/usr/include/sofa/helper/Quater.h is in libsofa1-dev 1.0~beta4-9.
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* SOFA, Simulation Open-Framework Architecture, version 1.0 beta 4 *
* (c) 2006-2009 MGH, INRIA, USTL, UJF, CNRS *
* *
* This library is free software; you can redistribute it and/or modify it *
* under the terms of the GNU Lesser General Public License as published by *
* the Free Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. *
* *
* This library 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 Lesser General Public License *
* for more details. *
* *
* You should have received a copy of the GNU Lesser General Public License *
* along with this library; if not, write to the Free Software Foundation, *
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. *
*******************************************************************************
* SOFA :: Framework *
* *
* Authors: M. Adam, J. Allard, B. Andre, P-J. Bensoussan, S. Cotin, C. Duriez,*
* H. Delingette, F. Falipou, F. Faure, S. Fonteneau, L. Heigeas, C. Mendoza, *
* M. Nesme, P. Neumann, J-P. de la Plata Alcade, F. Poyer and F. Roy *
* *
* Contact information: contact@sofa-framework.org *
******************************************************************************/
#ifndef SOFA_HELPER_QUATER_H
#define SOFA_HELPER_QUATER_H
#include <sofa/defaulttype/Vec.h>
#include <sofa/defaulttype/Mat.h>
#include <math.h>
#include <assert.h>
#include <iostream>
#include <sofa/helper/helper.h>
namespace sofa
{
namespace helper
{
template<class Real>
class SOFA_HELPER_API Quater
{
private:
Real _q[4];
public:
Quater();
virtual ~Quater();
Quater(Real x, Real y, Real z, Real w);
template<class Real2>
Quater(const Real2 q[]) { for (int i=0; i<4; i++) _q[i] = (Real)q[i]; }
template<class Real2>
Quater(const Quater<Real2>& q) { for (int i=0; i<4; i++) _q[i] = (Real)q[i]; }
Quater( const defaulttype::Vec<3,Real>& axis, Real angle );
static Quater identity() {
return Quater(0,0,0,1);
}
/// Cast into a standard C array of elements.
const Real* ptr() const
{
return this->_q;
}
/// Cast into a standard C array of elements.
Real* ptr()
{
return this->_q;
}
/// Normalize a quaternion
void normalize();
void clear()
{
_q[0]=0.0;
_q[1]=0.0;
_q[2]=0.0;
_q[3]=1.0;
}
void fromMatrix(const defaulttype::Matrix3 &m);
template<class Mat33>
void toMatrix(Mat33 &m) const
{
m[0][0] = (typename Mat33::Real) (1.0f - 2.0f * (_q[1] * _q[1] + _q[2] * _q[2]));
m[0][1] = (typename Mat33::Real) (2.0f * (_q[0] * _q[1] - _q[2] * _q[3]));
m[0][2] = (typename Mat33::Real) (2.0f * (_q[2] * _q[0] + _q[1] * _q[3]));
m[1][0] = (typename Mat33::Real) (2.0f * (_q[0] * _q[1] + _q[2] * _q[3]));
m[1][1] = (typename Mat33::Real) (1.0f - 2.0f * (_q[2] * _q[2] + _q[0] * _q[0]));
m[1][2] = (typename Mat33::Real) (2.0f * (_q[1] * _q[2] - _q[0] * _q[3]));
m[2][0] = (typename Mat33::Real) (2.0f * (_q[2] * _q[0] - _q[1] * _q[3]));
m[2][1] = (typename Mat33::Real) (2.0f * (_q[1] * _q[2] + _q[0] * _q[3]));
m[2][2] = (typename Mat33::Real) (1.0f - 2.0f * (_q[1] * _q[1] + _q[0] * _q[0]));
}
/// Apply the rotation to a given vector
template<class Vec>
Vec rotate( const Vec& v ) const
{
return Vec(
(typename Vec::value_type)((1.0f - 2.0f * (_q[1] * _q[1] + _q[2] * _q[2]))*v[0] + (2.0f * (_q[0] * _q[1] - _q[2] * _q[3])) * v[1] + (2.0f * (_q[2] * _q[0] + _q[1] * _q[3])) * v[2]),
(typename Vec::value_type)((2.0f * (_q[0] * _q[1] + _q[2] * _q[3]))*v[0] + (1.0f - 2.0f * (_q[2] * _q[2] + _q[0] * _q[0]))*v[1] + (2.0f * (_q[1] * _q[2] - _q[0] * _q[3]))*v[2]),
(typename Vec::value_type)((2.0f * (_q[2] * _q[0] - _q[1] * _q[3]))*v[0] + (2.0f * (_q[1] * _q[2] + _q[0] * _q[3]))*v[1] + (1.0f - 2.0f * (_q[1] * _q[1] + _q[0] * _q[0]))*v[2])
);
}
/// Apply the inverse rotation to a given vector
template<class Vec>
Vec inverseRotate( const Vec& v ) const
{
return Vec(
(typename Vec::value_type)((1.0f - 2.0f * (_q[1] * _q[1] + _q[2] * _q[2]))*v[0] + (2.0f * (_q[0] * _q[1] + _q[2] * _q[3])) * v[1] + (2.0f * (_q[2] * _q[0] - _q[1] * _q[3])) * v[2]),
(typename Vec::value_type)((2.0f * (_q[0] * _q[1] - _q[2] * _q[3]))*v[0] + (1.0f - 2.0f * (_q[2] * _q[2] + _q[0] * _q[0]))*v[1] + (2.0f * (_q[1] * _q[2] + _q[0] * _q[3]))*v[2]),
(typename Vec::value_type)((2.0f * (_q[2] * _q[0] + _q[1] * _q[3]))*v[0] + (2.0f * (_q[1] * _q[2] - _q[0] * _q[3]))*v[1] + (1.0f - 2.0f * (_q[1] * _q[1] + _q[0] * _q[0]))*v[2])
);
}
/// Given two quaternions, add them together to get a third quaternion.
/// Adding quaternions to get a compound rotation is analagous to adding
/// translations to get a compound translation.
//template <class T>
//friend Quater<T> operator+(Quater<T> q1, Quater<T> q2);
Quater<Real> operator+(const Quater<Real> &q1) const;
Quater<Real> operator*(const Quater<Real> &q1) const;
Quater<Real> operator*(const Real &r) const;
Quater<Real> operator/(const Real &r) const;
void operator*=(const Real &r);
void operator/=(const Real &r);
/// Given two Quaters, multiply them together to get a third quaternion.
//template <class T>
//friend Quater<T> operator*(const Quater<T>& q1, const Quater<T>& q2);
Quater quatVectMult(const defaulttype::Vec<3,Real>& vect);
Quater vectQuatMult(const defaulttype::Vec<3,Real>& vect);
Real& operator[](int index)
{
assert(index >= 0 && index < 4);
return _q[index];
}
const Real& operator[](int index) const
{
assert(index >= 0 && index < 4);
return _q[index];
}
Quater inverse() const;
defaulttype::Vec<3,Real> toEulerVector() const;
// A useful function, builds a rotation matrix in Matrix based on
// given quaternion.
void buildRotationMatrix(Real m[4][4]) const;
void writeOpenGlMatrix( double* m ) const;
void writeOpenGlMatrix( float* m ) const;
//void buildRotationMatrix(MATRIX4x4 m);
//void buildRotationMatrix(Matrix &m);
// This function computes a quaternion based on an axis (defined by
// the given vector) and an angle about which to rotate. The angle is
// expressed in radians.
Quater axisToQuat(defaulttype::Vec<3,Real> a, Real phi);
/// Create using rotation vector (axis*angle) given in parent coordinates
template<class V>
static Quater createFromRotationVector(const V& a)
{
Real phi = (Real)sqrt(a*a);
if( phi < 1.0e-5 )
return Quater(0,0,0,1);
else {
Real nor = 1/phi;
Real s = (Real)sin(phi/2);
return Quater( a[0]*s*nor, a[1]*s*nor,a[2]*s*nor, (Real)cos(phi/2) );
}
}
/// Create a quaternion from Euler
static Quater createQuaterFromEuler( defaulttype::Vec<3,Real> v) {
Real quat[4]; Real a0 = v.elems[0];
Real a1 = v.elems[1];
Real a2 = v.elems[2];
quat[3] = cos(a0/2)*cos(a1/2)*cos(a2/2) + sin(a0/2)*sin(a1/2)*sin(a2/2);
quat[0] = sin(a0/2)*cos(a1/2)*cos(a2/2) - cos(a0/2)*sin(a1/2)*sin(a2/2);
quat[1] = cos(a0/2)*sin(a1/2)*cos(a2/2) + sin(a0/2)*cos(a1/2)*sin(a2/2);
quat[2] = cos(a0/2)*cos(a1/2)*sin(a2/2) - sin(a0/2)*sin(a1/2)*cos(a2/2);
Quater quatResult( quat[0], quat[1], quat[2], quat[3] );
return quatResult;
}
/// Create using the entries of a rotation vector (axis*angle) given in parent coordinates
template<class T>
static Quater createFromRotationVector(T a0, T a1, T a2 )
{
Real phi = (Real)sqrt((Real)(a0*a0+a1*a1+a2*a2));
if( phi < 1.0e-5 )
return Quater(0,0,0,1);
else {
Real nor = 1/phi;
Real s = (Real)sin(phi/2.0);
return Quater( a0*s*nor, a1*s*nor,a2*s*nor, (Real)cos(phi/2.0) );
}
}
/// Create using rotation vector (axis*angle) given in parent coordinates
template<class V>
static Quater set(const V& a){ return createFromRotationVector(a); }
/// Create using using the entries of a rotation vector (axis*angle) given in parent coordinates
template<class T>
static Quater set(T a0, T a1, T a2){ return createFromRotationVector(a0,a1,a2); }
// Print the quaternion
// inline friend std::ostream& operator<<(std::ostream& out, Quater Q)
// {
// return (out << "(" << Q._q[0] << "," << Q._q[1] << "," << Q._q[2] << ","
// << Q._q[3] << ")");
// }
// Print the quaternion (C style)
void print();
void operator+=(const Quater& q2);
void operator*=(const Quater& q2);
bool operator==(const Quater& q) const
{
for (int i=0;i<4;i++)
if ( fabs( _q[i] - q._q[i] ) > EQUALITY_THRESHOLD ) return false;
return true;
}
bool operator!=(const Quater& q) const
{
for (int i=0;i<4;i++)
if ( fabs( _q[i] - q._q[i] ) > EQUALITY_THRESHOLD ) return true;
return false;
}
/// write to an output stream
inline friend std::ostream& operator << ( std::ostream& out, const Quater& v ){
out<<v._q[0]<<" "<<v._q[1]<<" "<<v._q[2]<<" "<<v._q[3];
return out;
}
/// read from an input stream
inline friend std::istream& operator >> ( std::istream& in, Quater& v ){
in>>v._q[0]>>v._q[1]>>v._q[2]>>v._q[3];
return in;
}
static unsigned int size(){return 4;};
};
//typedef Quater<double> Quat; ///< alias
//typedef Quater<float> Quatf; ///< alias
//typedef Quater<double> Quaternion; ///< alias
} // namespace helper
} // namespace sofa
#endif
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