350 lines
13 KiB
C++
350 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) 2007-2022 Juan Linietsky, Ariel Manzur. */
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/* Copyright (c) 2014-2022 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 "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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// 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 Quaternion::get_euler_xyz() const {
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Basis m(*this);
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return m.get_euler(Basis::EULER_ORDER_XYZ);
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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 Quaternion::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(Basis::EULER_ORDER_YXZ);
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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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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(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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x = sin_a1 * cos_a2 * sin_a3 + cos_a1 * sin_a2 * cos_a3;
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y = sin_a1 * cos_a2 * cos_a3 - cos_a1 * sin_a2 * sin_a3;
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z = -sin_a1 * sin_a2 * cos_a3 + cos_a1 * cos_a2 * sin_a3;
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w = sin_a1 * sin_a2 * sin_a3 + cos_a1 * cos_a2 * cos_a3;
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}
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