#include "wave_form_collapse.h" const int WaveFormCollapse::DIRECTIONS_X[4] = { 0, -1, 1, 0 }; const int WaveFormCollapse::DIRECTIONS_Y[4] = { -1, 0, 0, 1 }; // Normalize a vector so the sum of its elements is equal to 1.0f void WaveFormCollapse::normalize(Vector &v) { double sum_weights = 0.0; int size = v.size(); const double *vpr = v.ptr(); for (int i = 0; i < size; ++i) { sum_weights += vpr[i]; } double *vpw = v.ptrw(); double inv_sum_weights = 1.0 / sum_weights; for (int i = 0; i < size; ++i) { vpw[i] *= inv_sum_weights; } } // Return distribution * log(distribution). Vector WaveFormCollapse::get_plogp(const Vector &distribution) { Vector plogp; for (int i = 0; i < distribution.size(); i++) { plogp.push_back(distribution[i] * log(distribution[i])); } return plogp; } // Return min(v) / 2. double WaveFormCollapse::get_min_abs_half(const Vector &v) { double min_abs_half = Math_INF; for (int i = 0; i < v.size(); i++) { min_abs_half = MIN(min_abs_half, ABS(v[i] / 2.0)); } return min_abs_half; } int WaveFormCollapse::get_wave_width() const { return _wave_width; } void WaveFormCollapse::set_wave_width(const int val) { _wave_width = val; } int WaveFormCollapse::get_wave_height() const { return _wave_height; } void WaveFormCollapse::set_wave_height(const int val) { _wave_height = val; } bool WaveFormCollapse::get_periodic_output() const { return _periodic_output; } void WaveFormCollapse::set_periodic_output(const bool val) { _periodic_output = val; } void WaveFormCollapse::set_seed(const int seed) { _gen.seed(seed); } void WaveFormCollapse::set_wave_size(int p_width, int p_height) { _wave_width = p_width; _wave_height = p_height; _wave_size = p_height * p_width; } void WaveFormCollapse::init_wave() { _wave_size = _wave_height * _wave_width; } void WaveFormCollapse::set_propagator_state(const Vector &p_propagator_state) { _propagator_state = p_propagator_state; } void WaveFormCollapse::set_pattern_frequencies(const Vector &p_patterns_frequencies, const bool p_normalize) { _patterns_frequencies = p_patterns_frequencies; if (p_normalize) { normalize(_patterns_frequencies); } } void WaveFormCollapse::set_input(const PoolIntArray &p_data, int p_width, int p_height) { _input.resize(p_height, p_width); ERR_FAIL_COND(_input.data.size() != p_data.size()); int *w = _input.data.ptrw(); int s = _input.data.size(); PoolIntArray::Read r = p_data.read(); for (int i = 0; i < s; ++i) { w[i] = r[i]; } } Array2D WaveFormCollapse::run() { while (true) { // Define the value of an undefined cell. ObserveStatus result = observe(); // Check if the algorithm has terminated. if (result == OBSERVE_STATUS_FAILURE) { return Array2D(0, 0); } else if (result == OBSERVE_STATUS_SUCCESS) { return wave_to_output(); } propagate(); } } PoolIntArray WaveFormCollapse::generate_image_index_data() { PoolIntArray arr; Array2D a = run(); if (a.width == 0 && a.height == 0) { return arr; } const int *r = a.data.ptr(); int s = a.data.size(); arr.resize(s); PoolIntArray::Write w = arr.write(); for (int i = 0; i < s; ++i) { w[i] = r[i]; } w.release(); return arr; } WaveFormCollapse::ObserveStatus WaveFormCollapse::observe() { // Get the cell with lowest entropy. int argmin = wave_get_min_entropy(); // If there is a contradiction, the algorithm has failed. if (argmin == -2) { return OBSERVE_STATUS_FAILURE; } // If the lowest entropy is 0, then the algorithm has succeeded and finished. if (argmin == -1) { wave_to_output(); return OBSERVE_STATUS_SUCCESS; } // Choose an element according to the pattern distribution double s = 0; for (int k = 0; k < _patterns_frequencies.size(); k++) { s += wave_get(argmin, k) ? _patterns_frequencies[k] : 0; } double random_value = _gen.random(0.0, s); int chosen_value = _patterns_frequencies.size() - 1; for (int k = 0; k < _patterns_frequencies.size(); k++) { random_value -= wave_get(argmin, k) ? _patterns_frequencies[k] : 0; if (random_value <= 0) { chosen_value = k; break; } } // And define the cell with the pattern. for (int k = 0; k < _patterns_frequencies.size(); k++) { if (wave_get(argmin, k) != (k == chosen_value)) { add_to_propagator(argmin / _wave_width, argmin % _wave_width, k); wave_set(argmin, k, false); } } return OBSERVE_STATUS_TO_CONTINUE; } Array2D WaveFormCollapse::wave_to_output() const { Array2D output_patterns(_wave_height, _wave_width); for (int i = 0; i < _wave_size; i++) { for (int k = 0; k < _patterns_frequencies.size(); k++) { if (wave_get(i, k)) { output_patterns.data.write[i] = k; } } } return output_patterns; } void WaveFormCollapse::wave_set(int index, int pattern, bool value) { bool old_value = _wave_data.get(index, pattern); // If the value isn't changed, nothing needs to be done. if (old_value == value) { return; } // Otherwise, the memoisation should be updated. _wave_data.get(index, pattern) = value; _memoisation_plogp_sum.write[index] -= _plogp_patterns_frequencies[pattern]; _memoisation_sum.write[index] -= _patterns_frequencies[pattern]; _memoisation_log_sum.write[index] = Math::log(_memoisation_sum[index]); _memoisation_nb_patterns.write[index]--; _memoisation_entropy.write[index] = _memoisation_log_sum[index] - _memoisation_plogp_sum[index] / _memoisation_sum[index]; // If there is no patterns possible in the cell, then there is a contradiction. if (_memoisation_nb_patterns[index] == 0) { _is_impossible = true; } } int WaveFormCollapse::wave_get_min_entropy() const { if (_is_impossible) { return -2; } RandomPCG pcg; // The minimum entropy (plus a small noise) double min = Math_INF; int argmin = -1; for (int i = 0; i < _wave_size; i++) { // If the cell is decided, we do not compute the entropy (which is equal to 0). int nb_patterns_local = _memoisation_nb_patterns[i]; if (nb_patterns_local == 1) { continue; } // Otherwise, we take the memoised entropy. double entropy = _memoisation_entropy[i]; // We first check if the entropy is less than the minimum. // This is important to reduce noise computation (which is not // negligible). if (entropy <= min) { // Then, we add noise to decide randomly which will be chosen. // noise is smaller than the smallest p * log(p), so the minimum entropy // will always be chosen. double noise = pcg.random(0.0, _min_abs_half_plogp); if (entropy + noise < min) { min = entropy + noise; argmin = i; } } } return argmin; } void WaveFormCollapse::init_compatible() { // We compute the number of pattern compatible in all directions. for (int y = 0; y < _wave_height; y++) { for (int x = 0; x < _wave_width; x++) { for (int pattern = 0; pattern < _propagator_state.size(); pattern++) { CompatibilityEntry &value = _compatible.get(y, x, pattern); for (int direction = 0; direction < 4; direction++) { value.direction[direction] = _propagator_state[pattern].directions[get_opposite_direction(direction)].size(); } } } } } void WaveFormCollapse::propagate() { // We propagate every element while there is element to propagate. while (_propagating.size() != 0) { // The cell and pattern that has been set to false. const PropagatingEntry &e = _propagating[_propagating.size() - 1]; int y1 = e.data[0]; int x1 = e.data[1]; int pattern = e.data[2]; _propagating.resize(_propagating.size() - 1); // We propagate the information in all 4 directions. for (int direction = 0; direction < 4; direction++) { // We get the next cell in the direction direction. int dx = DIRECTIONS_X[direction]; int dy = DIRECTIONS_Y[direction]; int x2, y2; if (_periodic_output) { x2 = ((int)x1 + dx + _wave_width) % _wave_width; y2 = ((int)y1 + dy + _wave_height) % _wave_height; } else { x2 = x1 + dx; y2 = y1 + dy; if (x2 < 0 || x2 >= _wave_width) { continue; } if (y2 < 0 || y2 >= _wave_height) { continue; } } // The index of the second cell, and the patterns compatible int i2 = x2 + y2 * _wave_width; const Vector &patterns = _propagator_state[pattern].directions[direction]; // For every pattern that could be placed in that cell without being in // contradiction with pattern1 int size = patterns.size(); for (int i = 0; i < size; ++i) { int pattern_entry = patterns[i]; // We decrease the number of compatible patterns in the opposite // direction If the pattern was discarded from the wave, the element // is still negative, which is not a problem CompatibilityEntry &value = _compatible.get(y2, x2, pattern_entry); value.direction[direction]--; // If the element was set to 0 with this operation, we need to remove // the pattern from the wave, and propagate the information if (value.direction[direction] == 0) { add_to_propagator(y2, x2, pattern_entry); wave_set(i2, pattern_entry, false); } } } } } void WaveFormCollapse::initialize() { //wave init_wave(); _plogp_patterns_frequencies = get_plogp(_patterns_frequencies); _min_abs_half_plogp = get_min_abs_half(_plogp_patterns_frequencies); _is_impossible = false; _nb_patterns = _patterns_frequencies.size(); _wave_data.resize_fill(_wave_size, _nb_patterns, true); // Initialize the memoisation of entropy. double base_entropy = 0; double base_s = 0; for (int i = 0; i < _patterns_frequencies.size(); i++) { base_entropy += _plogp_patterns_frequencies[i]; base_s += _patterns_frequencies[i]; } double log_base_s = Math::log(base_s); double entropy_base = log_base_s - base_entropy / base_s; _memoisation_plogp_sum.resize(_wave_size); _memoisation_plogp_sum.fill(base_entropy); _memoisation_sum.resize(_wave_size); _memoisation_sum.fill(base_s); _memoisation_log_sum.resize(_wave_size); _memoisation_log_sum.fill(log_base_s); _memoisation_nb_patterns.resize(_wave_size); _memoisation_nb_patterns.fill(_patterns_frequencies.size()); _memoisation_entropy.resize(_wave_size); _memoisation_entropy.fill(entropy_base); //propagator _compatible.resize(_wave_height, _wave_width, _propagator_state.size()); init_compatible(); } WaveFormCollapse::WaveFormCollapse() { _periodic_output = true; _is_impossible = false; _nb_patterns = 0; _wave_width = 0; _wave_height = 0; _wave_size = 0; _min_abs_half_plogp = 0; } WaveFormCollapse::~WaveFormCollapse() { } void WaveFormCollapse::_bind_methods() { ClassDB::bind_method(D_METHOD("get_wave_width"), &WaveFormCollapse::get_wave_width); ClassDB::bind_method(D_METHOD("set_wave_width", "value"), &WaveFormCollapse::set_wave_width); ADD_PROPERTY(PropertyInfo(Variant::INT, "wave_width"), "set_wave_width", "get_wave_width"); ClassDB::bind_method(D_METHOD("get_wave_height"), &WaveFormCollapse::get_wave_height); ClassDB::bind_method(D_METHOD("set_wave_height", "value"), &WaveFormCollapse::set_wave_height); ADD_PROPERTY(PropertyInfo(Variant::INT, "wave_height"), "set_wave_height", "get_wave_height"); ClassDB::bind_method(D_METHOD("get_periodic_output"), &WaveFormCollapse::get_periodic_output); ClassDB::bind_method(D_METHOD("set_periodic_output", "value"), &WaveFormCollapse::set_periodic_output); ADD_PROPERTY(PropertyInfo(Variant::BOOL, "periodic_output"), "set_periodic_output", "get_periodic_output"); ClassDB::bind_method(D_METHOD("set_seed", "seed"), &WaveFormCollapse::set_seed); //ClassDB::bind_method(D_METHOD("set_wave_size", "width", "height"), &WaveFormCollapse::set_wave_size); ClassDB::bind_method(D_METHOD("propagate"), &WaveFormCollapse::propagate); ClassDB::bind_method(D_METHOD("initialize"), &WaveFormCollapse::initialize); ClassDB::bind_method(D_METHOD("set_input", "data", "width", "height"), &WaveFormCollapse::set_input); ClassDB::bind_method(D_METHOD("generate_image_index_data"), &WaveFormCollapse::generate_image_index_data); BIND_ENUM_CONSTANT(SYMMETRY_X); BIND_ENUM_CONSTANT(SYMMETRY_T); BIND_ENUM_CONSTANT(SYMMETRY_I); BIND_ENUM_CONSTANT(SYMMETRY_L); BIND_ENUM_CONSTANT(SYMMETRY_BACKSLASH); BIND_ENUM_CONSTANT(SYMMETRY_P); }