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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004-2016 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
#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>
#include <vcg/math/matrix33.h>
namespace vcg {
/** Class 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 Invert();
Quaternion<S> Inverse() const;
void SetIdentity();
void FromAxis(const S phi, const Point3<S> &a);
void ToAxis(S &phi, Point3<S> &a ) const;
///warning m must be a rotation matrix, result is unpredictable otherwise
void FromMatrix(const Matrix44<S> &m);
void FromMatrix(const Matrix33<S> &m);
void ToMatrix(Matrix44<S> &m) const;
void ToMatrix(Matrix33<S> &m) const;
void ToEulerAngles(S &alpha, S &beta, S &gamma) const;
void FromEulerAngles(S alpha, S beta, S gamma);
Point3<S> Rotate(const Point3<S> vec) const;
//duplicated ... because of gcc new confoming to ISO template derived classes
//do no 'see' parent members (unless explicitly specified)
const S & V ( const int i ) const { assert(i>=0 && i<4); return Point4<S>::V(i); }
S & V ( const int i ) { assert(i>=0 && i<4); return Point4<S>::V(i); }
/// constuctor that imports from different Quaternion types
template <class Q>
static inline Quaternion Construct( const Quaternion<Q> & b )
{
return Quaternion(S(b[0]),S(b[1]),S(b[2]),S(b[3]));
}
private:
};
/*template<classS, class M> void QuaternionToMatrix(Quaternion<S> &s, M &m);
template<classS, class M> void MatrixtoQuaternion(M &m, Quaternion<S> &s);*/
template <class S> Quaternion<S> Interpolate( Quaternion<S> a, Quaternion<S> b, double t);
template <class S> Quaternion<S> &Invert(Quaternion<S> &q);
template <class S> Quaternion<S> Inverse(const Quaternion<S> &q);
//Implementation
template <class S>
void Quaternion<S>::SetIdentity(){
FromAxis(0, Point3<S>(1, 0, 0));
}
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.dot(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>::Invert() {
V(1)*=-1;
V(2)*=-1;
V(3)*=-1;
}
template <class S> Quaternion<S> Quaternion<S>::Inverse() const{
return Quaternion<S>( V(0), -V(1), -V(2), -V(3) );
}
template <class S> void Quaternion<S>::FromAxis(const S phi, const Point3<S> &a) {
Point3<S> b = a;
b.Normalize();
S s = math::Sin(phi/(S(2.0)));
V(0) = math::Cos(phi/(S(2.0)));
V(1) = b[0]*s;
V(2) = b[1]*s;
V(3) = b[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.Invert();
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, class M> void QuaternionToMatrix(const Quaternion<S> &q, M &m) {
typedef typename M::ScalarType MScalarType;
MScalarType x2 = q.V(1) + q.V(1);
MScalarType y2 = q.V(2) + q.V(2);
MScalarType z2 = q.V(3) + q.V(3);
{
MScalarType xx2 = q.V(1) * x2;
MScalarType yy2 = q.V(2) * y2;
MScalarType zz2 = q.V(3) * z2;
m[0][0] = 1.0f - yy2 - zz2;
m[1][1] = 1.0f - xx2 - zz2;
m[2][2] = 1.0f - xx2 - yy2;
}
{
MScalarType yz2 = q.V(2) * z2;
MScalarType wx2 = q.V(0) * x2;
m[1][2] = yz2 - wx2;
m[2][1] = yz2 + wx2;
}
{
MScalarType xy2 = q.V(1) * y2;
MScalarType wz2 = q.V(0) * z2;
m[0][1] = xy2 - wz2;
m[1][0] = xy2 + wz2;
}
{
MScalarType xz2 = q.V(1) * z2;
MScalarType wy2 = q.V(0) * y2;
m[2][0] = xz2 - wy2;
m[0][2] = xz2 + wy2;
}
}
template <class S> void Quaternion<S>::ToMatrix(Matrix44<S> &m) const {
QuaternionToMatrix<S, Matrix44<S> >(*this, m);
m[0][3] = (S)0.0;
m[1][3] = (S)0.0;
m[2][3] = (S)0.0;
m[3][0] = (S)0.0;
m[3][1] = (S)0.0;
m[3][2] = (S)0.0;
m[3][3] = (S)1.0;
}
template <class S> void Quaternion<S>::ToMatrix(Matrix33<S> &m) const {
QuaternionToMatrix<S, Matrix33<S> >(*this, m);
}
template<class S, class M> void MatrixToQuaternion(const M &m, Quaternion<S> &q) {
if ( m[0][0] + m[1][1] + m[2][2] > 0.0f ) {
S t = m[0][0] + m[1][1] + m[2][2] + 1.0f;
S s = (S)0.5 / math::Sqrt(t);
q.V(0) = s * t;
q.V(3) = ( m[1][0] - m[0][1] ) * s;
q.V(2) = ( m[0][2] - m[2][0] ) * s;
q.V(1) = ( m[2][1] - m[1][2] ) * s;
} else if ( m[0][0] > m[1][1] && m[0][0] > m[2][2] ) {
S t = m[0][0] - m[1][1] - m[2][2] + 1.0f;
S s = (S)0.5 / math::Sqrt(t);
q.V(1) = s * t;
q.V(2) = ( m[1][0] + m[0][1] ) * s;
q.V(3) = ( m[0][2] + m[2][0] ) * s;
q.V(0) = ( m[2][1] - m[1][2] ) * s;
} else if ( m[1][1] > m[2][2] ) {
S t = - m[0][0] + m[1][1] - m[2][2] + 1.0f;
S s = (S)0.5 / math::Sqrt(t);
q.V(2) = s * t;
q.V(1) = ( m[1][0] + m[0][1] ) * s;
q.V(0) = ( m[0][2] - m[2][0] ) * s;
q.V(3) = ( m[2][1] + m[1][2] ) * s;
} else {
S t = - m[0][0] - m[1][1] + m[2][2] + 1.0f;
S s = (S)0.5 / math::Sqrt(t);
q.V(3) = s * t;
q.V(0) = ( m[1][0] - m[0][1] ) * s;
q.V(1) = ( m[0][2] + m[2][0] ) * s;
q.V(2) = ( m[2][1] + m[1][2] ) * s;
}
}
template <class S> void Quaternion<S>::FromMatrix(const Matrix44<S> &m) {
MatrixToQuaternion<S, Matrix44<S> >(m, *this);
}
template <class S> void Quaternion<S>::FromMatrix(const Matrix33<S> &m) {
MatrixToQuaternion<S, Matrix33<S> >(m, *this);
}
template<class S>
void Quaternion<S>::ToEulerAngles(S &alpha, S &beta, S &gamma) const
{
#define P(a,b,c,d) (2*(V(a)*V(b)+V(c)*V(d)))
#define M(a,b,c,d) (2*(V(a)*V(b)-V(c)*V(d)))
alpha = math::Atan2( P(0,1,2,3) , 1-P(1,1,2,2) );
beta = math::Asin ( M(0,2,3,1) );
gamma = math::Atan2( P(0,3,1,2) , 1-P(2,2,3,3) );
#undef P
#undef M
}
template<class S>
void Quaternion<S>::FromEulerAngles(S alpha, S beta, S gamma)
{
S cosalpha = math::Cos(alpha / 2.0);
S cosbeta = math::Cos(beta / 2.0);
S cosgamma = math::Cos(gamma / 2.0);
S sinalpha = math::Sin(alpha / 2.0);
S sinbeta = math::Sin(beta / 2.0);
S singamma = math::Sin(gamma / 2.0);
V(0) = cosalpha * cosbeta * cosgamma + sinalpha * sinbeta * singamma;
V(1) = sinalpha * cosbeta * cosgamma - cosalpha * sinbeta * singamma;
V(2) = cosalpha * sinbeta * cosgamma + sinalpha * cosbeta * singamma;
V(3) = cosalpha * cosbeta * singamma - sinalpha * sinbeta * cosgamma;
}
template <class S> Quaternion<S> &Invert(Quaternion<S> &m) {
m.Invert();
return m;
}
template <class S> Quaternion<S> Inverse(const Quaternion<S> &m) {
Quaternion<S> a = m;
a.Invert();
return a;
}
template <class S> Quaternion<S> Interpolate( Quaternion<S> a , 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 = math::Acos(v);
if(phi > 0.01) {
a = a * (math::Sin(phi *(1-t))/math::Sin(phi));
b = b * (math::Sin(phi * t)/math::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
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