665 lines
15 KiB
C++
665 lines
15 KiB
C++
#include "Basis.hpp"
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#include "Defs.hpp"
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#include "Vector3.hpp"
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#include "Quat.hpp"
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#include <algorithm>
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namespace godot {
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Basis::Basis(const Vector3& row0, const Vector3& row1, const Vector3& row2)
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{
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elements[0]=row0;
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elements[1]=row1;
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elements[2]=row2;
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}
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Basis::Basis(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
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set(xx, xy, xz, yx, yy, yz, zx, zy, zz);
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}
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Basis::Basis() {
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elements[0][0]=1;
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elements[0][1]=0;
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elements[0][2]=0;
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elements[1][0]=0;
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elements[1][1]=1;
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elements[1][2]=0;
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elements[2][0]=0;
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elements[2][1]=0;
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elements[2][2]=1;
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}
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const Vector3& Basis::operator[](int axis) const {
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return elements[axis];
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}
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Vector3&Basis:: operator[](int axis) {
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return elements[axis];
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}
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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 Basis::invert()
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{
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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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#undef cofac
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bool Basis::isequal_approx(const Basis& a, const Basis& 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 ((::fabs(a.elements[i][j]-b.elements[i][j]) < CMP_EPSILON) == 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 Basis::is_orthogonal() const
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{
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Basis id;
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Basis m = (*this)*transposed();
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return isequal_approx(id,m);
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}
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bool Basis::is_rotation() const
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{
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return ::fabs(determinant()-1) < CMP_EPSILON && is_orthogonal();
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}
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void Basis::transpose()
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{
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std::swap(elements[0][1],elements[1][0]);
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std::swap(elements[0][2],elements[2][0]);
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std::swap(elements[1][2],elements[2][1]);
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}
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Basis Basis::inverse() const
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{
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Basis b = *this;
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b.invert();
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return b;
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}
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Basis Basis::transposed() const
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{
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Basis b = *this;
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b.transpose();
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return b;
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}
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real_t Basis::determinant() const
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{
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return elements[0][0]*(elements[1][1]*elements[2][2] - elements[2][1]*elements[1][2]) -
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elements[1][0]*(elements[0][1]*elements[2][2] - elements[2][1]*elements[0][2]) +
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elements[2][0]*(elements[0][1]*elements[1][2] - elements[1][1]*elements[0][2]);
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}
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Vector3 Basis::get_axis(int p_axis) const {
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// get actual basis axis (elements is transposed for performance)
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return Vector3( elements[0][p_axis], elements[1][p_axis], elements[2][p_axis] );
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}
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void Basis::set_axis(int p_axis, const Vector3& p_value) {
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// get actual basis axis (elements is transposed for performance)
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elements[0][p_axis]=p_value.x;
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elements[1][p_axis]=p_value.y;
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elements[2][p_axis]=p_value.z;
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}
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void Basis::rotate(const Vector3& p_axis, real_t p_phi)
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{
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*this = rotated(p_axis, p_phi);
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}
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Basis Basis::rotated(const Vector3& p_axis, real_t p_phi) const
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{
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return Basis(p_axis, p_phi) * (*this);
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}
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void Basis::scale( const Vector3& p_scale )
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{
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elements[0][0]*=p_scale.x;
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elements[0][1]*=p_scale.x;
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elements[0][2]*=p_scale.x;
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elements[1][0]*=p_scale.y;
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elements[1][1]*=p_scale.y;
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elements[1][2]*=p_scale.y;
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elements[2][0]*=p_scale.z;
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elements[2][1]*=p_scale.z;
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elements[2][2]*=p_scale.z;
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}
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Basis Basis::scaled( const Vector3& p_scale ) const
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{
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Basis b = *this;
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b.scale(p_scale);
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return b;
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}
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Vector3 Basis::get_scale() const
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{
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// We are assuming M = R.S, and performing a polar decomposition to extract R and S.
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// FIXME: We eventually need a proper polar decomposition.
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// As a cheap workaround until then, to ensure that R is a proper rotation matrix with determinant +1
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// (such that it can be represented by a Quat or Euler angles), we absorb the sign flip into the scaling matrix.
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// As such, it works in conjuction with get_rotation().
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real_t det_sign = determinant() > 0 ? 1 : -1;
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return det_sign*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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Vector3 Basis::get_euler() const
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{
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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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if (is_rotation() == false)
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return euler;
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euler.y = ::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 = ::atan2(-elements[1][2],elements[2][2]);
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euler.z = ::atan2(-elements[0][1],elements[0][0]);
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} else {
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real_t r = ::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 = ::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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void Basis::set_euler(const Vector3& p_euler)
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{
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real_t c, s;
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c = ::cos(p_euler.x);
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s = ::sin(p_euler.x);
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Basis xmat(1.0,0.0,0.0,0.0,c,-s,0.0,s,c);
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c = ::cos(p_euler.y);
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s = ::sin(p_euler.y);
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Basis ymat(c,0.0,s,0.0,1.0,0.0,-s,0.0,c);
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c = ::cos(p_euler.z);
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s = ::sin(p_euler.z);
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Basis 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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// transposed dot products
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real_t Basis::tdotx(const Vector3& v) const {
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return elements[0][0] * v[0] + elements[1][0] * v[1] + elements[2][0] * v[2];
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}
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real_t Basis::tdoty(const Vector3& v) const {
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return elements[0][1] * v[0] + elements[1][1] * v[1] + elements[2][1] * v[2];
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}
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real_t Basis::tdotz(const Vector3& v) const {
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return elements[0][2] * v[0] + elements[1][2] * v[1] + elements[2][2] * v[2];
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}
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bool Basis::operator==(const Basis& p_matrix) const
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{
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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 Basis::operator!=(const Basis& p_matrix) const
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{
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return (!(*this==p_matrix));
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}
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Vector3 Basis::xform(const Vector3& p_vector) const {
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return Vector3(
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elements[0].dot(p_vector),
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elements[1].dot(p_vector),
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elements[2].dot(p_vector)
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);
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}
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Vector3 Basis::xform_inv(const Vector3& p_vector) const {
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return Vector3(
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(elements[0][0]*p_vector.x ) + ( elements[1][0]*p_vector.y ) + ( elements[2][0]*p_vector.z ),
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(elements[0][1]*p_vector.x ) + ( elements[1][1]*p_vector.y ) + ( elements[2][1]*p_vector.z ),
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(elements[0][2]*p_vector.x ) + ( elements[1][2]*p_vector.y ) + ( elements[2][2]*p_vector.z )
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);
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}
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void Basis::operator*=(const Basis& p_matrix)
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{
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set(
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p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
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p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
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p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]));
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}
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Basis Basis::operator*(const Basis& p_matrix) const
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{
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return Basis(
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p_matrix.tdotx(elements[0]), p_matrix.tdoty(elements[0]), p_matrix.tdotz(elements[0]),
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p_matrix.tdotx(elements[1]), p_matrix.tdoty(elements[1]), p_matrix.tdotz(elements[1]),
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p_matrix.tdotx(elements[2]), p_matrix.tdoty(elements[2]), p_matrix.tdotz(elements[2]) );
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}
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void Basis::operator+=(const Basis& p_matrix) {
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elements[0] += p_matrix.elements[0];
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elements[1] += p_matrix.elements[1];
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elements[2] += p_matrix.elements[2];
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}
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Basis Basis::operator+(const Basis& p_matrix) const {
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Basis ret(*this);
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ret += p_matrix;
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return ret;
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}
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void Basis::operator-=(const Basis& p_matrix) {
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elements[0] -= p_matrix.elements[0];
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elements[1] -= p_matrix.elements[1];
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elements[2] -= p_matrix.elements[2];
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}
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Basis Basis::operator-(const Basis& p_matrix) const {
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Basis ret(*this);
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ret -= p_matrix;
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return ret;
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}
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void Basis::operator*=(real_t p_val) {
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elements[0]*=p_val;
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elements[1]*=p_val;
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elements[2]*=p_val;
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}
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Basis Basis::operator*(real_t p_val) const {
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Basis ret(*this);
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ret *= p_val;
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return ret;
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}
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Basis::operator String() const
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{
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String s;
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// @Todo
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return s;
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}
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/* create / set */
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void Basis::set(real_t xx, real_t xy, real_t xz, real_t yx, real_t yy, real_t yz, real_t zx, real_t zy, real_t zz) {
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elements[0][0]=xx;
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elements[0][1]=xy;
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elements[0][2]=xz;
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elements[1][0]=yx;
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elements[1][1]=yy;
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elements[1][2]=yz;
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elements[2][0]=zx;
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elements[2][1]=zy;
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elements[2][2]=zz;
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}
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Vector3 Basis::get_column(int i) const {
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return Vector3(elements[0][i],elements[1][i],elements[2][i]);
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}
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Vector3 Basis::get_row(int i) const {
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return Vector3(elements[i][0],elements[i][1],elements[i][2]);
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}
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Vector3 Basis::get_main_diagonal() const {
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return Vector3(elements[0][0],elements[1][1],elements[2][2]);
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}
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void Basis::set_row(int i, const Vector3& p_row) {
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elements[i][0]=p_row.x;
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elements[i][1]=p_row.y;
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elements[i][2]=p_row.z;
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}
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Basis Basis::transpose_xform(const Basis& m) const
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{
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return Basis(
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elements[0].x * m[0].x + elements[1].x * m[1].x + elements[2].x * m[2].x,
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elements[0].x * m[0].y + elements[1].x * m[1].y + elements[2].x * m[2].y,
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elements[0].x * m[0].z + elements[1].x * m[1].z + elements[2].x * m[2].z,
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elements[0].y * m[0].x + elements[1].y * m[1].x + elements[2].y * m[2].x,
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elements[0].y * m[0].y + elements[1].y * m[1].y + elements[2].y * m[2].y,
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elements[0].y * m[0].z + elements[1].y * m[1].z + elements[2].y * m[2].z,
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elements[0].z * m[0].x + elements[1].z * m[1].x + elements[2].z * m[2].x,
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elements[0].z * m[0].y + elements[1].z * m[1].y + elements[2].z * m[2].y,
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elements[0].z * m[0].z + elements[1].z * m[1].z + elements[2].z * m[2].z);
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}
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void Basis::orthonormalize()
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{
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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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Basis Basis::orthonormalized() const
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{
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Basis b = *this;
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b.orthonormalize();
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return b;
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}
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bool Basis::is_symmetric() const
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{
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if (::fabs(elements[0][1] - elements[1][0]) > CMP_EPSILON)
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return false;
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if (::fabs(elements[0][2] - elements[2][0]) > CMP_EPSILON)
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return false;
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if (::fabs(elements[1][2] - elements[2][1]) > CMP_EPSILON)
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return false;
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return true;
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}
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Basis Basis::diagonalize()
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{
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// I love copy paste
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if (!is_symmetric())
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return Basis();
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const int ite_max = 1024;
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real_t off_matrix_norm_2 = elements[0][1] * elements[0][1] + elements[0][2] * elements[0][2] + elements[1][2] * elements[1][2];
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int ite = 0;
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Basis acc_rot;
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while (off_matrix_norm_2 > CMP_EPSILON2 && ite++ < ite_max ) {
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real_t el01_2 = elements[0][1] * elements[0][1];
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real_t el02_2 = elements[0][2] * elements[0][2];
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real_t el12_2 = elements[1][2] * elements[1][2];
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// Find the pivot element
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int i, j;
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if (el01_2 > el02_2) {
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if (el12_2 > el01_2) {
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i = 1;
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j = 2;
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} else {
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i = 0;
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j = 1;
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}
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} else {
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if (el12_2 > el02_2) {
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i = 1;
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j = 2;
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} else {
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i = 0;
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j = 2;
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}
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}
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// Compute the rotation angle
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real_t angle;
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if (::fabs(elements[j][j] - elements[i][i]) < CMP_EPSILON) {
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angle = Math_PI / 4;
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} else {
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angle = 0.5 * ::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
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}
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// Compute the rotation matrix
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Basis rot;
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rot.elements[i][i] = rot.elements[j][j] = ::cos(angle);
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rot.elements[i][j] = - (rot.elements[j][i] = ::sin(angle));
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// Update the off matrix norm
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off_matrix_norm_2 -= elements[i][j] * elements[i][j];
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// Apply the rotation
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*this = rot * *this * rot.transposed();
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acc_rot = rot * acc_rot;
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}
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return acc_rot;
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}
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static const Basis _ortho_bases[24]={
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Basis(1, 0, 0, 0, 1, 0, 0, 0, 1),
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Basis(0, -1, 0, 1, 0, 0, 0, 0, 1),
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Basis(-1, 0, 0, 0, -1, 0, 0, 0, 1),
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Basis(0, 1, 0, -1, 0, 0, 0, 0, 1),
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Basis(1, 0, 0, 0, 0, -1, 0, 1, 0),
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Basis(0, 0, 1, 1, 0, 0, 0, 1, 0),
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Basis(-1, 0, 0, 0, 0, 1, 0, 1, 0),
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Basis(0, 0, -1, -1, 0, 0, 0, 1, 0),
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Basis(1, 0, 0, 0, -1, 0, 0, 0, -1),
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Basis(0, 1, 0, 1, 0, 0, 0, 0, -1),
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Basis(-1, 0, 0, 0, 1, 0, 0, 0, -1),
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Basis(0, -1, 0, -1, 0, 0, 0, 0, -1),
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Basis(1, 0, 0, 0, 0, 1, 0, -1, 0),
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Basis(0, 0, -1, 1, 0, 0, 0, -1, 0),
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Basis(-1, 0, 0, 0, 0, -1, 0, -1, 0),
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Basis(0, 0, 1, -1, 0, 0, 0, -1, 0),
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Basis(0, 0, 1, 0, 1, 0, -1, 0, 0),
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Basis(0, -1, 0, 0, 0, 1, -1, 0, 0),
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Basis(0, 0, -1, 0, -1, 0, -1, 0, 0),
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Basis(0, 1, 0, 0, 0, -1, -1, 0, 0),
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Basis(0, 0, 1, 0, -1, 0, 1, 0, 0),
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Basis(0, 1, 0, 0, 0, 1, 1, 0, 0),
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Basis(0, 0, -1, 0, 1, 0, 1, 0, 0),
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Basis(0, -1, 0, 0, 0, -1, 1, 0, 0)
|
|
};
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|
|
|
|
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int Basis::get_orthogonal_index() const
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|
{
|
|
//could be sped up if i come up with a way
|
|
Basis orth=*this;
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|
for(int i=0;i<3;i++) {
|
|
for(int j=0;j<3;j++) {
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|
|
|
real_t v = orth[i][j];
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|
if (v>0.5)
|
|
v=1.0;
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|
else if (v<-0.5)
|
|
v=-1.0;
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|
else
|
|
v=0;
|
|
|
|
orth[i][j]=v;
|
|
}
|
|
}
|
|
|
|
for(int i=0;i<24;i++) {
|
|
|
|
if (_ortho_bases[i]==orth)
|
|
return i;
|
|
|
|
|
|
}
|
|
|
|
return 0;
|
|
}
|
|
|
|
|
|
void Basis::set_orthogonal_index(int p_index){
|
|
|
|
//there only exist 24 orthogonal bases in r3
|
|
ERR_FAIL_COND(p_index >= 24);
|
|
|
|
*this=_ortho_bases[p_index];
|
|
|
|
}
|
|
|
|
|
|
|
|
Basis::Basis(const Vector3& p_euler) {
|
|
|
|
set_euler( p_euler );
|
|
|
|
}
|
|
|
|
}
|
|
|
|
#include "Quat.hpp"
|
|
|
|
namespace godot {
|
|
|
|
Basis::Basis(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)) ;
|
|
|
|
}
|
|
|
|
Basis::Basis(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= ::cos(p_phi);
|
|
real_t sine= ::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 );
|
|
|
|
}
|
|
|
|
Basis::operator Quat() const {
|
|
ERR_FAIL_COND_V(is_rotation() == false, Quat());
|
|
|
|
real_t trace = elements[0][0] + elements[1][1] + elements[2][2];
|
|
real_t temp[4];
|
|
|
|
if (trace > 0.0)
|
|
{
|
|
real_t s = ::sqrt(trace + 1.0);
|
|
temp[3]=(s * 0.5);
|
|
s = 0.5 / s;
|
|
|
|
temp[0]=((elements[2][1] - elements[1][2]) * s);
|
|
temp[1]=((elements[0][2] - elements[2][0]) * s);
|
|
temp[2]=((elements[1][0] - elements[0][1]) * s);
|
|
}
|
|
else
|
|
{
|
|
int i = elements[0][0] < elements[1][1] ?
|
|
(elements[1][1] < elements[2][2] ? 2 : 1) :
|
|
(elements[0][0] < elements[2][2] ? 2 : 0);
|
|
int j = (i + 1) % 3;
|
|
int k = (i + 2) % 3;
|
|
|
|
real_t s = ::sqrt(elements[i][i] - elements[j][j] - elements[k][k] + 1.0);
|
|
temp[i] = s * 0.5;
|
|
s = 0.5 / s;
|
|
|
|
temp[3] = (elements[k][j] - elements[j][k]) * s;
|
|
temp[j] = (elements[j][i] + elements[i][j]) * s;
|
|
temp[k] = (elements[k][i] + elements[i][k]) * s;
|
|
}
|
|
|
|
return Quat(temp[0],temp[1],temp[2],temp[3]);
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
}
|