mirror of
https://github.com/Relintai/gdnative_cpp.git
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353 lines
11 KiB
C++
353 lines
11 KiB
C++
/*************************************************************************/
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/* Quaternion.cpp */
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/*************************************************************************/
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/* This file is part of: */
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/* PANDEMONIUM ENGINE */
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/* https://pandemoniumengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2022 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2022 Pandemonium Engine contributors (cf. AUTHORS.md). */
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/* */
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/* Permission is hereby granted, free of charge, to any person obtaining */
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/* a copy of this software and associated documentation files (the */
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/* "Software"), to deal in the Software without restriction, including */
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/* without limitation the rights to use, copy, modify, merge, publish, */
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/* distribute, sublicense, and/or sell copies of the Software, and to */
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/* permit persons to whom the Software is furnished to do so, subject to */
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/* the following conditions: */
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/* */
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/* The above copyright notice and this permission notice shall be */
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/* included in all copies or substantial portions of the Software. */
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/* */
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/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, */
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/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF */
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/* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
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/* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY */
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/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, */
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/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE */
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/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */
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/*************************************************************************/
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#include "quaternion.h"
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#include "basis.h"
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#include "defs.h"
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#include "vector3.h"
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#include <cmath>
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const Quaternion Quaternion::IDENTITY = Quaternion();
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// set_euler_xyz expects a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses XYZ convention (Z is the first rotation).
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void Quaternion::set_euler_xyz(const Vector3 &p_euler) {
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real_t half_a1 = p_euler.x * 0.5;
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real_t half_a2 = p_euler.y * 0.5;
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real_t half_a3 = p_euler.z * 0.5;
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// R = X(a1).Y(a2).Z(a3) convention for Euler angles.
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// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-2)
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// a3 is the angle of the first rotation, following the notation in this reference.
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real_t cos_a1 = ::cos(half_a1);
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real_t sin_a1 = ::sin(half_a1);
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real_t cos_a2 = ::cos(half_a2);
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real_t sin_a2 = ::sin(half_a2);
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real_t cos_a3 = ::cos(half_a3);
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real_t sin_a3 = ::sin(half_a3);
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set(sin_a1 * cos_a2 * cos_a3 + sin_a2 * sin_a3 * cos_a1,
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-sin_a1 * sin_a3 * cos_a2 + sin_a2 * cos_a1 * cos_a3,
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sin_a1 * sin_a2 * cos_a3 + sin_a3 * cos_a1 * cos_a2,
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-sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
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}
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// get_euler_xyz returns a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses XYZ convention (Z is the first rotation).
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Vector3 Quaternion::get_euler_xyz() const {
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Basis m(*this);
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return m.get_euler_xyz();
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}
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// set_euler_yxz expects a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses YXZ convention (Z is the first rotation).
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void Quaternion::set_euler_yxz(const Vector3 &p_euler) {
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real_t half_a1 = p_euler.y * 0.5;
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real_t half_a2 = p_euler.x * 0.5;
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real_t half_a3 = p_euler.z * 0.5;
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// R = Y(a1).X(a2).Z(a3) convention for Euler angles.
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// Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
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// a3 is the angle of the first rotation, following the notation in this reference.
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real_t cos_a1 = ::cos(half_a1);
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real_t sin_a1 = ::sin(half_a1);
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real_t cos_a2 = ::cos(half_a2);
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real_t sin_a2 = ::sin(half_a2);
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real_t cos_a3 = ::cos(half_a3);
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real_t sin_a3 = ::sin(half_a3);
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set(sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3,
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sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3,
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-sin_a1 * sin_a2 * cos_a3 + cos_a1 * sin_a2 * sin_a3,
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sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3);
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}
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// get_euler_yxz returns a vector containing the Euler angles in the format
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// (ax,ay,az), where ax is the angle of rotation around x axis,
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// and similar for other axes.
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// This implementation uses YXZ convention (Z is the first rotation).
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Vector3 Quaternion::get_euler_yxz() const {
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Basis m(*this);
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return m.get_euler_yxz();
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}
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real_t Quaternion::length() const {
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return ::sqrt(length_squared());
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}
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void Quaternion::normalize() {
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*this /= length();
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}
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Quaternion Quaternion::normalized() const {
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return *this / length();
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}
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bool Quaternion::is_normalized() const {
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return ABS(length_squared() - 1.0) < 0.00001;
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}
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Quaternion Quaternion::inverse() const {
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return Quaternion(-x, -y, -z, w);
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}
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Quaternion Quaternion::slerp(const Quaternion &q, const real_t &t) const {
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Quaternion to1;
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real_t omega, cosom, sinom, scale0, scale1;
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// calc cosine
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cosom = dot(q);
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// adjust signs (if necessary)
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if (cosom < 0.0) {
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cosom = -cosom;
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to1.x = -q.x;
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to1.y = -q.y;
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to1.z = -q.z;
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to1.w = -q.w;
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} else {
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to1.x = q.x;
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to1.y = q.y;
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to1.z = q.z;
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to1.w = q.w;
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}
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// calculate coefficients
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if ((1.0 - cosom) > CMP_EPSILON) {
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// standard case (slerp)
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omega = ::acos(cosom);
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sinom = ::sin(omega);
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scale0 = ::sin((1.0 - t) * omega) / sinom;
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scale1 = ::sin(t * omega) / sinom;
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} else {
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// "from" and "to" quaternions are very close
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// ... so we can do a linear interpolation
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scale0 = 1.0 - t;
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scale1 = t;
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}
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// calculate final values
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return Quaternion(
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scale0 * x + scale1 * to1.x,
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scale0 * y + scale1 * to1.y,
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scale0 * z + scale1 * to1.z,
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scale0 * w + scale1 * to1.w);
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}
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Quaternion Quaternion::slerpni(const Quaternion &q, const real_t &t) const {
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const Quaternion &from = *this;
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real_t dot = from.dot(q);
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if (::fabs(dot) > 0.9999)
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return from;
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real_t theta = ::acos(dot),
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sinT = 1.0 / ::sin(theta),
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newFactor = ::sin(t * theta) * sinT,
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invFactor = ::sin((1.0 - t) * theta) * sinT;
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return Quaternion(invFactor * from.x + newFactor * q.x,
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invFactor * from.y + newFactor * q.y,
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invFactor * from.z + newFactor * q.z,
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invFactor * from.w + newFactor * q.w);
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}
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Quaternion Quaternion::cubic_slerp(const Quaternion &q, const Quaternion &prep, const Quaternion &postq, const real_t &t) const {
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//the only way to do slerp :|
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real_t t2 = (1.0 - t) * t * 2;
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Quaternion sp = this->slerp(q, t);
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Quaternion sq = prep.slerpni(postq, t);
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return sp.slerpni(sq, t2);
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}
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void Quaternion::get_axis_and_angle(Vector3 &r_axis, real_t &r_angle) const {
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r_angle = 2 * ::acos(w);
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r_axis.x = x / ::sqrt(1 - w * w);
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r_axis.y = y / ::sqrt(1 - w * w);
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r_axis.z = z / ::sqrt(1 - w * w);
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}
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void Quaternion::set_axis_angle(const Vector3 &axis, const float angle) {
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ERR_FAIL_COND(!axis.is_normalized());
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real_t d = axis.length();
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if (d == 0)
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set(0, 0, 0, 0);
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else {
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real_t sin_angle = ::sin(angle * 0.5);
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real_t cos_angle = ::cos(angle * 0.5);
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real_t s = sin_angle / d;
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set(axis.x * s, axis.y * s, axis.z * s,
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cos_angle);
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}
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}
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Quaternion Quaternion::operator*(const Vector3 &v) const {
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return Quaternion(w * v.x + y * v.z - z * v.y,
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w * v.y + z * v.x - x * v.z,
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w * v.z + x * v.y - y * v.x,
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-x * v.x - y * v.y - z * v.z);
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}
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Vector3 Quaternion::xform(const Vector3 &v) const {
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Quaternion q = *this * v;
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q *= this->inverse();
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return Vector3(q.x, q.y, q.z);
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}
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Quaternion::operator String() const {
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return String(); // @Todo
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}
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Quaternion::Quaternion(const Vector3 &axis, const real_t &angle) {
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real_t d = axis.length();
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if (d == 0)
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set(0, 0, 0, 0);
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else {
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real_t sin_angle = ::sin(angle * 0.5);
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real_t cos_angle = ::cos(angle * 0.5);
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real_t s = sin_angle / d;
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set(axis.x * s, axis.y * s, axis.z * s,
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cos_angle);
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}
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}
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Quaternion::Quaternion(const Vector3 &v0, const Vector3 &v1) // shortest arc
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{
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Vector3 c = v0.cross(v1);
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real_t d = v0.dot(v1);
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if (d < -1.0 + CMP_EPSILON) {
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x = 0;
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y = 1;
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z = 0;
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w = 0;
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} else {
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real_t s = ::sqrt((1.0 + d) * 2.0);
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real_t rs = 1.0 / s;
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x = c.x * rs;
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y = c.y * rs;
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z = c.z * rs;
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w = s * 0.5;
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}
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}
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real_t Quaternion::dot(const Quaternion &q) const {
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return x * q.x + y * q.y + z * q.z + w * q.w;
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}
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real_t Quaternion::length_squared() const {
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return dot(*this);
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}
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void Quaternion::operator+=(const Quaternion &q) {
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x += q.x;
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y += q.y;
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z += q.z;
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w += q.w;
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}
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void Quaternion::operator-=(const Quaternion &q) {
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x -= q.x;
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y -= q.y;
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z -= q.z;
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w -= q.w;
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}
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void Quaternion::operator*=(const Quaternion &q) {
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set(w * q.x + x * q.w + y * q.z - z * q.y,
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w * q.y + y * q.w + z * q.x - x * q.z,
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w * q.z + z * q.w + x * q.y - y * q.x,
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w * q.w - x * q.x - y * q.y - z * q.z);
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}
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void Quaternion::operator*=(const real_t &s) {
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x *= s;
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y *= s;
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z *= s;
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w *= s;
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}
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void Quaternion::operator/=(const real_t &s) {
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*this *= 1.0 / s;
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}
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Quaternion Quaternion::operator+(const Quaternion &q2) const {
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const Quaternion &q1 = *this;
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return Quaternion(q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w);
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}
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Quaternion Quaternion::operator-(const Quaternion &q2) const {
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const Quaternion &q1 = *this;
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return Quaternion(q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w);
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}
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Quaternion Quaternion::operator*(const Quaternion &q2) const {
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Quaternion q1 = *this;
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q1 *= q2;
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return q1;
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}
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Quaternion Quaternion::operator-() const {
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const Quaternion &q2 = *this;
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return Quaternion(-q2.x, -q2.y, -q2.z, -q2.w);
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}
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Quaternion Quaternion::operator*(const real_t &s) const {
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return Quaternion(x * s, y * s, z * s, w * s);
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}
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Quaternion Quaternion::operator/(const real_t &s) const {
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return *this * (1.0 / s);
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}
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bool Quaternion::operator==(const Quaternion &p_quaternion) const {
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return x == p_quaternion.x && y == p_quaternion.y && z == p_quaternion.z && w == p_quaternion.w;
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}
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bool Quaternion::operator!=(const Quaternion &p_quaternion) const {
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return x != p_quaternion.x || y != p_quaternion.y || z != p_quaternion.z || w != p_quaternion.w;
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}
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