Added Basis.h and stub Quat.h
Karroffel
parent
0cd08a93ec
commit
5d543692eb
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#ifndef BASIS_H
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#define BASIS_H
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#include "Vector3.h"
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#include <algorithm>
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typedef float real_t; // @Todo move this to a global Godot.h
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#define CMP_EPSILON 0.00001 // @Todo move this somewhere more global
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#define CMP_EPSILON2 (CMP_EPSILON*CMP_EPSILON) // @Todo same as above
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#define Math_PI 3.14159265358979323846 // I feel like I'm talking to myself
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namespace godot {
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class Quat;
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class Basis {
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public:
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Vector3 elements[3];
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Basis(const Quat& p_quat); // euler
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Basis(const Vector3& p_euler); // euler
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Basis(const Vector3& p_axis, real_t p_phi);
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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(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() {
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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& operator[](int axis) const {
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return elements[axis];
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}
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Vector3& 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 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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if ( det != 0 ) {
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// WTF
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__builtin_trap(); // WTF WTF WTF
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// I shouldn't do this
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// @Todo @Fixme @Todo @Todo
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}
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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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void 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 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 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 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 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 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 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 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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Vector3 get_rotation() const; // need?!
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void 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 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 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 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 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 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 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 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 isequal_approx(const Basis& a, const Basis& b) const; // need?
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bool 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 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 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 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 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 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 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 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 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 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 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 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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int get_orthogonal_index() const; // down below
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void set_orthogonal_index(int p_index); // down below
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bool is_orthogonal() const; // need?
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bool is_rotation() const; // need?
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operator String() const;
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void get_axis_and_angle(Vector3 &r_axis,real_t& r_angle) const;
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/* create / set */
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void 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 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 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 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 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 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 orthonormalize()
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{
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if (determinant() != 0) {
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// not this crap again
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__builtin_trap(); // WTF WTF WTF
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// somebody please complain some day
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// so I can fix this
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// need propert error reporting here.
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}
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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 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 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 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];
|
||||
real_t el02_2 = elements[0][2] * elements[0][2];
|
||||
real_t el12_2 = elements[1][2] * elements[1][2];
|
||||
// Find the pivot element
|
||||
int i, j;
|
||||
if (el01_2 > el02_2) {
|
||||
if (el12_2 > el01_2) {
|
||||
i = 1;
|
||||
j = 2;
|
||||
} else {
|
||||
i = 0;
|
||||
j = 1;
|
||||
}
|
||||
} else {
|
||||
if (el12_2 > el02_2) {
|
||||
i = 1;
|
||||
j = 2;
|
||||
} else {
|
||||
i = 0;
|
||||
j = 2;
|
||||
}
|
||||
}
|
||||
|
||||
// Compute the rotation angle
|
||||
real_t angle;
|
||||
if (::fabs(elements[j][j] - elements[i][i]) < CMP_EPSILON) {
|
||||
angle = Math_PI / 4;
|
||||
} else {
|
||||
angle = 0.5 * ::atan(2 * elements[i][j] / (elements[j][j] - elements[i][i]));
|
||||
}
|
||||
|
||||
// Compute the rotation matrix
|
||||
Basis rot;
|
||||
rot.elements[i][i] = rot.elements[j][j] = ::cos(angle);
|
||||
rot.elements[i][j] = - (rot.elements[j][i] = ::sin(angle));
|
||||
|
||||
// Update the off matrix norm
|
||||
off_matrix_norm_2 -= elements[i][j] * elements[i][j];
|
||||
|
||||
// Apply the rotation
|
||||
*this = rot * *this * rot.transposed();
|
||||
acc_rot = rot * acc_rot;
|
||||
}
|
||||
|
||||
return acc_rot;
|
||||
}
|
||||
|
||||
operator Quat() const;
|
||||
|
||||
|
||||
};
|
||||
|
||||
static const Basis _ortho_bases[24]={
|
||||
Basis(1, 0, 0, 0, 1, 0, 0, 0, 1),
|
||||
Basis(0, -1, 0, 1, 0, 0, 0, 0, 1),
|
||||
Basis(-1, 0, 0, 0, -1, 0, 0, 0, 1),
|
||||
Basis(0, 1, 0, -1, 0, 0, 0, 0, 1),
|
||||
Basis(1, 0, 0, 0, 0, -1, 0, 1, 0),
|
||||
Basis(0, 0, 1, 1, 0, 0, 0, 1, 0),
|
||||
Basis(-1, 0, 0, 0, 0, 1, 0, 1, 0),
|
||||
Basis(0, 0, -1, -1, 0, 0, 0, 1, 0),
|
||||
Basis(1, 0, 0, 0, -1, 0, 0, 0, -1),
|
||||
Basis(0, 1, 0, 1, 0, 0, 0, 0, -1),
|
||||
Basis(-1, 0, 0, 0, 1, 0, 0, 0, -1),
|
||||
Basis(0, -1, 0, -1, 0, 0, 0, 0, -1),
|
||||
Basis(1, 0, 0, 0, 0, 1, 0, -1, 0),
|
||||
Basis(0, 0, -1, 1, 0, 0, 0, -1, 0),
|
||||
Basis(-1, 0, 0, 0, 0, -1, 0, -1, 0),
|
||||
Basis(0, 0, 1, -1, 0, 0, 0, -1, 0),
|
||||
Basis(0, 0, 1, 0, 1, 0, -1, 0, 0),
|
||||
Basis(0, -1, 0, 0, 0, 1, -1, 0, 0),
|
||||
Basis(0, 0, -1, 0, -1, 0, -1, 0, 0),
|
||||
Basis(0, 1, 0, 0, 0, -1, -1, 0, 0),
|
||||
Basis(0, 0, 1, 0, -1, 0, 1, 0, 0),
|
||||
Basis(0, 1, 0, 0, 0, 1, 1, 0, 0),
|
||||
Basis(0, 0, -1, 0, 1, 0, 1, 0, 0),
|
||||
Basis(0, -1, 0, 0, 0, -1, 1, 0, 0)
|
||||
};
|
||||
|
||||
|
||||
int Basis::get_orthogonal_index() const
|
||||
{
|
||||
//could be sped up if i come up with a way
|
||||
Basis orth=*this;
|
||||
for(int i=0;i<3;i++) {
|
||||
for(int j=0;j<3;j++) {
|
||||
|
||||
real_t v = orth[i][j];
|
||||
if (v>0.5)
|
||||
v=1.0;
|
||||
else if (v<-0.5)
|
||||
v=-1.0;
|
||||
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
|
||||
if (p_index >= 24) {
|
||||
__builtin_trap(); // kiiiiill me
|
||||
// I don't want to do shady stuff like that
|
||||
// @Todo WTF WTF
|
||||
}
|
||||
|
||||
|
||||
*this=_ortho_bases[p_index];
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
Basis::Basis(const Vector3& p_euler) {
|
||||
|
||||
set_euler( p_euler );
|
||||
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
#include "Quat.h"
|
||||
|
||||
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 );
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
|
||||
}
|
||||
|
||||
#endif // BASIS_H
|
||||
|
|
@ -0,0 +1,171 @@
|
|||
#ifndef QUAT_H
|
||||
#define QUAT_H
|
||||
|
||||
#include <cmath>
|
||||
|
||||
#include "Vector3.h"
|
||||
|
||||
namespace godot {
|
||||
|
||||
#define CMP_EPSILON 0.00001
|
||||
|
||||
typedef float real_t;
|
||||
|
||||
class Quat{
|
||||
public:
|
||||
|
||||
real_t x,y,z,w;
|
||||
|
||||
real_t length_squared() const;
|
||||
real_t length() const;
|
||||
void normalize();
|
||||
Quat normalized() const;
|
||||
Quat inverse() const;
|
||||
real_t dot(const Quat& q) const;
|
||||
void set_euler(const Vector3& p_euler);
|
||||
Vector3 get_euler() const;
|
||||
Quat slerp(const Quat& q, const real_t& t) const;
|
||||
Quat slerpni(const Quat& q, const real_t& t) const;
|
||||
Quat cubic_slerp(const Quat& q, const Quat& prep, const Quat& postq,const real_t& t) const;
|
||||
|
||||
void get_axis_and_angle(Vector3& r_axis, real_t &r_angle) const {
|
||||
r_angle = 2 * ::acos(w);
|
||||
r_axis.x = x / ::sqrt(1-w*w);
|
||||
r_axis.y = y / ::sqrt(1-w*w);
|
||||
r_axis.z = z / ::sqrt(1-w*w);
|
||||
}
|
||||
|
||||
void operator*=(const Quat& q);
|
||||
Quat operator*(const Quat& q) const;
|
||||
|
||||
|
||||
|
||||
Quat operator*(const Vector3& v) const
|
||||
{
|
||||
return Quat( w * v.x + y * v.z - z * v.y,
|
||||
w * v.y + z * v.x - x * v.z,
|
||||
w * v.z + x * v.y - y * v.x,
|
||||
-x * v.x - y * v.y - z * v.z);
|
||||
}
|
||||
|
||||
Vector3 xform(const Vector3& v) const {
|
||||
|
||||
Quat q = *this * v;
|
||||
q *= this->inverse();
|
||||
return Vector3(q.x,q.y,q.z);
|
||||
}
|
||||
|
||||
void operator+=(const Quat& q);
|
||||
void operator-=(const Quat& q);
|
||||
void operator*=(const real_t& s);
|
||||
void operator/=(const real_t& s);
|
||||
Quat operator+(const Quat& q2) const;
|
||||
Quat operator-(const Quat& q2) const;
|
||||
Quat operator-() const;
|
||||
Quat operator*(const real_t& s) const;
|
||||
Quat operator/(const real_t& s) const;
|
||||
|
||||
|
||||
bool operator==(const Quat& p_quat) const;
|
||||
bool operator!=(const Quat& p_quat) const;
|
||||
|
||||
operator String() const;
|
||||
|
||||
inline void set( real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
|
||||
x=p_x; y=p_y; z=p_z; w=p_w;
|
||||
}
|
||||
inline Quat(real_t p_x, real_t p_y, real_t p_z, real_t p_w) {
|
||||
x=p_x; y=p_y; z=p_z; w=p_w;
|
||||
}
|
||||
Quat(const Vector3& axis, const real_t& angle);
|
||||
|
||||
Quat(const Vector3& v0, const Vector3& v1) // shortest arc
|
||||
{
|
||||
Vector3 c = v0.cross(v1);
|
||||
real_t d = v0.dot(v1);
|
||||
|
||||
if (d < -1.0 + CMP_EPSILON) {
|
||||
x=0;
|
||||
y=1;
|
||||
z=0;
|
||||
w=0;
|
||||
} else {
|
||||
|
||||
real_t s = ::sqrt((1.0 + d) * 2.0);
|
||||
real_t rs = 1.0 / s;
|
||||
|
||||
x=c.x*rs;
|
||||
y=c.y*rs;
|
||||
z=c.z*rs;
|
||||
w=s * 0.5;
|
||||
}
|
||||
}
|
||||
|
||||
inline Quat() {x=y=z=0; w=1; }
|
||||
|
||||
|
||||
};
|
||||
|
||||
|
||||
real_t Quat::dot(const Quat& q) const {
|
||||
return x * q.x+y * q.y+z * q.z+w * q.w;
|
||||
}
|
||||
|
||||
real_t Quat::length_squared() const {
|
||||
return dot(*this);
|
||||
}
|
||||
|
||||
void Quat::operator+=(const Quat& q) {
|
||||
x += q.x; y += q.y; z += q.z; w += q.w;
|
||||
}
|
||||
|
||||
void Quat::operator-=(const Quat& q) {
|
||||
x -= q.x; y -= q.y; z -= q.z; w -= q.w;
|
||||
}
|
||||
|
||||
void Quat::operator*=(const real_t& s) {
|
||||
x *= s; y *= s; z *= s; w *= s;
|
||||
}
|
||||
|
||||
|
||||
void Quat::operator/=(const real_t& s) {
|
||||
|
||||
*this *= 1.0 / s;
|
||||
}
|
||||
|
||||
Quat Quat::operator+(const Quat& q2) const {
|
||||
const Quat& q1 = *this;
|
||||
return Quat( q1.x+q2.x, q1.y+q2.y, q1.z+q2.z, q1.w+q2.w );
|
||||
}
|
||||
|
||||
Quat Quat::operator-(const Quat& q2) const {
|
||||
const Quat& q1 = *this;
|
||||
return Quat( q1.x-q2.x, q1.y-q2.y, q1.z-q2.z, q1.w-q2.w);
|
||||
}
|
||||
|
||||
Quat Quat::operator-() const {
|
||||
const Quat& q2 = *this;
|
||||
return Quat( -q2.x, -q2.y, -q2.z, -q2.w);
|
||||
}
|
||||
|
||||
Quat Quat::operator*(const real_t& s) const {
|
||||
return Quat(x * s, y * s, z * s, w * s);
|
||||
}
|
||||
|
||||
Quat Quat::operator/(const real_t& s) const {
|
||||
return *this * (1.0 / s);
|
||||
}
|
||||
|
||||
|
||||
bool Quat::operator==(const Quat& p_quat) const {
|
||||
return x==p_quat.x && y==p_quat.y && z==p_quat.z && w==p_quat.w;
|
||||
}
|
||||
|
||||
bool Quat::operator!=(const Quat& p_quat) const {
|
||||
return x!=p_quat.x || y!=p_quat.y || z!=p_quat.z || w!=p_quat.w;
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
|
||||
#endif // QUAT_H
|
||||
Loading…
Reference in New Issue