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Federico Ponchio 2004-03-04 00:21:33 +00:00
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vcg/math/quaternion.h Normal file
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#ifndef QUATERNION_H
#define QUATERNION_H
#include <vcg/space/point3.h>
#include <vcg/space/point4.h>
#include <vcg/math/base.h>
#include <vcg/math/matrix44.h>
namespace vcg {
/** Classe quaternion.
A quaternion is a point in the unit sphere in four dimension: all
rotations in three-dimensional space can be represented by a quaternion.
*/
template<class S> class Quaternion: public Point4<S> {
public:
Quaternion() {}
Quaternion(const S v0, const S v1, const S v2, const S v3): Point4<S>(v0,v1,v2,v3){}
Quaternion(const Point4<S> p) : Point4<S>(p) {}
Quaternion(const S phi, const Point3<S> &a);
Quaternion operator*(const S &s) const;
//Quaternion &operator*=(S d);
Quaternion operator*(const Quaternion &q) const;
Quaternion &operator*=(const Quaternion &q);
void Conjugate();
void FromAxis(const S phi, const Point3<S> &a);
void ToAxis(S &phi, Point3<S> &a ) const;
void FromMatrix(Matrix44<S> &m);
void ToMatrix(Matrix44<S> &m) const;
Point3<S> Rotate(const Point3<S> vec) const;
};
template <class S> Quaternion<S> interpolate(const Quaternion<S> a, const Quaternion<S> b, double t);
//Implementation
template <class S> Quaternion<S>::Quaternion(const S phi, const Point3<S> &a) {
FromAxis(phi, a);
}
template <class S> Quaternion<S> Quaternion<S>::operator*(const S &s) const {
return (Quaternion(V(0)*s,V(1)*s,V(2)*s,V(3)*s));
}
template <class S> Quaternion<S> Quaternion<S>::operator*(const Quaternion &q) const {
Point3<S> t1(V(1), V(2), V(3));
Point3<S> t2(q.V(1), q.V(2), q.V(3));
S d = t2 * t1;
Point3<S> t3 = t1 ^ t2;
t1 *= q.V(0);
t2 *= V(0);
Point3<S> tf = t1 + t2 +t3;
Quaternion<S> t;
t.V(0) = V(0) * q.V(0) - d;
t.V(1) = tf[0];
t.V(2) = tf[1];
t.V(3) = tf[2];
return t;
}
template <class S> Quaternion<S> &Quaternion<S>::operator*=(const Quaternion &q) {
S ww = V(0) * q.V(0) - V(1) * q.V(1) - V(2) * q.V(2) - V(3) * q.V(3);
S xx = V(0) * q.V(1) + V(1) * q.V(0) + V(2) * q.V(3) - V(3) * q.V(2);
S yy = V(0) * q.V(2) - V(1) * q.V(3) + V(2) * q.V(0) + V(3) * q.V(1);
V(0) = ww;
V(1) = xx;
V(2) = yy;
V(3) = V(0) * q.V(3) + V(1) * q.V(2) - V(2) * q.V(1) + V(3) * q.V(0);
return *this;
}
template <class S> void Quaternion<S>::Conjugate() {
V(1)*=-1;
V(2)*=-1;
V(3)*=-1;
}
template <class S> void Quaternion<S>::FromAxis(const S phi, const Point3<S> &a) {
S s = math::Sin(phi/(S(2.0)));
V(0) = math::Cos(phi/(S(2.0)));
V(1) = a[0]*s;
V(2) = a[1]*s;
V(3) = a[2]*s;
}
template <class S> void Quaternion<S>::ToAxis(S &phi, Point3<S> &a) const {
S s = math::Asin(V(0))*S(2.0);
phi = math::Acos(V(0))*S(2.0);
if(s < 0)
phi = - phi;
a.V(0) = V(1);
a.V(1) = V(2);
a.V(2) = V(3);
a.Normalize();
}
template <class S> Point3<S> Quaternion<S>::Rotate(const Point3<S> p) const {
Quaternion<S> co = *this;
co.Conjugate();
Quaternion<S> tmp(0, p.V(0), p.V(1), p.V(2));
tmp = (*this) * tmp * co;
return Point3<S>(tmp.V(1), tmp.V(2), tmp.V(3));
}
template <class S> void Quaternion<S>::ToMatrix(Matrix44<S> &m) const {
S q00 = V(1)*V(1);
S q01 = V(1)*V(2);
S q02 = V(1)*V(3);
S q03 = V(1)*V(0);
S q11 = V(2)*V(2);
S q12 = V(2)*V(3);
S q13 = V(2)*V(0);
S q22 = V(3)*V(3);
S q23 = V(3)*V(0);
m.element(0, 0) = 1.0-(q11 + q22)*2.0;
m.element(1, 0) = (q01 - q23)*2.0;
m.element(2, 0) = (q02 + q13)*2.0;
m.element(3, 0) = 0.0;
m.element(0, 1) = (q01 + q23)*2.0;
m.element(1, 1) = 1.0-(q22 + q00)*2.0;
m.element(2, 1) = (q12 - q03)*2.0;
m.element(3, 1) = 0.0;
m.element(0, 2) = (q02 - q13)*2.0;
m.element(1, 2) = (q12 + q03)*2.0;
m.element(2, 2) = 1.0-(q11 + q00)*2.0;
m.element(3, 2) = 0.0;
m.element(0, 3) = 0.0;
m.element(1, 3) = 0.0;
m.element(2, 3) = 0.0;
m.element(3, 3) = 1.0;
}
///warning m deve essere una matrice di rotazione pena il disastro.
template <class S> void Quaternion<S>::FromMatrix(Matrix44<S> &m) {
double Sc;
double t = (m[0] + m[5] + m[10] + 1);
if(t > 0) {
Sc = 0.5 / sqrt(t);
V(0) = 0.25 / Sc;
V(1) = ( m[9] - m[6] ) * Sc;
V(2) = ( m[2] - m[8] ) * Sc;
V(3) = ( m[4] - m[1] ) * Sc;
} else {
if(m[0] > m[5] && m[0] > m[10]) {
Sc = sqrt( 1.0 + m[0] - m[5] - m[10] ) * 2;
V(1) = 0.5 / Sc;
V(2) = (m[1] + m[4] ) / Sc;
V(3) = (m[2] + m[8] ) / Sc;
V(0) = (m[6] + m[9] ) / Sc;
} else if( m[5] > m[10]) {
Sc = sqrt( 1.0 + m[5] - m[0] - m[10] ) * 2;
V(1) = (m[1] + m[4] ) / Sc;
V(2) = 0.5 / Sc;
V(3) = (m[6] + m[9] ) / Sc;
V(0) = (m[2] + m[8] ) / Sc;
} else {
Sc = sqrt( 1.0 + m[10] - m[0] - m[5] ) * 2;
V(1) = (m[2] + m[8] ) / Sc;
V(2) = (m[6] + m[9] ) / Sc;
V(3) = 0.5 / Sc;
V(0) = (m[1] + m[4] ) / Sc;
}
}
}
template <class S> Quaternion<S> interpolate(const Quaternion<S> a, const Quaternion<S> b, double t) {
double v = a.V(0) * b.V(0) + a.V(1) * b.V(1) + a.V(2) * b.V(2) + a.V(3) * b.V(3);
double phi = Acos(v);
if(phi > 0.01) {
a = a * (Sin(phi *(1-t))/Sin(phi));
b = b * (Sin(phi * t)/Sin(phi));
}
Quaternion<S> c;
c.V(0) = a.V(0) + b.V(0);
c.V(1) = a.V(1) + b.V(1);
c.V(2) = a.V(2) + b.V(2);
c.V(3) = a.V(3) + b.V(3);
if(v < -0.999) { //almost opposite
double d = t * (1 - t);
if(c.V(0) == 0)
c.V(0) += d;
else
c.V(1) += d;
}
c.Normalize();
return c;
}
typedef Quaternion<float> Quaternionf;
typedef Quaternion<double> Quaterniond;
} // end namespace
#endif