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+/*************************************************************************/
+/* quaternion.cpp */
+/*************************************************************************/
+/* This file is part of: */
+/* GODOT ENGINE */
+/* https://godotengine.org */
+/*************************************************************************/
+/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
+/* Copyright (c) 2014-2021 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 "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);
+ return Math::acos(CLAMP(d * d * 2 - 1, -1, 1));
+}
+
+// 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();
+}
+
+// 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) {
+ real_t xx = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
+ real_t yy = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
+ real_t zz = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
+ w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
+ x = xx;
+ y = yy;
+ z = zz;
+}
+
+Quaternion Quaternion::operator*(const Quaternion &p_q) const {
+ Quaternion r = *this;
+ r *= p_q;
+ return r;
+}
+
+bool Quaternion::is_equal_approx(const Quaternion &p_quaternion) const {
+ return Math::is_equal_approx(x, p_quaternion.x) && Math::is_equal_approx(y, p_quaternion.y) && Math::is_equal_approx(z, p_quaternion.z) && Math::is_equal_approx(w, p_quaternion.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::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 < 0.0) {
+ 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 ((1.0 - cosom) > CMP_EPSILON) {
+ // standard case (slerp)
+ omega = Math::acos(cosom);
+ sinom = Math::sin(omega);
+ scale0 = Math::sin((1.0 - 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 = 1.0 - 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) > 0.9999) {
+ return from;
+ }
+
+ real_t theta = Math::acos(dot),
+ sinT = 1.0 / Math::sin(theta),
+ newFactor = Math::sin(p_weight * theta) * sinT,
+ invFactor = Math::sin((1.0 - 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 = (1.0 - 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::operator String() const {
+ return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
+}
+
+Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
+#ifdef MATH_CHECKS
+ ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
+#endif
+ real_t d = p_axis.length();
+ if (d == 0) {
+ x = 0;
+ y = 0;
+ z = 0;
+ w = 0;
+ } else {
+ real_t sin_angle = Math::sin(p_angle * 0.5);
+ real_t cos_angle = Math::cos(p_angle * 0.5);
+ real_t s = sin_angle / d;
+ x = p_axis.x * s;
+ y = p_axis.y * s;
+ z = p_axis.z * s;
+ w = cos_angle;
+ }
+}
+
+// Euler constructor 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).
+Quaternion::Quaternion(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);
+
+ x = sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3;
+ y = sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3;
+ z = -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3;
+ w = sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3;
+}
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