bd7ba0b664
Furthermore, functions which expect a rotation matrix will now give an error simply, rather than trying to orthonormalize such matrices. The documentation for such functions has be updated accordingly. This commit breaks code using 3D rotations, and is a part of the breaking changes in 2.1 -> 3.0 transition. The code affected within Godot code base is fixed in this commit.
287 lines
8 KiB
C++
287 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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Matrix3 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 = 1.0f / sine;
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real_t coeff_0 = Math::sin((1.0f - 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 * (1.0f - 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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float dot = from.dot(q);
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if (Math::absf(dot) > 0.9999f) return from;
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float theta = Math::acos(dot),
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sinT = 1.0f / Math::sin(theta),
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newFactor = Math::sin(t * theta) * sinT,
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invFactor = Math::sin((1.0f - 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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float 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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