
+bool Vector4::is_equal_approx(const Vector4 &p_vec4) const {
+	return Math::is_equal_approx(x, p_vec4.x) && Math::is_equal_approx(y, p_vec4.y) && Math::is_equal_approx(z, p_vec4.z) && Math::is_equal_approx(w, p_vec4.w);
+}
+
+real_t Vector4::length() const {
+	return Math::sqrt(length_squared());
+}
+
+void Vector4::normalize() {
+	*this /= length();
+}
+
+Vector4 Vector4::normalized() const {
+	return *this / length();
+}
+
+bool Vector4::is_normalized() const {
+	return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON); // Use less epsilon.
+}
+
+Vector4 Vector4::limit_length(const real_t p_len) const {
+	const real_t l = length();
+	Vector4 v = *this;
+	if (l > 0 && p_len < l) {
+		v /= l;
+		v *= p_len;
+	}
+
+	return v;
+}
+
+real_t Vector4::distance_to(const Vector4 &p_to) const {
+	return (p_to - *this).length();
+}
+
+Vector4 Vector4::direction_to(const Vector4 &p_to) const {
+	Vector4 ret(p_to.x - x, p_to.y - y, p_to.z - z, p_to.w - w);
+	ret.normalize();
+	return ret;
+}
+
+real_t Vector4::distance_squared_to(const Vector4 &p_to) const {
+	return (p_to - *this).length_squared();
+}
+
+Vector4 Vector4::abs() const {
+	return Vector4(Math::abs(x), Math::abs(y), Math::abs(z), Math::abs(w));
+}
+
+Vector4 Vector4::sign() const {
+	return Vector4(SGN(x), SGN(y), SGN(z), SGN(w));
+}
+
+Vector4 Vector4::floor() const {
+	return Vector4(Math::floor(x), Math::floor(y), Math::floor(z), Math::floor(w));
+}
+
+Vector4 Vector4::ceil() const {
+	return Vector4(Math::ceil(x), Math::ceil(y), Math::ceil(z), Math::ceil(w));
+}
+
+Vector4 Vector4::round() const {
+	return Vector4(Math::round(x), Math::round(y), Math::round(z), Math::round(w));
+}
+
+Vector4 Vector4::linear_interpolate(const Vector4 &p_to, const real_t p_weight) const {
+	return Vector4(
+			x + (p_weight * (p_to.x - x)),
+			y + (p_weight * (p_to.y - y)),
+			z + (p_weight * (p_to.z - z)),
+			w + (p_weight * (p_to.w - w)));
+}
+
+Vector4 Vector4::cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight) const {
+	Vector4 res = *this;
+	res.x = Math::cubic_interpolate(res.x, p_b.x, p_pre_a.x, p_post_b.x, p_weight);
+	res.y = Math::cubic_interpolate(res.y, p_b.y, p_pre_a.y, p_post_b.y, p_weight);
+	res.z = Math::cubic_interpolate(res.z, p_b.z, p_pre_a.z, p_post_b.z, p_weight);
+	res.w = Math::cubic_interpolate(res.w, p_b.w, p_pre_a.w, p_post_b.w, p_weight);
+	return res;
+}
+
+Vector4 Vector4::posmod(const real_t p_mod) const {
+	return Vector4(Math::fposmod(x, p_mod), Math::fposmod(y, p_mod), Math::fposmod(z, p_mod), Math::fposmod(w, p_mod));
+}
+
+Vector4 Vector4::posmodv(const Vector4 &p_modv) const {
+	return Vector4(Math::fposmod(x, p_modv.x), Math::fposmod(y, p_modv.y), Math::fposmod(z, p_modv.z), Math::fposmod(w, p_modv.w));
+}
+
+void Vector4::snap(const Vector4 &p_step) {
+	x = Math::stepify(x, p_step.x);
+	y = Math::stepify(y, p_step.y);
+	z = Math::stepify(z, p_step.z);
+	w = Math::stepify(w, p_step.w);
+}
+
+Vector4 Vector4::snapped(const Vector4 &p_step) const {
+	Vector4 v = *this;
+	v.snap(p_step);
+	return v;
+}
+
+Vector4 Vector4::inverse() const {
+	return Vector4(1.0f / x, 1.0f / y, 1.0f / z, 1.0f / w);
+}
+
+Vector4 Vector4::clamp(const Vector4 &p_min, const Vector4 &p_max) const {
+	return Vector4(
+			CLAMP(x, p_min.x, p_max.x),
+			CLAMP(y, p_min.y, p_max.y),
+			CLAMP(z, p_min.z, p_max.z),
+			CLAMP(w, p_min.w, p_max.w));
+}
+
+Vector4::operator String() const {
+	return "(" + String::num_real(x) + ", " + String::num_real(y) + ", " + String::num_real(z) + ", " + String::num_real(w) + ")";
+}

core/math/vector4.h

@@ -0,0 +1,316 @@
+/*************************************************************************/
+/*  vector4.h                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef VECTOR4_H
+#define VECTOR4_H
+
+#include "core/math/math_defs.h"
+#include "core/math/math_funcs.h"
+#include "core/string/ustring.h"
+
+struct _NO_DISCARD_CLASS_ Vector4 {
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+		AXIS_Z,
+		AXIS_W,
+	};
+
+	union {
+		struct {
+			real_t x;
+			real_t y;
+			real_t z;
+			real_t w;
+		};
+		real_t components[4];
+	};
+
+	_FORCE_INLINE_ real_t &operator[](const int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 4);
+		return components[p_axis];
+	}
+	_FORCE_INLINE_ const real_t &operator[](const int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 4);
+		return components[p_axis];
+	}
+
+	_FORCE_INLINE_ void set_all(const real_t p_value);
+
+	void set_axis(const int p_axis, const real_t p_value);
+	real_t get_axis(const int p_axis) const;
+
+	Vector4::Axis min_axis() const;
+	Vector4::Axis max_axis() const;
+
+	_FORCE_INLINE_ real_t length_squared() const;
+	bool is_equal_approx(const Vector4 &p_vec4) const;
+	real_t length() const;
+	void normalize();
+	Vector4 normalized() const;
+	bool is_normalized() const;
+	Vector4 limit_length(const real_t p_len = 1.0) const;
+
+	_FORCE_INLINE_ void zero();
+
+	real_t distance_to(const Vector4 &p_to) const;
+	real_t distance_squared_to(const Vector4 &p_to) const;
+	Vector4 direction_to(const Vector4 &p_to) const;
+
+	Vector4 abs() const;
+	Vector4 sign() const;
+	Vector4 floor() const;
+	Vector4 ceil() const;
+	Vector4 round() const;
+
+	Vector4 linear_interpolate(const Vector4 &p_to, const real_t p_weight) const;
+	Vector4 cubic_interpolate(const Vector4 &p_b, const Vector4 &p_pre_a, const Vector4 &p_post_b, const real_t p_weight) const;
+
+	Vector4 posmod(const real_t p_mod) const;
+	Vector4 posmodv(const Vector4 &p_modv) const;
+	void snap(const Vector4 &p_step);
+	Vector4 snapped(const Vector4 &p_step) const;
+	Vector4 clamp(const Vector4 &p_min, const Vector4 &p_max) const;
+
+	Vector4 inverse() const;
+	_FORCE_INLINE_ real_t dot(const Vector4 &p_vec4) const;
+
+	_FORCE_INLINE_ void operator+=(const Vector4 &p_vec4);
+	_FORCE_INLINE_ void operator-=(const Vector4 &p_vec4);
+	_FORCE_INLINE_ void operator*=(const Vector4 &p_vec4);
+	_FORCE_INLINE_ void operator/=(const Vector4 &p_vec4);
+	_FORCE_INLINE_ void operator*=(const real_t &s);
+	_FORCE_INLINE_ void operator/=(const real_t &s);
+	_FORCE_INLINE_ Vector4 operator+(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ Vector4 operator-(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ Vector4 operator*(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ Vector4 operator/(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ Vector4 operator-() const;
+	_FORCE_INLINE_ Vector4 operator*(const real_t &s) const;
+	_FORCE_INLINE_ Vector4 operator/(const real_t &s) const;
+
+	_FORCE_INLINE_ bool operator==(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ bool operator!=(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ bool operator>(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ bool operator<(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ bool operator>=(const Vector4 &p_vec4) const;
+	_FORCE_INLINE_ bool operator<=(const Vector4 &p_vec4) const;
+
+	operator String() const;
+
+	_FORCE_INLINE_ Vector4() {
+		x = 0;
+		y = 0;
+		z = 0;
+		w = 0;
+	}
+
+	_FORCE_INLINE_ Vector4(real_t p_x, real_t p_y, real_t p_z, real_t p_w) :
+			x(p_x),
+			y(p_y),
+			z(p_z),
+			w(p_w) {
+	}
+
+	Vector4(const Vector4 &p_vec4) :
+			x(p_vec4.x),
+			y(p_vec4.y),
+			z(p_vec4.z),
+			w(p_vec4.w) {
+	}
+
+	void operator=(const Vector4 &p_vec4) {
+		x = p_vec4.x;
+		y = p_vec4.y;
+		z = p_vec4.z;
+		w = p_vec4.w;
+	}
+};
+
+void Vector4::set_all(const real_t p_value) {
+	x = y = z = p_value;
+}
+
+real_t Vector4::dot(const Vector4 &p_vec4) const {
+	return x * p_vec4.x + y * p_vec4.y + z * p_vec4.z + w * p_vec4.w;
+}
+
+real_t Vector4::length_squared() const {
+	return dot(*this);
+}
+
+void Vector4::zero() {
+	x = y = z = 0;
+}
+
+void Vector4::operator+=(const Vector4 &p_vec4) {
+	x += p_vec4.x;
+	y += p_vec4.y;
+	z += p_vec4.z;
+	w += p_vec4.w;
+}
+
+void Vector4::operator-=(const Vector4 &p_vec4) {
+	x -= p_vec4.x;
+	y -= p_vec4.y;
+	z -= p_vec4.z;
+	w -= p_vec4.w;
+}
+
+void Vector4::operator*=(const Vector4 &p_vec4) {
+	x *= p_vec4.x;
+	y *= p_vec4.y;
+	z *= p_vec4.z;
+	w *= p_vec4.w;
+}
+
+void Vector4::operator/=(const Vector4 &p_vec4) {
+	x /= p_vec4.x;
+	y /= p_vec4.y;
+	z /= p_vec4.z;
+	w /= p_vec4.w;
+}
+void Vector4::operator*=(const real_t &s) {
+	x *= s;
+	y *= s;
+	z *= s;
+	w *= s;
+}
+
+void Vector4::operator/=(const real_t &s) {
+	*this *= 1.0f / s;
+}
+
+Vector4 Vector4::operator+(const Vector4 &p_vec4) const {
+	return Vector4(x + p_vec4.x, y + p_vec4.y, z + p_vec4.z, w + p_vec4.w);
+}
+
+Vector4 Vector4::operator-(const Vector4 &p_vec4) const {
+	return Vector4(x - p_vec4.x, y - p_vec4.y, z - p_vec4.z, w - p_vec4.w);
+}
+
+Vector4 Vector4::operator*(const Vector4 &p_vec4) const {
+	return Vector4(x * p_vec4.x, y * p_vec4.y, z * p_vec4.z, w * p_vec4.w);
+}
+
+Vector4 Vector4::operator/(const Vector4 &p_vec4) const {
+	return Vector4(x / p_vec4.x, y / p_vec4.y, z / p_vec4.z, w / p_vec4.w);
+}
+
+Vector4 Vector4::operator-() const {
+	return Vector4(-x, -y, -z, -w);
+}
+
+Vector4 Vector4::operator*(const real_t &s) const {
+	return Vector4(x * s, y * s, z * s, w * s);
+}
+
+Vector4 Vector4::operator/(const real_t &s) const {
+	return *this * (1.0f / s);
+}
+
+bool Vector4::operator==(const Vector4 &p_vec4) const {
+	return x == p_vec4.x && y == p_vec4.y && z == p_vec4.z && w == p_vec4.w;
+}
+
+bool Vector4::operator!=(const Vector4 &p_vec4) const {
+	return x != p_vec4.x || y != p_vec4.y || z != p_vec4.z || w != p_vec4.w;
+}
+
+bool Vector4::operator<(const Vector4 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w < p_v.w;
+			}
+			return z < p_v.z;
+		}
+		return y < p_v.y;
+	}
+	return x < p_v.x;
+}
+
+bool Vector4::operator>(const Vector4 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w > p_v.w;
+			}
+			return z > p_v.z;
+		}
+		return y > p_v.y;
+	}
+	return x > p_v.x;
+}
+
+bool Vector4::operator<=(const Vector4 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w <= p_v.w;
+			}
+			return z < p_v.z;
+		}
+		return y < p_v.y;
+	}
+	return x < p_v.x;
+}
+
+bool Vector4::operator>=(const Vector4 &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w >= p_v.w;
+			}
+			return z > p_v.z;
+		}
+		return y > p_v.y;
+	}
+	return x > p_v.x;
+}
+
+_FORCE_INLINE_ Vector4 operator*(const float p_scalar, const Vector4 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+_FORCE_INLINE_ Vector4 operator*(const double p_scalar, const Vector4 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+_FORCE_INLINE_ Vector4 operator*(const int32_t p_scalar, const Vector4 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+_FORCE_INLINE_ Vector4 operator*(const int64_t p_scalar, const Vector4 &p_vec) {
+	return p_vec * p_scalar;
+}
+
+#endif // VECTOR4_H

core/math/vector4i.cpp

@@ -0,0 +1,106 @@
+/*************************************************************************/
+/*  vector4i.cpp                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "vector4i.h"
+
+#include "core/math/vector4.h"
+#include "core/string/ustring.h"
+
+void Vector4i::set_axis(const int p_axis, const int32_t p_value) {
+	ERR_FAIL_INDEX(p_axis, 4);
+	coord[p_axis] = p_value;
+}
+
+int32_t Vector4i::get_axis(const int p_axis) const {
+	ERR_FAIL_INDEX_V(p_axis, 4, 0);
+	return operator[](p_axis);
+}
+
+Vector4i::Axis Vector4i::min_axis() const {
+	uint32_t min_index = 0;
+	int32_t min_value = x;
+	for (uint32_t i = 1; i < 4; i++) {
+		if (operator[](i) <= min_value) {
+			min_index = i;
+			min_value = operator[](i);
+		}
+	}
+	return Vector4i::Axis(min_index);
+}
+
+Vector4i::Axis Vector4i::max_axis() const {
+	uint32_t max_index = 0;
+	int32_t max_value = x;
+	for (uint32_t i = 1; i < 4; i++) {
+		if (operator[](i) > max_value) {
+			max_index = i;
+			max_value = operator[](i);
+		}
+	}
+	return Vector4i::Axis(max_index);
+}
+
+Vector4i Vector4i::clamp(const Vector4i &p_min, const Vector4i &p_max) const {
+	return Vector4i(
+			CLAMP(x, p_min.x, p_max.x),
+			CLAMP(y, p_min.y, p_max.y),
+			CLAMP(z, p_min.z, p_max.z),
+			CLAMP(w, p_min.w, p_max.w));
+}
+
+Vector4i Vector4i::linear_interpolate(const Vector4i &p_to, const real_t p_weight) const {
+	return Vector4i(
+			x + (p_weight * (p_to.x - x)),
+			y + (p_weight * (p_to.y - y)),
+			z + (p_weight * (p_to.z - z)),
+			w + (p_weight * (p_to.w - w)));
+}
+
+Vector4 Vector4i::to_vector4() const {
+	return Vector4(x, y, z, w);
+}
+
+Vector4i::operator String() const {
+	return "(" + itos(x) + ", " + itos(y) + ", " + itos(z) + ", " + itos(w) + ")";
+}
+
+Vector4i::operator Vector4() const {
+	return Vector4(x, y, z, w);
+}
+
+/*
+Vector4i::Vector4i(const Vector4 &p_vec4) {
+	x = p_vec4.x;
+	y = p_vec4.y;
+	z = p_vec4.z;
+	w = p_vec4.w;
+}
+*/

core/math/vector4i.h

@@ -0,0 +1,359 @@
+/*************************************************************************/
+/*  vector4i.h                                                           */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef VECTOR4I_H
+#define VECTOR4I_H
+
+#include "core/error/error_macros.h"
+#include "core/math/math_funcs.h"
+
+class String;
+struct Vector4;
+
+struct _NO_DISCARD_CLASS_ Vector4i {
+	enum Axis {
+		AXIS_X,
+		AXIS_Y,
+		AXIS_Z,
+		AXIS_W,
+	};
+
+	union {
+		struct {
+			int32_t x;
+			int32_t y;
+			int32_t z;
+			int32_t w;
+		};
+
+		int32_t coord[4];
+	};
+
+	_FORCE_INLINE_ const int32_t &operator[](const int p_axis) const {
+		DEV_ASSERT((unsigned int)p_axis < 4);
+		return coord[p_axis];
+	}
+
+	_FORCE_INLINE_ int32_t &operator[](const int p_axis) {
+		DEV_ASSERT((unsigned int)p_axis < 4);
+		return coord[p_axis];
+	}
+
+	_FORCE_INLINE_ void set_all(const int32_t p_value);
+
+	void set_axis(const int p_axis, const int32_t p_value);
+	int32_t get_axis(const int p_axis) const;
+
+	Vector4i::Axis min_axis() const;
+	Vector4i::Axis max_axis() const;
+
+	_FORCE_INLINE_ int64_t length_squared() const;
+	_FORCE_INLINE_ double length() const;
+
+	_FORCE_INLINE_ void zero();
+
+	_FORCE_INLINE_ Vector4i abs() const;
+	_FORCE_INLINE_ Vector4i sign() const;
+	Vector4i clamp(const Vector4i &p_min, const Vector4i &p_max) const;
+
+	Vector4i linear_interpolate(const Vector4i &p_to, const real_t p_weight) const;
+
+	/* Operators */
+
+	_FORCE_INLINE_ Vector4i &operator+=(const Vector4i &p_v);
+	_FORCE_INLINE_ Vector4i operator+(const Vector4i &p_v) const;
+	_FORCE_INLINE_ Vector4i &operator-=(const Vector4i &p_v);
+	_FORCE_INLINE_ Vector4i operator-(const Vector4i &p_v) const;
+	_FORCE_INLINE_ Vector4i &operator*=(const Vector4i &p_v);
+	_FORCE_INLINE_ Vector4i operator*(const Vector4i &p_v) const;
+	_FORCE_INLINE_ Vector4i &operator/=(const Vector4i &p_v);
+	_FORCE_INLINE_ Vector4i operator/(const Vector4i &p_v) const;
+	_FORCE_INLINE_ Vector4i &operator%=(const Vector4i &p_v);
+	_FORCE_INLINE_ Vector4i operator%(const Vector4i &p_v) const;
+
+	_FORCE_INLINE_ Vector4i &operator*=(const int32_t p_scalar);
+	_FORCE_INLINE_ Vector4i operator*(const int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector4i &operator/=(const int32_t p_scalar);
+	_FORCE_INLINE_ Vector4i operator/(const int32_t p_scalar) const;
+	_FORCE_INLINE_ Vector4i &operator%=(const int32_t p_scalar);
+	_FORCE_INLINE_ Vector4i operator%(const int32_t p_scalar) const;
+
+	_FORCE_INLINE_ Vector4i operator-() const;
+
+	_FORCE_INLINE_ bool operator==(const Vector4i &p_v) const;
+	_FORCE_INLINE_ bool operator!=(const Vector4i &p_v) const;
+	_FORCE_INLINE_ bool operator<(const Vector4i &p_v) const;
+	_FORCE_INLINE_ bool operator<=(const Vector4i &p_v) const;
+	_FORCE_INLINE_ bool operator>(const Vector4i &p_v) const;
+	_FORCE_INLINE_ bool operator>=(const Vector4i &p_v) const;
+
+	Vector4 to_vector4() const;
+
+	operator String() const;
+	operator Vector4() const;
+
+	_FORCE_INLINE_ Vector4i() {
+		x = 0;
+		y = 0;
+		z = 0;
+		w = 0;
+	}
+
+	//Vector4i(const Vector4 &p_vec4);
+
+	_FORCE_INLINE_ Vector4i(const int32_t p_x, const int32_t p_y, const int32_t p_z, const int32_t p_w) {
+		x = p_x;
+		y = p_y;
+		z = p_z;
+		w = p_w;
+	}
+};
+
+void Vector4i::set_all(const int32_t p_value) {
+	x = y = z = p_value;
+}
+
+int64_t Vector4i::length_squared() const {
+	return x * (int64_t)x + y * (int64_t)y + z * (int64_t)z + w * (int64_t)w;
+}
+
+double Vector4i::length() const {
+	return Math::sqrt((double)length_squared());
+}
+
+Vector4i Vector4i::abs() const {
+	return Vector4i(ABS(x), ABS(y), ABS(z), ABS(w));
+}
+
+Vector4i Vector4i::sign() const {
+	return Vector4i(SGN(x), SGN(y), SGN(z), SGN(w));
+}
+
+/* Operators */
+
+Vector4i &Vector4i::operator+=(const Vector4i &p_v) {
+	x += p_v.x;
+	y += p_v.y;
+	z += p_v.z;
+	w += p_v.w;
+	return *this;
+}
+
+Vector4i Vector4i::operator+(const Vector4i &p_v) const {
+	return Vector4i(x + p_v.x, y + p_v.y, z + p_v.z, w + p_v.w);
+}
+
+Vector4i &Vector4i::operator-=(const Vector4i &p_v) {
+	x -= p_v.x;
+	y -= p_v.y;
+	z -= p_v.z;
+	w -= p_v.w;
+	return *this;
+}
+
+Vector4i Vector4i::operator-(const Vector4i &p_v) const {
+	return Vector4i(x - p_v.x, y - p_v.y, z - p_v.z, w - p_v.w);
+}
+
+Vector4i &Vector4i::operator*=(const Vector4i &p_v) {
+	x *= p_v.x;
+	y *= p_v.y;
+	z *= p_v.z;
+	w *= p_v.w;
+	return *this;
+}
+
+Vector4i Vector4i::operator*(const Vector4i &p_v) const {
+	return Vector4i(x * p_v.x, y * p_v.y, z * p_v.z, w * p_v.w);
+}
+
+Vector4i &Vector4i::operator/=(const Vector4i &p_v) {
+	x /= p_v.x;
+	y /= p_v.y;
+	z /= p_v.z;
+	w /= p_v.w;
+	return *this;
+}
+
+Vector4i Vector4i::operator/(const Vector4i &p_v) const {
+	return Vector4i(x / p_v.x, y / p_v.y, z / p_v.z, w / p_v.w);
+}
+
+Vector4i &Vector4i::operator%=(const Vector4i &p_v) {
+	x %= p_v.x;
+	y %= p_v.y;
+	z %= p_v.z;
+	w %= p_v.w;
+	return *this;
+}
+
+Vector4i Vector4i::operator%(const Vector4i &p_v) const {
+	return Vector4i(x % p_v.x, y % p_v.y, z % p_v.z, w % p_v.w);
+}
+
+Vector4i &Vector4i::operator*=(const int32_t p_scalar) {
+	x *= p_scalar;
+	y *= p_scalar;
+	z *= p_scalar;
+	w *= p_scalar;
+	return *this;
+}
+
+Vector4i Vector4i::operator*(const int32_t p_scalar) const {
+	return Vector4i(x * p_scalar, y * p_scalar, z * p_scalar, w * p_scalar);
+}
+
+// Multiplication operators required to workaround issues with LLVM using implicit conversion.
+
+_FORCE_INLINE_ Vector4i operator*(const int32_t p_scalar, const Vector4i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+_FORCE_INLINE_ Vector4i operator*(const int64_t p_scalar, const Vector4i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+_FORCE_INLINE_ Vector4i operator*(const float p_scalar, const Vector4i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+_FORCE_INLINE_ Vector4i operator*(const double p_scalar, const Vector4i &p_vector) {
+	return p_vector * p_scalar;
+}
+
+Vector4i &Vector4i::operator/=(const int32_t p_scalar) {
+	x /= p_scalar;
+	y /= p_scalar;
+	z /= p_scalar;
+	w /= p_scalar;
+	return *this;
+}
+
+Vector4i Vector4i::operator/(const int32_t p_scalar) const {
+	return Vector4i(x / p_scalar, y / p_scalar, z / p_scalar, w / p_scalar);
+}
+
+Vector4i &Vector4i::operator%=(const int32_t p_scalar) {
+	x %= p_scalar;
+	y %= p_scalar;
+	z %= p_scalar;
+	w %= p_scalar;
+	return *this;
+}
+
+Vector4i Vector4i::operator%(const int32_t p_scalar) const {
+	return Vector4i(x % p_scalar, y % p_scalar, z % p_scalar, w % p_scalar);
+}
+
+Vector4i Vector4i::operator-() const {
+	return Vector4i(-x, -y, -z, -w);
+}
+
+bool Vector4i::operator==(const Vector4i &p_v) const {
+	return (x == p_v.x && y == p_v.y && z == p_v.z && w == p_v.w);
+}
+
+bool Vector4i::operator!=(const Vector4i &p_v) const {
+	return (x != p_v.x || y != p_v.y || z != p_v.z || w != p_v.w);
+}
+
+bool Vector4i::operator<(const Vector4i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w < p_v.w;
+			} else {
+				return z < p_v.z;
+			}
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector4i::operator>(const Vector4i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w > p_v.w;
+			} else {
+				return z > p_v.z;
+			}
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+bool Vector4i::operator<=(const Vector4i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w <= p_v.w;
+			} else {
+				return z < p_v.z;
+			}
+		} else {
+			return y < p_v.y;
+		}
+	} else {
+		return x < p_v.x;
+	}
+}
+
+bool Vector4i::operator>=(const Vector4i &p_v) const {
+	if (x == p_v.x) {
+		if (y == p_v.y) {
+			if (z == p_v.z) {
+				return w >= p_v.w;
+			} else {
+				return z > p_v.z;
+			}
+		} else {
+			return y > p_v.y;
+		}
+	} else {
+		return x > p_v.x;
+	}
+}
+
+void Vector4i::zero() {
+	x = y = z = w = 0;
+}
+
+typedef Vector4i Size4i;
+typedef Vector4i Point4i;
+
+#endif // VECTOR4I_H

core/string/char_utils.h

@@ -0,0 +1,113 @@
+/*************************************************************************/
+/*  char_utils.h                                                         */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#ifndef CHAR_UTILS_H
+#define CHAR_UTILS_H
+
+#include "core/typedefs.h"
+
+#include "char_range.inc"
+
+static _FORCE_INLINE_ bool is_unicode_identifier_start(char32_t c) {
+	for (int i = 0; xid_start[i].start != 0; i++) {
+		if (c >= xid_start[i].start && c <= xid_start[i].end) {
+			return true;
+		}
+	}
+	return false;
+}
+
+static _FORCE_INLINE_ bool is_unicode_identifier_continue(char32_t c) {
+	for (int i = 0; xid_continue[i].start != 0; i++) {
+		if (c >= xid_continue[i].start && c <= xid_continue[i].end) {
+			return true;
+		}
+	}
+	return false;
+}
+
+static _FORCE_INLINE_ bool is_ascii_upper_case(char32_t c) {
+	return (c >= 'A' && c <= 'Z');
+}
+
+static _FORCE_INLINE_ bool is_ascii_lower_case(char32_t c) {
+	return (c >= 'a' && c <= 'z');
+}
+
+static _FORCE_INLINE_ bool is_digit(char32_t c) {
+	return (c >= '0' && c <= '9');
+}
+
+static _FORCE_INLINE_ bool is_hex_digit(char32_t c) {
+	return (is_digit(c) || (c >= 'a' && c <= 'f') || (c >= 'A' && c <= 'F'));
+}
+
+static _FORCE_INLINE_ bool is_binary_digit(char32_t c) {
+	return (c == '0' || c == '1');
+}
+
+static _FORCE_INLINE_ bool is_ascii_char(char32_t c) {
+	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z');
+}
+
+static _FORCE_INLINE_ bool is_ascii_alphanumeric_char(char32_t c) {
+	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || (c >= '0' && c <= '9');
+}
+
+static _FORCE_INLINE_ bool is_ascii_identifier_char(char32_t c) {
+	return (c >= 'a' && c <= 'z') || (c >= 'A' && c <= 'Z') || (c >= '0' && c <= '9') || c == '_';
+}
+
+static _FORCE_INLINE_ bool is_symbol(char32_t c) {
+	return c != '_' && ((c >= '!' && c <= '/') || (c >= ':' && c <= '@') || (c >= '[' && c <= '`') || (c >= '{' && c <= '~') || c == '\t' || c == ' ');
+}
+
+static _FORCE_INLINE_ bool is_control(char32_t p_char) {
+	return (p_char <= 0x001f) || (p_char >= 0x007f && p_char <= 0x009f);
+}
+
+static _FORCE_INLINE_ bool is_whitespace(char32_t p_char) {
+	return (p_char == ' ') || (p_char == 0x00a0) || (p_char == 0x1680) || (p_char >= 0x2000 && p_char <= 0x200a) || (p_char == 0x202f) || (p_char == 0x205f) || (p_char == 0x3000) || (p_char == 0x2028) || (p_char == 0x2029) || (p_char >= 0x0009 && p_char <= 0x000d) || (p_char == 0x0085);
+}
+
+static _FORCE_INLINE_ bool is_linebreak(char32_t p_char) {
+	return (p_char >= 0x000a && p_char <= 0x000d) || (p_char == 0x0085) || (p_char == 0x2028) || (p_char == 0x2029);
+}
+
+static _FORCE_INLINE_ bool is_punct(char32_t p_char) {
+	return (p_char >= ' ' && p_char <= '/') || (p_char >= ':' && p_char <= '@') || (p_char >= '[' && p_char <= '^') || (p_char == '`') || (p_char >= '{' && p_char <= '~') || (p_char >= 0x2000 && p_char <= 0x206f) || (p_char >= 0x3000 && p_char <= 0x303f);
+}
+
+static _FORCE_INLINE_ bool is_underscore(char32_t p_char) {
+	return (p_char == '_');
+}
+
+#endif // CHAR_UTILS_H

core/string/ustring.h

@@ -0,0 +1,639 @@
+#ifndef USTRING_H
+#define USTRING_H
+
+/*************************************************************************/
+/*  ustring.h                                                            */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "core/containers/cowdata.h"
+#include "core/containers/vector.h"
+#include "core/string/char_utils.h"
+#include "core/typedefs.h"
+#include "core/variant/array.h"
+
+/*************************************************************************/
+/*  CharProxy                                                            */
+/*************************************************************************/
+
+template <class T>
+class CharProxy {
+	friend class Char16String;
+	friend class CharString;
+	friend class String;
+
+	const int _index;
+	CowData<T> &_cowdata;
+	static const T _null = 0;
+
+	_FORCE_INLINE_ CharProxy(const int &p_index, CowData<T> &p_cowdata) :
+			_index(p_index),
+			_cowdata(p_cowdata) {}
+
+public:
+	_FORCE_INLINE_ CharProxy(const CharProxy<T> &p_other) :
+			_index(p_other._index),
+			_cowdata(p_other._cowdata) {}
+
+	_FORCE_INLINE_ operator T() const {
+		if (unlikely(_cowdata.size() == 0)) {
+			return _null;
+		}
+
+		return _cowdata.get(_index);
+	}
+
+	_FORCE_INLINE_ const T *operator&() const {
+		return _cowdata.ptr() + _index;
+	}
+
+	_FORCE_INLINE_ void operator=(const T &p_other) const {
+		_cowdata.set(_index, p_other);
+	}
+
+	_FORCE_INLINE_ void operator=(const CharProxy<T> &p_other) const {
+		_cowdata.set(_index, p_other.operator T());
+	}
+};
+
+/*************************************************************************/
+/*  Char16String                                                         */
+/*************************************************************************/
+
+class Char16String {
+	CowData<char16_t> _cowdata;
+	static const char16_t _null;
+
+public:
+	_FORCE_INLINE_ char16_t *ptrw() { return _cowdata.ptrw(); }
+	_FORCE_INLINE_ const char16_t *ptr() const { return _cowdata.ptr(); }
+	_FORCE_INLINE_ int size() const { return _cowdata.size(); }
+	Error resize(int p_size) {
+		Error err = _cowdata.resize(p_size);
+
+		//Ensure null terminator
+		if (err == OK && _cowdata.size() > 0) {
+			_cowdata.set(_cowdata.size() - 1, '\0');
+		}
+
+		return err;
+	}
+
+	_FORCE_INLINE_ char16_t get(int p_index) const { return _cowdata.get(p_index); }
+	_FORCE_INLINE_ void set(int p_index, const char16_t &p_elem) { _cowdata.set(p_index, p_elem); }
+	_FORCE_INLINE_ const char16_t &operator[](int p_index) const {
+		if (unlikely(_cowdata.size() == 0)) {
+			return _null;
+		}
+
+		return _cowdata.get(p_index);
+	}
+	_FORCE_INLINE_ CharProxy<char16_t> operator[](int p_index) { return CharProxy<char16_t>(p_index, _cowdata); }
+
+	_FORCE_INLINE_ Char16String() {}
+	_FORCE_INLINE_ Char16String(const Char16String &p_str) { _cowdata._ref(p_str._cowdata); }
+	_FORCE_INLINE_ void operator=(const Char16String &p_str) { _cowdata._ref(p_str._cowdata); }
+	_FORCE_INLINE_ Char16String(const char16_t *p_cstr) { copy_from(p_cstr); }
+
+	void operator=(const char16_t *p_cstr);
+	bool operator<(const Char16String &p_right) const;
+	Char16String &operator+=(char16_t p_char);
+	int length() const { return size() ? size() - 1 : 0; }
+	const char16_t *get_data() const;
+	operator const char16_t *() const { return get_data(); };
+
+protected:
+	void copy_from(const char16_t *p_cstr);
+};
+
+/*************************************************************************/
+/*  CharString                                                           */
+/*************************************************************************/
+
+class CharString {
+	CowData<char> _cowdata;
+	static const char _null;
+
+public:
+	_FORCE_INLINE_ char *ptrw() { return _cowdata.ptrw(); }
+	_FORCE_INLINE_ const char *ptr() const { return _cowdata.ptr(); }
+	_FORCE_INLINE_ int size() const { return _cowdata.size(); }
+	Error resize(int p_size) {
+		Error err = _cowdata.resize(p_size);
+
+		//Ensure null terminator
+		if (err == OK && _cowdata.size() > 0) {
+			_cowdata.set(_cowdata.size() - 1, '\0');
+		}
+
+		return err;
+	}
+
+	_FORCE_INLINE_ char get(int p_index) const { return _cowdata.get(p_index); }
+	_FORCE_INLINE_ void set(int p_index, const char &p_elem) { _cowdata.set(p_index, p_elem); }
+	_FORCE_INLINE_ const char &operator[](int p_index) const {
+		if (unlikely(_cowdata.size() == 0)) {
+			return _null;
+		}
+
+		return _cowdata.get(p_index);
+	}
+	_FORCE_INLINE_ CharProxy<char> operator[](int p_index) { return CharProxy<char>(p_index, _cowdata); }
+
+	_FORCE_INLINE_ CharString() {}
+	_FORCE_INLINE_ CharString(const CharString &p_str) { _cowdata._ref(p_str._cowdata); }
+	_FORCE_INLINE_ void operator=(const CharString &p_str) { _cowdata._ref(p_str._cowdata); }
+	_FORCE_INLINE_ CharString(const char *p_cstr) { copy_from(p_cstr); }
+
+	void operator=(const char *p_cstr);
+	bool operator<(const CharString &p_right) const;
+	CharString &operator+=(char p_char);
+	int length() const { return size() ? size() - 1 : 0; }
+	const char *get_data() const;
+	operator const char *() const { return get_data(); };
+
+protected:
+	void copy_from(const char *p_cstr);
+};
+
+/*************************************************************************/
+/*  String                                                               */
+/*************************************************************************/
+
+typedef char32_t CharType;
+
+struct StrRange {
+	const CharType *c_str;
+	int len;
+
+	StrRange(const CharType *p_c_str = nullptr, int p_len = 0) {
+		c_str = p_c_str;
+		len = p_len;
+	}
+};
+
+class String {
+public:
+	enum {
+		npos = -1 ///<for "some" compatibility with std::string (npos is a huge value in std::string)
+	};
+
+	_FORCE_INLINE_ CharType *ptrw() { return _cowdata.ptrw(); }
+	_FORCE_INLINE_ const CharType *ptr() const { return _cowdata.ptr(); }
+
+	_FORCE_INLINE_ void remove(int p_index) {
+		_cowdata.remove(p_index);
+
+		//Ensure null terminator
+		if (_cowdata.size() > 0) {
+			_cowdata.set(_cowdata.size() - 1, '\0');
+		}
+	}
+
+	_FORCE_INLINE_ void clear() { resize(0); }
+
+	_FORCE_INLINE_ CharType get(int p_index) const { return _cowdata.get(p_index); }
+	_FORCE_INLINE_ void set(int p_index, const CharType &p_elem) { _cowdata.set(p_index, p_elem); }
+	_FORCE_INLINE_ int size() const { return _cowdata.size(); }
+	_FORCE_INLINE_ Error resize(int p_size) {
+		Error err = _cowdata.resize(p_size);
+
+		//Ensure null terminator
+		if (err == OK && _cowdata.size() > 0) {
+			_cowdata.set(_cowdata.size() - 1, '\0');
+		}
+
+		return err;
+	}
+	_FORCE_INLINE_ Error set_length(int p_length) { return resize(p_length + 1); }
+
+	_FORCE_INLINE_ const CharType &operator[](int p_index) const {
+		return _cowdata.get(p_index);
+	}
+	_FORCE_INLINE_ CharProxy<CharType> operator[](int p_index) { return CharProxy<CharType>(p_index, _cowdata); }
+
+	bool operator==(const String &p_str) const;
+	bool operator!=(const String &p_str) const;
+	String operator+(const String &p_str) const;
+	//String operator+(CharType p_char) const;
+
+	String &operator+=(const String &);
+	String &operator+=(CharType p_char);
+	String &operator+=(const char *p_str);
+	String &operator+=(const wchar_t *p_str);
+	String &operator+=(const CharType *p_str);
+
+	/* Compatibility Operators */
+
+	void operator=(const char *p_str);
+	void operator=(const wchar_t *p_str);
+	void operator=(const CharType *p_str);
+
+	bool operator==(const char *p_str) const;
+	bool operator==(const wchar_t *p_str) const;
+	bool operator==(const CharType *p_str) const;
+	bool operator==(const StrRange &p_str_range) const;
+
+	bool operator!=(const char *p_str) const;
+	bool operator!=(const wchar_t *p_str) const;
+	bool operator!=(const CharType *p_str) const;
+
+	bool operator<(const CharType *p_str) const;
+	bool operator<(const char *p_str) const;
+	bool operator<(const wchar_t *p_str) const;
+
+	bool operator<(const String &p_str) const;
+	bool operator<=(const String &p_str) const;
+	bool operator>(const String &p_str) const;
+	bool operator>=(const String &p_str) const;
+
+	signed char casecmp_to(const String &p_str) const;
+	signed char nocasecmp_to(const String &p_str) const;
+	signed char naturalnocasecmp_to(const String &p_str) const;
+
+	const CharType *get_data() const;
+
+	/* standard size stuff */
+
+	_FORCE_INLINE_ int length() const {
+		int s = size();
+		return s ? (s - 1) : 0; // length does not include zero
+	}
+
+	bool is_valid_string() const;
+
+	/* debug, error messages */
+	void print_unicode_error(const String &p_message, bool p_critical = false) const;
+
+	/* complex helpers */
+	String substr(int p_from, int p_chars = -1) const;
+	String substr_index(const int p_start_index, const int p_end_index) const; //end_index is not included
+
+	int find(const String &p_str, int p_from = 0) const; ///< return <0 if failed
+	int find(const char *p_str, int p_from = 0) const; ///< return <0 if failed
+	int find_char(const CharType &p_char, int p_from = 0) const; ///< return <0 if failed
+	int find_last(const String &p_str) const; ///< return <0 if failed
+	int findn(const String &p_str, int p_from = 0) const; ///< return <0 if failed, case insensitive
+	int rfind(const String &p_str, int p_from = -1) const; ///< return <0 if failed
+	int rfindn(const String &p_str, int p_from = -1) const; ///< return <0 if failed, case insensitive
+	int findmk(const Vector<String> &p_keys, int p_from = 0, int *r_key = nullptr) const; ///< return <0 if failed
+	int find_first_difference_index(const String &p_str) const;
+
+	bool is_word_at(const int p_index, const char *p_str) const;
+	bool is_word_at(const int p_index, const String &p_str) const;
+
+	bool match(const String &p_wildcard) const;
+	bool matchn(const String &p_wildcard) const;
+
+	bool begins_with(const String &p_string) const;
+	bool begins_with(const char *p_string) const;
+	bool ends_with(const String &p_string) const;
+
+	bool is_enclosed_in(const String &p_string) const;
+	bool is_subsequence_of(const String &p_string) const;
+	bool is_subsequence_ofi(const String &p_string) const;
+	bool is_quoted() const;
+
+	Vector<String> bigrams() const;
+	float similarity(const String &p_string) const;
+	String format(const Variant &values, String placeholder = "{_}") const;
+
+	String replace_first(const String &p_key, const String &p_with) const;
+	String replace(const String &p_key, const String &p_with) const;
+	String replace(const char *p_key, const char *p_with) const;
+	String replacen(const String &p_key, const String &p_with) const;
+
+	String newline_to_br() const;
+
+	String repeat(int p_count) const;
+	String insert(int p_at_pos, const String &p_string) const;
+
+	String pad_decimals(int p_digits) const;
+	String pad_zeros(int p_digits) const;
+
+	String trim_prefix(const String &p_prefix) const;
+	String trim_suffix(const String &p_suffix) const;
+
+	String lpad(int min_length, const String &character = " ") const;
+	String rpad(int min_length, const String &character = " ") const;
+
+	String sprintf(const Array &values, bool *error) const;
+
+	String quote(String quotechar = "\"") const;
+	String unquote() const;
+
+	static String num(double p_num, int p_decimals = -1);
+	static String num_scientific(double p_num);
+	static String num_real(double p_num);
+	static String num_int64(int64_t p_num, int base = 10, bool capitalize_hex = false);
+	static String num_uint64(uint64_t p_num, int base = 10, bool capitalize_hex = false);
+
+	static String chr(CharType p_char);
+
+	static String md5(const uint8_t *p_md5);
+
+	static String hex_encode_buffer(const uint8_t *p_buffer, int p_len);
+
+	static String bool_num(bool p_val);
+	static String bool_str(bool p_val);
+
+	bool is_numeric() const;
+	bool is_zero() const;
+
+	double to_double() const;
+	float to_float() const;
+	int to_int() const;
+	bool to_bool() const;
+	uint32_t to_uint() const;
+
+	int hex_to_int(bool p_with_prefix = true) const;
+	int64_t hex_to_int64(bool p_with_prefix = true) const;
+	int64_t bin_to_int64(bool p_with_prefix = true) const;
+	int64_t to_int64() const;
+
+	static int64_t to_int(const char *p_str, int p_len = -1);
+	static int64_t to_int(const wchar_t *p_str, int p_len = -1);
+	static int64_t to_int(const CharType *p_str, int p_len = -1, bool p_clamp = false);
+
+	static double to_float(const char *p_str);
+	static double to_float(const wchar_t *p_str, const wchar_t **r_end = nullptr);
+	static double to_float(const CharType *p_str, const CharType **r_end = nullptr);
+
+	static double to_double(const char *p_str);
+	static double to_double(const wchar_t *p_str, const wchar_t **r_end = nullptr);
+	static double to_double(const CharType *p_str, const CharType **r_end = nullptr);
+
+	static uint32_t num_characters(int64_t p_int);
+
+	String capitalize() const;
+	String camelcase_to_underscore(bool lowercase = true) const;
+
+	String get_with_code_lines() const;
+	int get_slice_count(String p_splitter) const;
+	String get_slice(String p_splitter, int p_slice) const;
+	String get_slicec(CharType p_splitter, int p_slice) const;
+
+	Vector<String> split(const String &p_splitter, bool p_allow_empty = true, int p_maxsplit = 0) const;
+	Vector<String> rsplit(const String &p_splitter, bool p_allow_empty = true, int p_maxsplit = 0) const;
+	Vector<String> split_spaces() const;
+	Vector<float> split_floats(const String &p_splitter, bool p_allow_empty = true) const;
+	Vector<float> split_floats_mk(const Vector<String> &p_splitters, bool p_allow_empty = true) const;
+	Vector<int> split_ints(const String &p_splitter, bool p_allow_empty = true) const;
+	Vector<int> split_ints_mk(const Vector<String> &p_splitters, bool p_allow_empty = true) const;
+
+	String join(const Vector<String> &parts) const;
+
+	static CharType char_uppercase(CharType p_char);
+	static CharType char_lowercase(CharType p_char);
+	String to_upper() const;
+	String to_lower() const;
+
+	int count(const String &p_string, int p_from = 0, int p_to = 0) const;
+	int countn(const String &p_string, int p_from = 0, int p_to = 0) const;
+
+	String left(int p_pos) const;
+	String right(int p_pos) const;
+	String indent(const String &p_prefix) const;
+	String dedent() const;
+
+	String strip_edges(bool left = true, bool right = true) const;
+	String strip_escapes() const;
+	String lstrip(const String &p_chars) const;
+	String rstrip(const String &p_chars) const;
+
+	String get_extension() const;
+	String get_basename() const;
+	String plus_file(const String &p_file) const;
+
+	CharType unicode_at(int p_idx) const;
+	CharType ord_at(int p_idx) const;
+
+	void erase(int p_pos, int p_chars);
+
+	CharString ascii(bool p_allow_extended = false) const;
+	CharString utf8() const;
+	Error parse_utf8(const char *p_utf8, int p_len = -1, bool p_skip_cr = false); //return true on error
+	static String utf8(const char *p_utf8, int p_len = -1);
+	int utf8_byte_length() const;
+
+	Char16String utf16() const;
+	Error parse_utf16(const char16_t *p_utf16, int p_len = -1);
+	static String utf16(const char16_t *p_utf16, int p_len = -1);
+	int utf16_byte_length() const;
+
+	static uint32_t hash(const char *p_cstr); /* hash the string */
+	static uint32_t hash(const char *p_cstr, int p_len); /* hash the string */
+	static uint32_t hash(const wchar_t *p_cstr); /* hash the string */
+	static uint32_t hash(const wchar_t *p_cstr, int p_len); /* hash the string */
+	static uint32_t hash(const CharType *p_cstr); /* hash the string */
+	static uint32_t hash(const CharType *p_cstr, int p_len); /* hash the string */
+
+	uint32_t hash() const; /* hash the string */
+	uint64_t hash64() const; /* hash the string */
+
+	String md5_text() const;
+	String sha1_text() const;
+	String sha256_text() const;
+	Vector<uint8_t> md5_buffer() const;
+	Vector<uint8_t> sha1_buffer() const;
+	Vector<uint8_t> sha256_buffer() const;
+
+	_FORCE_INLINE_ bool empty() const { return length() == 0; }
+	_FORCE_INLINE_ bool contains(const char *p_str) const { return find(p_str) != -1; }
+	_FORCE_INLINE_ bool contains(const String &p_str) const { return find(p_str) != -1; }
+
+	// path functions
+	bool is_abs_path() const;
+	bool is_rel_path() const;
+	bool is_resource_file() const;
+	String path_to(const String &p_path) const;
+	String path_to_file(const String &p_path) const;
+	String get_base_dir() const;
+	String get_file() const;
+	static String humanize_size(uint64_t p_size);
+	String simplify_path() const;
+	bool is_network_share_path() const;
+	String append_path(const char *p_path) const;
+	String append_path(const String &p_path) const;
+	String path_clean_end_slash() const;
+	String path_ensure_end_slash() const;
+	String path_get_prev_dir() const;
+
+	String xml_escape(bool p_escape_quotes = false) const;
+	String xml_unescape() const;
+	String http_escape() const;
+	String http_unescape() const;
+	String uri_encode() const;
+	String uri_decode() const;
+	String c_escape() const;
+	String c_escape_multiline() const;
+	String c_unescape() const;
+	String json_escape() const;
+	String word_wrap(int p_chars_per_line) const;
+	Error parse_url(String &r_scheme, String &r_host, int &r_port, String &r_path) const;
+
+	String percent_encode() const;
+	String percent_decode() const;
+
+	String property_name_encode() const;
+
+	// node functions
+	static String get_invalid_node_name_characters();
+	String validate_node_name() const;
+	String validate_identifier() const;
+
+	bool is_valid_identifier() const;
+	bool is_valid_integer() const;
+	bool is_valid_float() const;
+	bool is_valid_hex_number(bool p_with_prefix) const;
+	bool is_valid_html_color() const;
+	bool is_valid_ip_address() const;
+	bool is_valid_filename() const;
+	bool is_valid_bool() const;
+	bool is_valid_unsigned_integer() const;
+
+	/**
+	 * The constructors must not depend on other overloads
+	 */
+
+	/*	String(CharType p_char);*/
+	_FORCE_INLINE_ String() {}
+	_FORCE_INLINE_ String(const String &p_str) { _cowdata._ref(p_str._cowdata); }
+
+	void operator=(const String &p_str) {
+		_cowdata._ref(p_str._cowdata);
+	}
+
+	Vector<uint8_t> to_ascii_buffer() const;
+	Vector<uint8_t> to_utf8_buffer() const;
+	Vector<uint8_t> to_utf16_buffer() const;
+	Vector<uint8_t> to_utf32_buffer() const;
+
+	String(const char *p_str);
+	String(const wchar_t *p_str);
+	String(const CharType *p_str);
+	String(const char *p_str, int p_clip_to_len);
+	String(const wchar_t *p_str, int p_clip_to_len);
+	String(const CharType *p_str, int p_clip_to_len);
+	String(const StrRange &p_range);
+
+private:
+	CowData<CharType> _cowdata;
+	static const CharType _null;
+
+	void copy_from(const char *p_cstr);
+	void copy_from(const char *p_cstr, const int p_clip_to);
+	void copy_from(const wchar_t *p_cstr);
+	void copy_from(const wchar_t *p_cstr, const int p_clip_to);
+	void copy_from(const CharType *p_cstr);
+	void copy_from(const CharType *p_cstr, const int p_clip_to);
+
+	void copy_from(const CharType &p_char);
+
+	void copy_from_unchecked(const CharType *p_char, const int p_length);
+
+	bool _base_is_subsequence_of(const String &p_string, bool case_insensitive) const;
+	int _count(const String &p_string, int p_from, int p_to, bool p_case_insensitive) const;
+};
+
+bool operator==(const char *p_chr, const String &p_str);
+bool operator==(const wchar_t *p_chr, const String &p_str);
+bool operator!=(const char *p_chr, const String &p_str);
+bool operator!=(const wchar_t *p_chr, const String &p_str);
+
+String operator+(const char *p_chr, const String &p_str);
+String operator+(const wchar_t *p_chr, const String &p_str);
+String operator+(CharType p_chr, const String &p_str);
+
+String itos(int64_t p_val);
+String uitos(uint64_t p_val);
+String rtos(double p_val);
+String rtoss(double p_val); //scientific version
+
+struct NoCaseComparator {
+	bool operator()(const String &p_a, const String &p_b) const {
+		return p_a.nocasecmp_to(p_b) < 0;
+	}
+};
+
+struct NaturalNoCaseComparator {
+	bool operator()(const String &p_a, const String &p_b) const {
+		return p_a.naturalnocasecmp_to(p_b) < 0;
+	}
+};
+
+template <typename L, typename R>
+_FORCE_INLINE_ bool is_str_less(const L *l_ptr, const R *r_ptr) {
+	while (true) {
+		const CharType l = *l_ptr;
+		const CharType r = *r_ptr;
+
+		if (l == 0 && r == 0) {
+			return false;
+		} else if (l == 0) {
+			return true;
+		} else if (r == 0) {
+			return false;
+		} else if (l < r) {
+			return true;
+		} else if (l > r) {
+			return false;
+		}
+
+		l_ptr++;
+		r_ptr++;
+	}
+}
+
+/* end of namespace */
+
+// Tool translate (TTR and variants) for the editor UI,
+// and doc translate for the class reference (DTR).
+#ifdef TOOLS_ENABLED
+// Gets parsed.
+String TTR(const String &p_text, const String &p_context = "");
+String DTR(const String &);
+// Use for C strings.
+#define TTRC(m_value) (m_value)
+// Use to avoid parsing (for use later with C strings).
+#define TTRGET(m_value) TTR(m_value)
+
+#else
+#define TTR(m_value) (String())
+#define DTR(m_value) (String())
+#define TTRC(m_value) (m_value)
+#define TTRGET(m_value) (m_value)
+#endif
+
+// Runtime translate for the public node API.
+String RTR(const String &);
+
+bool select_word(const String &p_s, int p_col, int &r_beg, int &r_end);
+
+#endif // USTRING_H

render/primitive_meshes.h

@@ -0,0 +1,447 @@
+#ifndef PRIMITIVE_MESHES_H
+#define PRIMITIVE_MESHES_H
+
+/*************************************************************************/
+/*  primitive_meshes.h                                                   */
+/*************************************************************************/
+/*                         This file is part of:                         */
+/*                          PANDEMONIUM ENGINE                           */
+/*             https://github.com/Relintai/pandemonium_engine            */
+/*************************************************************************/
+/* Copyright (c) 2022-present Péter Magyar.                              */
+/* Copyright (c) 2014-2022 Godot Engine contributors (cf. AUTHORS.md).   */
+/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur.                 */
+/*                                                                       */
+/* Permission is hereby granted, free of charge, to any person obtaining */
+/* a copy of this software and associated documentation files (the       */
+/* "Software"), to deal in the Software without restriction, including   */
+/* without limitation the rights to use, copy, modify, merge, publish,   */
+/* distribute, sublicense, and/or sell copies of the Software, and to    */
+/* permit persons to whom the Software is furnished to do so, subject to */
+/* the following conditions:                                             */
+/*                                                                       */
+/* The above copyright notice and this permission notice shall be        */
+/* included in all copies or substantial portions of the Software.       */
+/*                                                                       */
+/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
+/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
+/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
+/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
+/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
+/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
+/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
+/*************************************************************************/
+
+#include "scene/resources/font/font.h"
+#include "scene/resources/mesh/mesh.h"
+
+///@TODO probably should change a few integers to unsigned integers...
+
+/**
+	@author Bastiaan Olij <mux213@gmail.com>
+
+	Base class for all the classes in this file, handles a number of code functions that are shared among all meshes.
+	This class is set apart that it assumes a single surface is always generated for our mesh.
+*/
+class PrimitiveMesh : public Mesh {
+	GDCLASS(PrimitiveMesh, Mesh);
+
+private:
+	RID mesh;
+	mutable AABB aabb;
+	AABB custom_aabb;
+
+	Ref<Material> material;
+	bool flip_faces;
+
+	mutable bool pending_request;
+	void _update() const;
+
+protected:
+	Mesh::PrimitiveType primitive_type;
+
+	static void _bind_methods();
+
+	virtual void _create_mesh_array(Array &p_arr) const = 0;
+	void _request_update();
+
+public:
+	virtual int get_surface_count() const;
+	virtual int surface_get_array_len(int p_idx) const;
+	virtual int surface_get_array_index_len(int p_idx) const;
+	virtual Array surface_get_arrays(int p_surface) const;
+	virtual Array surface_get_blend_shape_arrays(int p_surface) const;
+	virtual uint32_t surface_get_format(int p_idx) const;
+	virtual Mesh::PrimitiveType surface_get_primitive_type(int p_idx) const;
+	virtual void surface_set_material(int p_idx, const Ref<Material> &p_material);
+	virtual Ref<Material> surface_get_material(int p_idx) const;
+	virtual int get_blend_shape_count() const;
+	virtual StringName get_blend_shape_name(int p_index) const;
+	virtual void set_blend_shape_name(int p_index, const StringName &p_name);
+	virtual AABB get_aabb() const;
+	virtual RID get_rid() const;
+
+	void set_material(const Ref<Material> &p_material);
+	Ref<Material> get_material() const;
+
+	Array get_mesh_arrays() const;
+
+	void set_custom_aabb(const AABB &p_custom);
+	AABB get_custom_aabb() const;
+
+	void set_flip_faces(bool p_enable);
+	bool get_flip_faces() const;
+
+	PrimitiveMesh();
+	~PrimitiveMesh();
+};
+
+/**
+	Mesh for a simple capsule
+*/
+class CapsuleMesh : public PrimitiveMesh {
+	GDCLASS(CapsuleMesh, PrimitiveMesh);
+
+private:
+	float radius;
+	float mid_height;
+	int radial_segments;
+	int rings;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	static void create_mesh_array(Array &p_arr, float radius, float mid_height, int radial_segments = 64, int rings = 8);
+
+	void set_radius(const float p_radius);
+	float get_radius() const;
+
+	void set_mid_height(const float p_mid_height);
+	float get_mid_height() const;
+
+	void set_radial_segments(const int p_segments);
+	int get_radial_segments() const;
+
+	void set_rings(const int p_rings);
+	int get_rings() const;
+
+	CapsuleMesh();
+};
+
+/**
+	Similar to test cube but with subdivision support and different texture coordinates
+*/
+class CubeMesh : public PrimitiveMesh {
+	GDCLASS(CubeMesh, PrimitiveMesh);
+
+private:
+	Vector3 size;
+	int subdivide_w;
+	int subdivide_h;
+	int subdivide_d;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	static void create_mesh_array(Array &p_arr, Vector3 size, int subdivide_w = 0, int subdivide_h = 0, int subdivide_d = 0);
+
+	void set_size(const Vector3 &p_size);
+	Vector3 get_size() const;
+
+	void set_subdivide_width(const int p_divisions);
+	int get_subdivide_width() const;
+
+	void set_subdivide_height(const int p_divisions);
+	int get_subdivide_height() const;
+
+	void set_subdivide_depth(const int p_divisions);
+	int get_subdivide_depth() const;
+
+	CubeMesh();
+};
+
+/**
+	A cylinder
+*/
+
+class CylinderMesh : public PrimitiveMesh {
+	GDCLASS(CylinderMesh, PrimitiveMesh);
+
+private:
+	float top_radius;
+	float bottom_radius;
+	float height;
+	int radial_segments;
+	int rings;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	static void create_mesh_array(Array &p_arr, float top_radius, float bottom_radius, float height, int radial_segments = 64, int rings = 4);
+
+	void set_top_radius(const float p_radius);
+	float get_top_radius() const;
+
+	void set_bottom_radius(const float p_radius);
+	float get_bottom_radius() const;
+
+	void set_height(const float p_height);
+	float get_height() const;
+
+	void set_radial_segments(const int p_segments);
+	int get_radial_segments() const;
+
+	void set_rings(const int p_rings);
+	int get_rings() const;
+
+	CylinderMesh();
+};
+
+/**
+	Similar to quadmesh but with tessellation support
+*/
+class PlaneMesh : public PrimitiveMesh {
+	GDCLASS(PlaneMesh, PrimitiveMesh);
+
+private:
+	Size2 size;
+	int subdivide_w;
+	int subdivide_d;
+	Vector3 center_offset;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	void set_size(const Size2 &p_size);
+	Size2 get_size() const;
+
+	void set_subdivide_width(const int p_divisions);
+	int get_subdivide_width() const;
+
+	void set_subdivide_depth(const int p_divisions);
+	int get_subdivide_depth() const;
+
+	void set_center_offset(const Vector3 p_offset);
+	Vector3 get_center_offset() const;
+
+	PlaneMesh();
+};
+
+/**
+	A prism shapen, handy for ramps, triangles, etc.
+*/
+class PrismMesh : public PrimitiveMesh {
+	GDCLASS(PrismMesh, PrimitiveMesh);
+
+private:
+	float left_to_right;
+	Vector3 size;
+	int subdivide_w;
+	int subdivide_h;
+	int subdivide_d;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	void set_left_to_right(const float p_left_to_right);
+	float get_left_to_right() const;
+
+	void set_size(const Vector3 &p_size);
+	Vector3 get_size() const;
+
+	void set_subdivide_width(const int p_divisions);
+	int get_subdivide_width() const;
+
+	void set_subdivide_height(const int p_divisions);
+	int get_subdivide_height() const;
+
+	void set_subdivide_depth(const int p_divisions);
+	int get_subdivide_depth() const;
+
+	PrismMesh();
+};
+
+/**
+	Our original quadmesh...
+*/
+
+class QuadMesh : public PrimitiveMesh {
+	GDCLASS(QuadMesh, PrimitiveMesh);
+
+private:
+	Size2 size;
+	Vector3 center_offset;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	QuadMesh();
+
+	void set_size(const Size2 &p_size);
+	Size2 get_size() const;
+
+	void set_center_offset(const Vector3 p_offset);
+	Vector3 get_center_offset() const;
+};
+
+/**
+	A sphere..
+*/
+class SphereMesh : public PrimitiveMesh {
+	GDCLASS(SphereMesh, PrimitiveMesh);
+
+private:
+	float radius;
+	float height;
+	int radial_segments;
+	int rings;
+	bool is_hemisphere;
+
+protected:
+	static void _bind_methods();
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	static void create_mesh_array(Array &p_arr, float radius, float height, int radial_segments = 64, int rings = 32, bool is_hemisphere = false);
+
+	void set_radius(const float p_radius);
+	float get_radius() const;
+
+	void set_height(const float p_height);
+	float get_height() const;
+
+	void set_radial_segments(const int p_radial_segments);
+	int get_radial_segments() const;
+
+	void set_rings(const int p_rings);
+	int get_rings() const;
+
+	void set_is_hemisphere(const bool p_is_hemisphere);
+	bool get_is_hemisphere() const;
+
+	SphereMesh();
+};
+
+/**
+	A single point for use in particle systems
+*/
+
+class PointMesh : public PrimitiveMesh {
+	GDCLASS(PointMesh, PrimitiveMesh)
+
+protected:
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	PointMesh();
+};
+
+/**
+	Text...
+*/
+
+class TextMesh : public PrimitiveMesh {
+	GDCLASS(TextMesh, PrimitiveMesh);
+
+public:
+	enum Align {
+
+		ALIGN_LEFT,
+		ALIGN_CENTER,
+		ALIGN_RIGHT
+	};
+
+private:
+	struct ContourPoint {
+		Vector2 point;
+		bool sharp = false;
+
+		ContourPoint(){};
+		ContourPoint(const Vector2 &p_pt, bool p_sharp) {
+			point = p_pt;
+			sharp = p_sharp;
+		};
+	};
+	struct ContourInfo {
+		real_t length = 0.0;
+		bool ccw = true;
+		ContourInfo(){};
+		ContourInfo(real_t p_len, bool p_ccw) {
+			length = p_len;
+			ccw = p_ccw;
+		}
+	};
+	struct GlyphMeshData {
+		Vector<Vector2> triangles;
+		Vector<Vector<ContourPoint>> contours;
+		Vector<ContourInfo> contours_info;
+		Vector2 min_p = Vector2(INFINITY, INFINITY);
+		Vector2 max_p = Vector2(-INFINITY, -INFINITY);
+	};
+	mutable HashMap<uint32_t, GlyphMeshData> cache;
+
+	String text;
+	String xl_text;
+
+	Ref<Font> font_override;
+
+	Align horizontal_alignment = ALIGN_CENTER;
+	bool uppercase = false;
+
+	real_t depth = 0.05;
+	real_t pixel_size = 0.01;
+	real_t curve_step = 0.5;
+
+	mutable bool dirty_cache = true;
+
+	void _generate_glyph_mesh_data(uint32_t p_utf32_char, const Ref<Font> &p_font, CharType p_char, CharType p_next) const;
+	void _font_changed();
+
+protected:
+	static void _bind_methods();
+	void _notification(int p_what);
+
+	virtual void _create_mesh_array(Array &p_arr) const;
+
+public:
+	TextMesh();
+	~TextMesh();
+
+	void set_horizontal_alignment(Align p_alignment);
+	Align get_horizontal_alignment() const;
+
+	void set_text(const String &p_string);
+	String get_text() const;
+
+	void set_font(const Ref<Font> &p_font);
+	Ref<Font> get_font() const;
+	Ref<Font> _get_font_or_default() const;
+
+	void set_uppercase(bool p_uppercase);
+	bool is_uppercase() const;
+
+	void set_depth(real_t p_depth);
+	real_t get_depth() const;
+
+	void set_curve_step(real_t p_step);
+	real_t get_curve_step() const;
+
+	void set_pixel_size(real_t p_amount);
+	real_t get_pixel_size() const;
+};
+
+VARIANT_ENUM_CAST(TextMesh::Align);
+
+#endif