251 lines
9.1 KiB
C++
251 lines
9.1 KiB
C++
/*************************************************************************/
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/* quat.cpp */
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/*************************************************************************/
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/* This file is part of: */
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/* GODOT ENGINE */
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/* https://godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2021 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2021 Godot 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 "quat.h"
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#include "core/math/basis.h"
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#include "core/print_string.h"
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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 Quat::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 = Math::cos(half_a1);
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real_t sin_a1 = Math::sin(half_a1);
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real_t cos_a2 = Math::cos(half_a2);
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real_t sin_a2 = Math::sin(half_a2);
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real_t cos_a3 = Math::cos(half_a3);
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real_t sin_a3 = Math::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 Quat::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 Quat::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 = Math::cos(half_a1);
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real_t sin_a1 = Math::sin(half_a1);
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real_t cos_a2 = Math::cos(half_a2);
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real_t sin_a2 = Math::sin(half_a2);
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real_t cos_a3 = Math::cos(half_a3);
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real_t sin_a3 = Math::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 * cos_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 Quat::get_euler_yxz() const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Vector3(0, 0, 0), "The quaternion must be normalized.");
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#endif
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Basis m(*this);
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return m.get_euler_yxz();
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}
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void Quat::operator*=(const Quat &p_q) {
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set(w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y,
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w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z,
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w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x,
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w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z);
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}
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Quat Quat::operator*(const Quat &p_q) const {
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Quat r = *this;
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r *= p_q;
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return r;
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}
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bool Quat::is_equal_approx(const Quat &p_quat) const {
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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);
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}
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real_t Quat::length() const {
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return Math::sqrt(length_squared());
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}
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void Quat::normalize() {
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*this /= length();
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}
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Quat Quat::normalized() const {
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return *this / length();
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}
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bool Quat::is_normalized() const {
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return Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON); //use less epsilon
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}
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Quat Quat::inverse() const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The quaternion must be normalized.");
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#endif
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return Quat(-x, -y, -z, w);
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}
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Quat Quat::slerp(const Quat &p_to, const real_t &p_weight) const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quat(), "The end quaternion must be normalized.");
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#endif
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Quat to1;
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real_t omega, cosom, sinom, scale0, scale1;
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// calc cosine
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cosom = dot(p_to);
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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 = -p_to.x;
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to1.y = -p_to.y;
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to1.z = -p_to.z;
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to1.w = -p_to.w;
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} else {
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to1.x = p_to.x;
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to1.y = p_to.y;
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to1.z = p_to.z;
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to1.w = p_to.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 = Math::acos(cosom);
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sinom = Math::sin(omega);
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scale0 = Math::sin((1.0 - p_weight) * omega) / sinom;
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scale1 = Math::sin(p_weight * 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 - p_weight;
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scale1 = p_weight;
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}
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// calculate final values
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return Quat(
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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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Quat Quat::slerpni(const Quat &p_to, const real_t &p_weight) const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quat(), "The end quaternion must be normalized.");
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#endif
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const Quat &from = *this;
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real_t dot = from.dot(p_to);
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if (Math::absf(dot) > 0.9999) {
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return from;
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}
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real_t theta = Math::acos(dot),
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sinT = 1.0 / Math::sin(theta),
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newFactor = Math::sin(p_weight * theta) * sinT,
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invFactor = Math::sin((1.0 - p_weight) * theta) * sinT;
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return Quat(invFactor * from.x + newFactor * p_to.x,
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invFactor * from.y + newFactor * p_to.y,
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invFactor * from.z + newFactor * p_to.z,
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invFactor * from.w + newFactor * p_to.w);
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}
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Quat Quat::cubic_slerp(const Quat &p_b, const Quat &p_pre_a, const Quat &p_post_b, const real_t &p_weight) const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Quat(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quat(), "The end quaternion must be normalized.");
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#endif
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//the only way to do slerp :|
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real_t t2 = (1.0 - p_weight) * p_weight * 2;
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Quat sp = this->slerp(p_b, p_weight);
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Quat sq = p_pre_a.slerpni(p_post_b, p_weight);
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return sp.slerpni(sq, t2);
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}
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Quat::operator String() const {
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return String::num(x) + ", " + String::num(y) + ", " + String::num(z) + ", " + String::num(w);
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}
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void Quat::set_axis_angle(const Vector3 &axis, const real_t &angle) {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_MSG(!axis.is_normalized(), "The axis Vector3 must be normalized.");
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#endif
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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 = Math::sin(angle * 0.5);
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real_t cos_angle = Math::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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