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.
526 lines
15 KiB
C++
526 lines
15 KiB
C++
/*************************************************************************/
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/* matrix3.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 "matrix3.h"
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#include "math_funcs.h"
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#include "os/copymem.h"
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#define cofac(row1,col1, row2, col2)\
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(elements[row1][col1] * elements[row2][col2] - elements[row1][col2] * elements[row2][col1])
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void Matrix3::from_z(const Vector3& p_z) {
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if (Math::abs(p_z.z) > Math_SQRT12 ) {
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// choose p in y-z plane
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real_t a = p_z[1]*p_z[1] + p_z[2]*p_z[2];
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real_t k = 1.0/Math::sqrt(a);
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elements[0]=Vector3(0,-p_z[2]*k,p_z[1]*k);
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elements[1]=Vector3(a*k,-p_z[0]*elements[0][2],p_z[0]*elements[0][1]);
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} else {
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// choose p in x-y plane
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real_t a = p_z.x*p_z.x + p_z.y*p_z.y;
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real_t k = 1.0/Math::sqrt(a);
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elements[0]=Vector3(-p_z.y*k,p_z.x*k,0);
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elements[1]=Vector3(-p_z.z*elements[0].y,p_z.z*elements[0].x,a*k);
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}
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elements[2]=p_z;
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}
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void Matrix3::invert() {
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real_t co[3]={
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cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1)
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};
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real_t det = elements[0][0] * co[0]+
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elements[0][1] * co[1]+
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elements[0][2] * co[2];
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ERR_FAIL_COND( det == 0 );
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real_t s = 1.0/det;
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set( co[0]*s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
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co[1]*s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
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co[2]*s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s );
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}
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void Matrix3::orthonormalize() {
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ERR_FAIL_COND(determinant() == 0);
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// Gram-Schmidt Process
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Vector3 x=get_axis(0);
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Vector3 y=get_axis(1);
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Vector3 z=get_axis(2);
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x.normalize();
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y = (y-x*(x.dot(y)));
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y.normalize();
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z = (z-x*(x.dot(z))-y*(y.dot(z)));
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z.normalize();
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set_axis(0,x);
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set_axis(1,y);
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set_axis(2,z);
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}
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Matrix3 Matrix3::orthonormalized() const {
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Matrix3 c = *this;
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c.orthonormalize();
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return c;
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}
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bool Matrix3::is_orthogonal() const {
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Matrix3 id;
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Matrix3 m = (*this)*transposed();
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return isequal_approx(id,m);
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}
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bool Matrix3::is_rotation() const {
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return Math::isequal_approx(determinant(), 1) && is_orthogonal();
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}
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Matrix3 Matrix3::inverse() const {
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Matrix3 inv=*this;
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inv.invert();
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return inv;
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}
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void Matrix3::transpose() {
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SWAP(elements[0][1],elements[1][0]);
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SWAP(elements[0][2],elements[2][0]);
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SWAP(elements[1][2],elements[2][1]);
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}
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Matrix3 Matrix3::transposed() const {
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Matrix3 tr=*this;
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tr.transpose();
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return tr;
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}
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void Matrix3::scale(const Vector3& p_scale) {
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elements[0][0]*=p_scale.x;
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elements[1][0]*=p_scale.x;
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elements[2][0]*=p_scale.x;
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elements[0][1]*=p_scale.y;
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elements[1][1]*=p_scale.y;
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elements[2][1]*=p_scale.y;
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elements[0][2]*=p_scale.z;
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elements[1][2]*=p_scale.z;
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elements[2][2]*=p_scale.z;
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}
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Matrix3 Matrix3::scaled( const Vector3& p_scale ) const {
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Matrix3 m = *this;
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m.scale(p_scale);
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return m;
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}
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Vector3 Matrix3::get_scale() const {
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return Vector3(
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Vector3(elements[0][0],elements[1][0],elements[2][0]).length(),
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Vector3(elements[0][1],elements[1][1],elements[2][1]).length(),
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Vector3(elements[0][2],elements[1][2],elements[2][2]).length()
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);
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}
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// Matrix3::rotate and Matrix3::rotated return M * R(axis,phi), and is a convenience function. They do *not* perform proper matrix rotation.
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void Matrix3::rotate(const Vector3& p_axis, real_t p_phi) {
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// TODO: This function should also be renamed as the current name is misleading: rotate does *not* perform matrix rotation.
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// Same problem affects Matrix3::rotated.
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// A similar problem exists in 2D math, which will be handled separately.
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// After Matrix3 is renamed to Basis, this comments needs to be revised.
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*this = *this * Matrix3(p_axis, p_phi);
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}
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Matrix3 Matrix3::rotated(const Vector3& p_axis, real_t p_phi) const {
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return *this * Matrix3(p_axis, p_phi);
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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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// (following the convention they are commonly defined in the literature).
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//
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// The current implementation uses XYZ convention (Z is the first rotation),
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// so euler.z is the angle of the (first) rotation around Z axis and so on,
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//
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// And thus, assuming the matrix is a rotation matrix, this function returns
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// the angles in the decomposition R = X(a1).Y(a2).Z(a3) where Z(a) rotates
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// around the z-axis by a and so on.
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Vector3 Matrix3::get_euler() const {
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// Euler angles in XYZ convention.
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// See https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix
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//
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// rot = cy*cz -cy*sz sy
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// cz*sx*sy+cx*sz cx*cz-sx*sy*sz -cy*sx
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// -cx*cz*sy+sx*sz cz*sx+cx*sy*sz cx*cy
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Vector3 euler;
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ERR_FAIL_COND_V(is_rotation() == false, euler);
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euler.y = Math::asin(elements[0][2]);
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if ( euler.y < Math_PI*0.5) {
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if ( euler.y > -Math_PI*0.5) {
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euler.x = Math::atan2(-elements[1][2],elements[2][2]);
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euler.z = Math::atan2(-elements[0][1],elements[0][0]);
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} else {
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real_t r = Math::atan2(elements[1][0],elements[1][1]);
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euler.z = 0.0;
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euler.x = euler.z - r;
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}
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} else {
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real_t r = Math::atan2(elements[0][1],elements[1][1]);
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euler.z = 0;
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euler.x = r - euler.z;
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}
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return euler;
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}
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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 Matrix3::set_euler(const Vector3& p_euler) {
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real_t c, s;
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c = Math::cos(p_euler.x);
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s = Math::sin(p_euler.x);
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Matrix3 xmat(1.0,0.0,0.0,0.0,c,-s,0.0,s,c);
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c = Math::cos(p_euler.y);
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s = Math::sin(p_euler.y);
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Matrix3 ymat(c,0.0,s,0.0,1.0,0.0,-s,0.0,c);
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c = Math::cos(p_euler.z);
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s = Math::sin(p_euler.z);
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Matrix3 zmat(c,-s,0.0,s,c,0.0,0.0,0.0,1.0);
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//optimizer will optimize away all this anyway
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*this = xmat*(ymat*zmat);
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}
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bool Matrix3::isequal_approx(const Matrix3& a, const Matrix3& b) const {
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for (int i=0;i<3;i++) {
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for (int j=0;j<3;j++) {
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if (Math::isequal_approx(a.elements[i][j],b.elements[i][j]) == false)
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return false;
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}
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}
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return true;
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}
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bool Matrix3::operator==(const Matrix3& p_matrix) const {
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for (int i=0;i<3;i++) {
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for (int j=0;j<3;j++) {
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if (elements[i][j] != p_matrix.elements[i][j])
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return false;
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}
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}
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return true;
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}
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bool Matrix3::operator!=(const Matrix3& p_matrix) const {
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return (!(*this==p_matrix));
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}
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Matrix3::operator String() const {
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String mtx;
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for (int i=0;i<3;i++) {
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for (int j=0;j<3;j++) {
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if (i!=0 || j!=0)
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mtx+=", ";
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mtx+=rtos( elements[i][j] );
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}
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}
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return mtx;
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}
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Matrix3::operator Quat() const {
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ERR_FAIL_COND_V(is_rotation() == false, Quat());
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real_t trace = elements[0][0] + elements[1][1] + elements[2][2];
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real_t temp[4];
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if (trace > 0.0)
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{
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real_t s = Math::sqrt(trace + 1.0);
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temp[3]=(s * 0.5);
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s = 0.5 / s;
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temp[0]=((elements[2][1] - elements[1][2]) * s);
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temp[1]=((elements[0][2] - elements[2][0]) * s);
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temp[2]=((elements[1][0] - elements[0][1]) * s);
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}
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else
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{
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int i = elements[0][0] < elements[1][1] ?
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(elements[1][1] < elements[2][2] ? 2 : 1) :
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(elements[0][0] < elements[2][2] ? 2 : 0);
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int j = (i + 1) % 3;
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int k = (i + 2) % 3;
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real_t s = Math::sqrt(elements[i][i] - elements[j][j] - elements[k][k] + 1.0);
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temp[i] = s * 0.5;
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s = 0.5 / s;
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temp[3] = (elements[k][j] - elements[j][k]) * s;
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temp[j] = (elements[j][i] + elements[i][j]) * s;
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temp[k] = (elements[k][i] + elements[i][k]) * s;
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}
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return Quat(temp[0],temp[1],temp[2],temp[3]);
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}
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static const Matrix3 _ortho_bases[24]={
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Matrix3(1, 0, 0, 0, 1, 0, 0, 0, 1),
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Matrix3(0, -1, 0, 1, 0, 0, 0, 0, 1),
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Matrix3(-1, 0, 0, 0, -1, 0, 0, 0, 1),
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Matrix3(0, 1, 0, -1, 0, 0, 0, 0, 1),
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Matrix3(1, 0, 0, 0, 0, -1, 0, 1, 0),
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Matrix3(0, 0, 1, 1, 0, 0, 0, 1, 0),
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Matrix3(-1, 0, 0, 0, 0, 1, 0, 1, 0),
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Matrix3(0, 0, -1, -1, 0, 0, 0, 1, 0),
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Matrix3(1, 0, 0, 0, -1, 0, 0, 0, -1),
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Matrix3(0, 1, 0, 1, 0, 0, 0, 0, -1),
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Matrix3(-1, 0, 0, 0, 1, 0, 0, 0, -1),
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Matrix3(0, -1, 0, -1, 0, 0, 0, 0, -1),
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Matrix3(1, 0, 0, 0, 0, 1, 0, -1, 0),
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Matrix3(0, 0, -1, 1, 0, 0, 0, -1, 0),
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Matrix3(-1, 0, 0, 0, 0, -1, 0, -1, 0),
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Matrix3(0, 0, 1, -1, 0, 0, 0, -1, 0),
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Matrix3(0, 0, 1, 0, 1, 0, -1, 0, 0),
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Matrix3(0, -1, 0, 0, 0, 1, -1, 0, 0),
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Matrix3(0, 0, -1, 0, -1, 0, -1, 0, 0),
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Matrix3(0, 1, 0, 0, 0, -1, -1, 0, 0),
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Matrix3(0, 0, 1, 0, -1, 0, 1, 0, 0),
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Matrix3(0, 1, 0, 0, 0, 1, 1, 0, 0),
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Matrix3(0, 0, -1, 0, 1, 0, 1, 0, 0),
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Matrix3(0, -1, 0, 0, 0, -1, 1, 0, 0)
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};
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int Matrix3::get_orthogonal_index() const {
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//could be sped up if i come up with a way
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Matrix3 orth=*this;
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for(int i=0;i<3;i++) {
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for(int j=0;j<3;j++) {
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float v = orth[i][j];
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if (v>0.5)
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v=1.0;
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else if (v<-0.5)
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v=-1.0;
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else
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v=0;
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orth[i][j]=v;
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}
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}
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for(int i=0;i<24;i++) {
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if (_ortho_bases[i]==orth)
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return i;
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}
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return 0;
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}
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void Matrix3::set_orthogonal_index(int p_index){
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//there only exist 24 orthogonal bases in r3
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ERR_FAIL_INDEX(p_index,24);
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*this=_ortho_bases[p_index];
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}
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void Matrix3::get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const {
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// TODO: We can handle improper matrices here too, in which case axis will also correspond to the axis of reflection.
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// See Eq. (52) in http://scipp.ucsc.edu/~haber/ph251/rotreflect_13.pdf for example
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// After that change, we should fail on is_orthogonal() == false.
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ERR_FAIL_COND(is_rotation() == false);
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double angle,x,y,z; // variables for result
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double epsilon = 0.01; // margin to allow for rounding errors
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double epsilon2 = 0.1; // margin to distinguish between 0 and 180 degrees
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if ( (Math::abs(elements[1][0]-elements[0][1])< epsilon)
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&& (Math::abs(elements[2][0]-elements[0][2])< epsilon)
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&& (Math::abs(elements[2][1]-elements[1][2])< epsilon)) {
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// singularity found
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// first check for identity matrix which must have +1 for all terms
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// in leading diagonaland zero in other terms
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if ((Math::abs(elements[1][0]+elements[0][1]) < epsilon2)
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&& (Math::abs(elements[2][0]+elements[0][2]) < epsilon2)
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&& (Math::abs(elements[2][1]+elements[1][2]) < epsilon2)
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&& (Math::abs(elements[0][0]+elements[1][1]+elements[2][2]-3) < epsilon2)) {
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// this singularity is identity matrix so angle = 0
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r_axis=Vector3(0,1,0);
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r_angle=0;
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return;
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}
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// otherwise this singularity is angle = 180
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angle = Math_PI;
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double xx = (elements[0][0]+1)/2;
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double yy = (elements[1][1]+1)/2;
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double zz = (elements[2][2]+1)/2;
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double xy = (elements[1][0]+elements[0][1])/4;
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double xz = (elements[2][0]+elements[0][2])/4;
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double yz = (elements[2][1]+elements[1][2])/4;
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if ((xx > yy) && (xx > zz)) { // elements[0][0] is the largest diagonal term
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if (xx< epsilon) {
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x = 0;
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y = 0.7071;
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z = 0.7071;
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} else {
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x = Math::sqrt(xx);
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y = xy/x;
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z = xz/x;
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}
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} else if (yy > zz) { // elements[1][1] is the largest diagonal term
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if (yy< epsilon) {
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x = 0.7071;
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y = 0;
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z = 0.7071;
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} else {
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y = Math::sqrt(yy);
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x = xy/y;
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z = yz/y;
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}
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} else { // elements[2][2] is the largest diagonal term so base result on this
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if (zz< epsilon) {
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x = 0.7071;
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y = 0.7071;
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z = 0;
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} else {
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z = Math::sqrt(zz);
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x = xz/z;
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y = yz/z;
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}
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}
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r_axis=Vector3(x,y,z);
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r_angle=angle;
|
|
return;
|
|
}
|
|
// as we have reached here there are no singularities so we can handle normally
|
|
double s = Math::sqrt((elements[1][2] - elements[2][1])*(elements[1][2] - elements[2][1])
|
|
+(elements[2][0] - elements[0][2])*(elements[2][0] - elements[0][2])
|
|
+(elements[0][1] - elements[1][0])*(elements[0][1] - elements[1][0])); // s=|axis||sin(angle)|, used to normalise
|
|
|
|
angle = Math::acos(( elements[0][0] + elements[1][1] + elements[2][2] - 1)/2);
|
|
if (angle < 0) s = -s;
|
|
x = (elements[2][1] - elements[1][2])/s;
|
|
y = (elements[0][2] - elements[2][0])/s;
|
|
z = (elements[1][0] - elements[0][1])/s;
|
|
|
|
r_axis=Vector3(x,y,z);
|
|
r_angle=angle;
|
|
}
|
|
|
|
Matrix3::Matrix3(const Vector3& p_euler) {
|
|
|
|
set_euler( p_euler );
|
|
|
|
}
|
|
|
|
Matrix3::Matrix3(const Quat& p_quat) {
|
|
|
|
real_t d = p_quat.length_squared();
|
|
real_t s = 2.0 / d;
|
|
real_t xs = p_quat.x * s, ys = p_quat.y * s, zs = p_quat.z * s;
|
|
real_t wx = p_quat.w * xs, wy = p_quat.w * ys, wz = p_quat.w * zs;
|
|
real_t xx = p_quat.x * xs, xy = p_quat.x * ys, xz = p_quat.x * zs;
|
|
real_t yy = p_quat.y * ys, yz = p_quat.y * zs, zz = p_quat.z * zs;
|
|
set( 1.0 - (yy + zz), xy - wz, xz + wy,
|
|
xy + wz, 1.0 - (xx + zz), yz - wx,
|
|
xz - wy, yz + wx, 1.0 - (xx + yy)) ;
|
|
|
|
}
|
|
|
|
Matrix3::Matrix3(const Vector3& p_axis, real_t p_phi) {
|
|
// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
|
|
|
|
Vector3 axis_sq(p_axis.x*p_axis.x,p_axis.y*p_axis.y,p_axis.z*p_axis.z);
|
|
|
|
real_t cosine= Math::cos(p_phi);
|
|
real_t sine= Math::sin(p_phi);
|
|
|
|
elements[0][0] = axis_sq.x + cosine * ( 1.0 - axis_sq.x );
|
|
elements[0][1] = p_axis.x * p_axis.y * ( 1.0 - cosine ) - p_axis.z * sine;
|
|
elements[0][2] = p_axis.z * p_axis.x * ( 1.0 - cosine ) + p_axis.y * sine;
|
|
|
|
elements[1][0] = p_axis.x * p_axis.y * ( 1.0 - cosine ) + p_axis.z * sine;
|
|
elements[1][1] = axis_sq.y + cosine * ( 1.0 - axis_sq.y );
|
|
elements[1][2] = p_axis.y * p_axis.z * ( 1.0 - cosine ) - p_axis.x * sine;
|
|
|
|
elements[2][0] = p_axis.z * p_axis.x * ( 1.0 - cosine ) - p_axis.y * sine;
|
|
elements[2][1] = p_axis.y * p_axis.z * ( 1.0 - cosine ) + p_axis.x * sine;
|
|
elements[2][2] = axis_sq.z + cosine * ( 1.0 - axis_sq.z );
|
|
|
|
}
|
|
|