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As many open source projects have started doing it, we're removing the current year from the copyright notice, so that we don't need to bump it every year. It seems like only the first year of publication is technically relevant for copyright notices, and even that seems to be something that many companies stopped listing altogether (in a version controlled codebase, the commits are a much better source of date of publication than a hardcoded copyright statement). We also now list Godot Engine contributors first as we're collectively the current maintainers of the project, and we clarify that the "exclusive" copyright of the co-founders covers the timespan before opensourcing (their further contributions are included as part of Godot Engine contributors). Also fixed "cf." Frenchism - it's meant as "refer to / see".
341 lines
13 KiB
C++
341 lines
13 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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/* GODOT ENGINE */
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/* https://godotengine.org */
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/**************************************************************************/
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/* Copyright (c) 2014-present Godot Engine contributors (see AUTHORS.md). */
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/* Copyright (c) 2007-2014 Juan Linietsky, Ariel Manzur. */
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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 "core/math/basis.h"
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#include "core/string/ustring.h"
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real_t Quaternion::angle_to(const Quaternion &p_to) const {
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real_t d = dot(p_to);
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return Math::acos(CLAMP(d * d * 2 - 1, -1, 1));
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}
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Vector3 Quaternion::get_euler(EulerOrder p_order) 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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return Basis(*this).get_euler(p_order);
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}
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void Quaternion::operator*=(const Quaternion &p_q) {
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real_t xx = w * p_q.x + x * p_q.w + y * p_q.z - z * p_q.y;
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real_t yy = w * p_q.y + y * p_q.w + z * p_q.x - x * p_q.z;
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real_t zz = w * p_q.z + z * p_q.w + x * p_q.y - y * p_q.x;
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w = w * p_q.w - x * p_q.x - y * p_q.y - z * p_q.z;
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x = xx;
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y = yy;
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z = zz;
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}
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Quaternion Quaternion::operator*(const Quaternion &p_q) const {
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Quaternion r = *this;
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r *= p_q;
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return r;
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}
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bool Quaternion::is_equal_approx(const Quaternion &p_quaternion) const {
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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);
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}
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bool Quaternion::is_finite() const {
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return Math::is_finite(x) && Math::is_finite(y) && Math::is_finite(z) && Math::is_finite(w);
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}
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real_t Quaternion::length() const {
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return Math::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 Math::is_equal_approx(length_squared(), 1, (real_t)UNIT_EPSILON); //use less epsilon
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}
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Quaternion Quaternion::inverse() const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The quaternion must be normalized.");
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#endif
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return Quaternion(-x, -y, -z, w);
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}
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Quaternion Quaternion::log() const {
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Quaternion src = *this;
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Vector3 src_v = src.get_axis() * src.get_angle();
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return Quaternion(src_v.x, src_v.y, src_v.z, 0);
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}
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Quaternion Quaternion::exp() const {
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Quaternion src = *this;
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Vector3 src_v = Vector3(src.x, src.y, src.z);
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real_t theta = src_v.length();
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src_v = src_v.normalized();
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if (theta < CMP_EPSILON || !src_v.is_normalized()) {
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return Quaternion(0, 0, 0, 1);
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}
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return Quaternion(src_v, theta);
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}
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Quaternion Quaternion::slerp(const Quaternion &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(), Quaternion(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
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#endif
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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(p_to);
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// adjust signs (if necessary)
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if (cosom < 0.0f) {
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cosom = -cosom;
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to1 = -p_to;
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} else {
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to1 = p_to;
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}
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// calculate coefficients
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if ((1.0f - cosom) > (real_t)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 = 1.0f - 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 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 &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(), Quaternion(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_to.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
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#endif
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const Quaternion &from = *this;
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real_t dot = from.dot(p_to);
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if (Math::absf(dot) > 0.9999f) {
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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 = 1.0f / Math::sin(theta),
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newFactor = Math::sin(p_weight * theta) * sinT,
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invFactor = Math::sin((1.0f - p_weight) * theta) * sinT;
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return Quaternion(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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Quaternion Quaternion::spherical_cubic_interpolate(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &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(), Quaternion(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
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#endif
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Quaternion from_q = *this;
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Quaternion pre_q = p_pre_a;
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Quaternion to_q = p_b;
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Quaternion post_q = p_post_b;
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// Align flip phases.
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from_q = Basis(from_q).get_rotation_quaternion();
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pre_q = Basis(pre_q).get_rotation_quaternion();
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to_q = Basis(to_q).get_rotation_quaternion();
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post_q = Basis(post_q).get_rotation_quaternion();
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// Flip quaternions to shortest path if necessary.
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bool flip1 = signbit(from_q.dot(pre_q));
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pre_q = flip1 ? -pre_q : pre_q;
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bool flip2 = signbit(from_q.dot(to_q));
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to_q = flip2 ? -to_q : to_q;
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bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
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post_q = flip3 ? -post_q : post_q;
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// Calc by Expmap in from_q space.
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Quaternion ln_from = Quaternion(0, 0, 0, 0);
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Quaternion ln_to = (from_q.inverse() * to_q).log();
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Quaternion ln_pre = (from_q.inverse() * pre_q).log();
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Quaternion ln_post = (from_q.inverse() * post_q).log();
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Quaternion ln = Quaternion(0, 0, 0, 0);
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ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
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ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
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ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
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Quaternion q1 = from_q * ln.exp();
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// Calc by Expmap in to_q space.
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ln_from = (to_q.inverse() * from_q).log();
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ln_to = Quaternion(0, 0, 0, 0);
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ln_pre = (to_q.inverse() * pre_q).log();
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ln_post = (to_q.inverse() * post_q).log();
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ln = Quaternion(0, 0, 0, 0);
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ln.x = Math::cubic_interpolate(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight);
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ln.y = Math::cubic_interpolate(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight);
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ln.z = Math::cubic_interpolate(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight);
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Quaternion q2 = to_q * ln.exp();
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// To cancel error made by Expmap ambiguity, do blends.
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return q1.slerp(q2, p_weight);
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}
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Quaternion Quaternion::spherical_cubic_interpolate_in_time(const Quaternion &p_b, const Quaternion &p_pre_a, const Quaternion &p_post_b, const real_t &p_weight,
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const real_t &p_b_t, const real_t &p_pre_a_t, const real_t &p_post_b_t) const {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_V_MSG(!is_normalized(), Quaternion(), "The start quaternion must be normalized.");
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ERR_FAIL_COND_V_MSG(!p_b.is_normalized(), Quaternion(), "The end quaternion must be normalized.");
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#endif
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Quaternion from_q = *this;
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Quaternion pre_q = p_pre_a;
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Quaternion to_q = p_b;
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Quaternion post_q = p_post_b;
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// Align flip phases.
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from_q = Basis(from_q).get_rotation_quaternion();
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pre_q = Basis(pre_q).get_rotation_quaternion();
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to_q = Basis(to_q).get_rotation_quaternion();
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post_q = Basis(post_q).get_rotation_quaternion();
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// Flip quaternions to shortest path if necessary.
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bool flip1 = signbit(from_q.dot(pre_q));
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pre_q = flip1 ? -pre_q : pre_q;
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bool flip2 = signbit(from_q.dot(to_q));
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to_q = flip2 ? -to_q : to_q;
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bool flip3 = flip2 ? to_q.dot(post_q) <= 0 : signbit(to_q.dot(post_q));
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post_q = flip3 ? -post_q : post_q;
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// Calc by Expmap in from_q space.
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Quaternion ln_from = Quaternion(0, 0, 0, 0);
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Quaternion ln_to = (from_q.inverse() * to_q).log();
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Quaternion ln_pre = (from_q.inverse() * pre_q).log();
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Quaternion ln_post = (from_q.inverse() * post_q).log();
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Quaternion ln = Quaternion(0, 0, 0, 0);
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ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
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ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
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ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
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Quaternion q1 = from_q * ln.exp();
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// Calc by Expmap in to_q space.
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ln_from = (to_q.inverse() * from_q).log();
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ln_to = Quaternion(0, 0, 0, 0);
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ln_pre = (to_q.inverse() * pre_q).log();
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ln_post = (to_q.inverse() * post_q).log();
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ln = Quaternion(0, 0, 0, 0);
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ln.x = Math::cubic_interpolate_in_time(ln_from.x, ln_to.x, ln_pre.x, ln_post.x, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
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ln.y = Math::cubic_interpolate_in_time(ln_from.y, ln_to.y, ln_pre.y, ln_post.y, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
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ln.z = Math::cubic_interpolate_in_time(ln_from.z, ln_to.z, ln_pre.z, ln_post.z, p_weight, p_b_t, p_pre_a_t, p_post_b_t);
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Quaternion q2 = to_q * ln.exp();
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// To cancel error made by Expmap ambiguity, do blends.
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return q1.slerp(q2, p_weight);
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}
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Quaternion::operator String() const {
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return "(" + String::num_real(x, false) + ", " + String::num_real(y, false) + ", " + String::num_real(z, false) + ", " + String::num_real(w, false) + ")";
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}
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Vector3 Quaternion::get_axis() const {
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if (Math::abs(w) > 1 - CMP_EPSILON) {
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return Vector3(x, y, z);
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}
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real_t r = ((real_t)1) / Math::sqrt(1 - w * w);
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return Vector3(x * r, y * r, z * r);
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}
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real_t Quaternion::get_angle() const {
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return 2 * Math::acos(w);
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}
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Quaternion::Quaternion(const Vector3 &p_axis, real_t p_angle) {
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#ifdef MATH_CHECKS
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ERR_FAIL_COND_MSG(!p_axis.is_normalized(), "The axis Vector3 must be normalized.");
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#endif
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real_t d = p_axis.length();
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if (d == 0) {
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x = 0;
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y = 0;
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z = 0;
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w = 0;
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} else {
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real_t sin_angle = Math::sin(p_angle * 0.5f);
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real_t cos_angle = Math::cos(p_angle * 0.5f);
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real_t s = sin_angle / d;
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x = p_axis.x * s;
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y = p_axis.y * s;
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z = p_axis.z * s;
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w = cos_angle;
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}
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}
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// Euler constructor 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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Quaternion Quaternion::from_euler(const Vector3 &p_euler) {
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real_t half_a1 = p_euler.y * 0.5f;
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real_t half_a2 = p_euler.x * 0.5f;
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real_t half_a3 = p_euler.z * 0.5f;
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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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return Quaternion(
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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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