286 lines
8 KiB
C++
286 lines
8 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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/* http://www.godotengine.org */
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/*************************************************************************/
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/* Copyright (c) 2007-2017 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 "quat.h"
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#include "matrix3.h"
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#include "print_string.h"
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// set_euler expects a vector containing the Euler angles in the format
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// (c,b,a), where a is the angle of the first rotation, and c is the last.
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// The current implementation uses XYZ convention (Z is the first rotation).
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void Quat::set_euler(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 returns a vector containing the Euler angles in the format
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// (a1,a2,a3), where a3 is the angle of the first rotation, and a1 is the last.
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// The current implementation uses XYZ convention (Z is the first rotation).
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Vector3 Quat::get_euler() const {
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Basis m(*this);
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return m.get_euler();
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}
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void Quat::operator*=(const Quat& q) {
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set(w * q.x+x * q.w+y * q.z - z * q.y,
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w * q.y+y * q.w+z * q.x - x * q.z,
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w * q.z+z * q.w+x * q.y - y * q.x,
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w * q.w - x * q.x - y * q.y - z * q.z);
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}
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Quat Quat::operator*(const Quat& q) const {
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Quat r=*this;
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r*=q;
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return r;
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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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Quat Quat::inverse() const {
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return Quat( -x, -y, -z, w );
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}
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Quat Quat::slerp(const Quat& q, const real_t& t) const {
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#if 0
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Quat dst=q;
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Quat src=*this;
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src.normalize();
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dst.normalize();
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real_t cosine = dst.dot(src);
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if (cosine < 0 && true) {
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cosine = -cosine;
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dst = -dst;
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} else {
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dst = dst;
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}
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if (Math::abs(cosine) < 1 - CMP_EPSILON) {
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// Standard case (slerp)
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real_t sine = Math::sqrt(1 - cosine*cosine);
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real_t angle = Math::atan2(sine, cosine);
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real_t inv_sine = 1.0 / sine;
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real_t coeff_0 = Math::sin((1.0 - t) * angle) * inv_sine;
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real_t coeff_1 = Math::sin(t * angle) * inv_sine;
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Quat ret= src * coeff_0 + dst * coeff_1;
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return ret;
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} else {
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// There are two situations:
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// 1. "rkP" and "q" are very close (cosine ~= +1), so we can do a linear
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// interpolation safely.
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// 2. "rkP" and "q" are almost invedste of each other (cosine ~= -1), there
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// are an infinite number of possibilities interpolation. but we haven't
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// have method to fix this case, so just use linear interpolation here.
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Quat ret = src * (1.0 - t) + dst *t;
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// taking the complement requires renormalisation
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ret.normalize();
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return ret;
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}
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#else
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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(q);
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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 = - q.x;
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to1.y = - q.y;
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to1.z = - q.z;
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to1.w = - q.w;
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} else {
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to1.x = q.x;
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to1.y = q.y;
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to1.z = q.z;
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to1.w = q.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 - t) * omega) / sinom;
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scale1 = Math::sin(t * 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 - t;
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scale1 = t;
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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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#endif
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}
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Quat Quat::slerpni(const Quat& q, const real_t& t) const {
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const Quat &from = *this;
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real_t dot = from.dot(q);
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if (Math::absf(dot) > 0.9999) return from;
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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(t * theta) * sinT,
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invFactor = Math::sin((1.0 - t) * theta) * sinT;
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return Quat(invFactor * from.x + newFactor * q.x,
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invFactor * from.y + newFactor * q.y,
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invFactor * from.z + newFactor * q.z,
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invFactor * from.w + newFactor * q.w);
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#if 0
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real_t to1[4];
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real_t omega, cosom, sinom, scale0, scale1;
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// calc cosine
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cosom = x * q.x + y * q.y + z * q.z
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+ w * q.w;
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// adjust signs (if necessary)
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if ( cosom <0.0 && false) {
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cosom = -cosom;to1[0] = - q.x;
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to1[1] = - q.y;
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to1[2] = - q.z;
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to1[3] = - q.w;
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} else {
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to1[0] = q.x;
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to1[1] = q.y;
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to1[2] = q.z;
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to1[3] = q.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 - t) * omega) / sinom;
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scale1 = Math::sin(t * 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 - t;
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scale1 = t;
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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[0],
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scale0 * y + scale1 * to1[1],
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scale0 * z + scale1 * to1[2],
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scale0 * w + scale1 * to1[3]
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);
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#endif
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}
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Quat Quat::cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const {
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//the only way to do slerp :|
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real_t t2 = (1.0-t)*t*2;
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Quat sp = this->slerp(q,t);
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Quat sq = prep.slerpni(postq,t);
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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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Quat::Quat(const Vector3& axis, const real_t& angle) {
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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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