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-/*************************************************************************/
-/* quat.cpp */
-/*************************************************************************/
-/* This file is part of: */
-/* GODOT ENGINE */
-/* https://godotengine.org */
-/*************************************************************************/
-/* Copyright (c) 2007-2020 Juan Linietsky, Ariel Manzur. */
-/* Copyright (c) 2014-2020 Godot Engine contributors (cf. AUTHORS.md). */
-/* */
-/* 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 "quat.h"
-
-#include "core/math/basis.h"
-#include "core/print_string.h"
-
-// 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 Quat::set_euler_xyz(const Vector3 &p_euler) {
- real_t half_a1 = p_euler.x * 0.5;
- real_t half_a2 = p_euler.y * 0.5;
- real_t half_a3 = p_euler.z * 0.5;
-
- // 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 Quat::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 Quat::set_euler_yxz(const Vector3 &p_euler) {
- real_t half_a1 = p_euler.y * 0.5;
- real_t half_a2 = p_euler.x * 0.5;
- real_t half_a3 = p_euler.z * 0.5;
-
- // 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 Quat::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 Quat::operator*=(const Quat &q) {
- set(w * q.x + x * q.w + y * q.z - z * q.y,
- w * q.y + y * q.w + z * q.x - x * q.z,
- w * q.z + z * q.w + x * q.y - y * q.x,
- w * q.w - x * q.x - y * q.y - z * q.z);
-}
-
-Quat Quat::operator*(const Quat &q) const {
- Quat r = *this;
- r *= q;
- return r;
-}
-
-bool Quat::is_equal_approx(const Quat &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 Quat::length() const {
- return Math::sqrt(length_squared());
-}
-
-void Quat::normalize() {
- *this /= length();
-}
-
-Quat Quat::normalized() const {
- return *this / length();
-}
-
-bool Quat::is_normalized() const {
- return Math::is_equal_approx(length_squared(), 1.0, UNIT_EPSILON); //use less epsilon
-}
-
-Quat Quat::inverse() const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The quaternion must be normalized.");
-#endif
- return Quat(-x, -y, -z, w);
-}
-
-Quat Quat::slerp(const Quat &q, const real_t &t) const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
- ERR_FAIL_COND_V_MSG(!q.is_normalized(), Quat(), "The end quaternion must be normalized.");
-#endif
- Quat to1;
- real_t omega, cosom, sinom, scale0, scale1;
-
- // calc cosine
- cosom = dot(q);
-
- // adjust signs (if necessary)
- if (cosom < 0.0) {
- cosom = -cosom;
- to1.x = -q.x;
- to1.y = -q.y;
- to1.z = -q.z;
- to1.w = -q.w;
- } else {
- to1.x = q.x;
- to1.y = q.y;
- to1.z = q.z;
- to1.w = q.w;
- }
-
- // calculate coefficients
-
- if ((1.0 - cosom) > CMP_EPSILON) {
- // standard case (slerp)
- omega = Math::acos(cosom);
- sinom = Math::sin(omega);
- scale0 = Math::sin((1.0 - t) * omega) / sinom;
- scale1 = Math::sin(t * omega) / sinom;
- } else {
- // "from" and "to" quaternions are very close
- // ... so we can do a linear interpolation
- scale0 = 1.0 - t;
- scale1 = t;
- }
- // calculate final values
- return Quat(
- scale0 * x + scale1 * to1.x,
- scale0 * y + scale1 * to1.y,
- scale0 * z + scale1 * to1.z,
- scale0 * w + scale1 * to1.w);
-}
-
-Quat Quat::slerpni(const Quat &q, const real_t &t) const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
- ERR_FAIL_COND_V_MSG(!q.is_normalized(), Quat(), "The end quaternion must be normalized.");
-#endif
- const Quat &from = *this;
-
- real_t dot = from.dot(q);
-
- if (Math::absf(dot) > 0.9999) {
- return from;
- }
-
- real_t theta = Math::acos(dot),
- sinT = 1.0 / Math::sin(theta),
- newFactor = Math::sin(t * theta) * sinT,
- invFactor = Math::sin((1.0 - t) * theta) * sinT;
-
- return Quat(invFactor * from.x + newFactor * q.x,
- invFactor * from.y + newFactor * q.y,
- invFactor * from.z + newFactor * q.z,
- invFactor * from.w + newFactor * q.w);
-}
-
-Quat Quat::cubic_slerp(const Quat &q, const Quat &prep, const Quat &postq, const real_t &t) const {
-#ifdef MATH_CHECKS
- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
- ERR_FAIL_COND_V_MSG(!q.is_normalized(), Quat(), "The end quaternion must be normalized.");
-#endif
- //the only way to do slerp :|
- real_t t2 = (1.0 - t) * t * 2;
- Quat sp = this->slerp(q, t);
- Quat sq = prep.slerpni(postq, t);
- return sp.slerpni(sq, t2);
-}
-
-Quat::operator String() const {
- return String::num(x) + ", " + String::num(y) + ", " + String::num(z) + ", " + String::num(w);
-}
-
-void Quat::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 * 0.5);
- real_t cos_angle = Math::cos(angle * 0.5);
- real_t s = sin_angle / d;
- set(axis.x * s, axis.y * s, axis.z * s,
- cos_angle);
- }
-}
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