-/*************************************************************************/

-/* quat.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 "quat.h"

-

-#include "core/math/basis.h"

-#include "core/string/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 &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);

-}

-

-Quat Quat::operator*(const Quat &p_q) const {

- Quat r = *this;

- r *= p_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 &p_to, const real_t &p_weight) const {

-#ifdef MATH_CHECKS

- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");

- ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quat(), "The end quaternion must be normalized.");

-#endif

- Quat 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 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 &p_to, const real_t &p_weight) const {

-#ifdef MATH_CHECKS

- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");

- ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quat(), "The end quaternion must be normalized.");

-#endif

- const Quat &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 Quat(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);

-}

-

-Quat Quat::cubic_slerp(const Quat &p_b, const Quat &p_pre_a, const Quat &p_post_b, const real_t &p_weight) const {

-#ifdef MATH_CHECKS

- ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");

- ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quat(), "The end quaternion must be normalized.");

-#endif

- //the only way to do slerp :|

- real_t t2 = (1.0 - p_weight) * p_weight * 2;

- Quat sp = this->slerp(p_b, p_weight);

- Quat sq = p_pre_a.slerpni(p_post_b, p_weight);

- 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);

- }

-}