Quaternion.h

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#ifndef SimTK_SimTKCOMMON_QUATERNION_H 
#define SimTK_SimTKCOMMON_QUATERNION_H 
 
/* -------------------------------------------------------------------------- *
 *                       Simbody(tm): SimTKcommon                             *
 * -------------------------------------------------------------------------- *
 * This is part of the SimTK biosimulation toolkit originating from           *
 * Simbios, the NIH National Center for Physics-Based Simulation of           *
 * Biological Structures at Stanford, funded under the NIH Roadmap for        *
 * Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody.  *
 *                                                                            *
 * Portions copyright (c) 2005-12 Stanford University and the Authors.        *
 * Authors: Michael Sherman, Paul Mitiguy                                     *
 * Contributors:                                                              *
 *                                                                            *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may    *
 * not use this file except in compliance with the License. You may obtain a  *
 * copy of the License at http://www.apache.org/licenses/LICENSE-2.0.         *
 *                                                                            *
 * Unless required by applicable law or agreed to in writing, software        *
 * distributed under the License is distributed on an "AS IS" BASIS,          *
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   *
 * See the License for the specific language governing permissions and        *
 * limitations under the License.                                             *
 * -------------------------------------------------------------------------- */
 
//-----------------------------------------------------------------------------
#include "SimTKcommon/SmallMatrix.h"
#include "SimTKcommon/internal/UnitVec.h"
//-----------------------------------------------------------------------------
#include <iosfwd>  // Forward declaration of iostream
//-----------------------------------------------------------------------------
 
 
//-----------------------------------------------------------------------------
namespace SimTK {
 
//-----------------------------------------------------------------------------
// Forward declarations
template <class P> class Rotation_;
template <class P> class Quaternion_;
 
typedef Quaternion_<Real>    Quaternion;
typedef Quaternion_<float>  fQuaternion;
typedef Quaternion_<double> dQuaternion;
 
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
template <class P>
class Quaternion_ : public Vec<4,P> {
    typedef P           RealP;
    typedef Vec<3,P>    Vec3P;
    typedef Vec<4,P>    Vec4P;
public:
    Quaternion_() :  Vec4P(1,0,0,0) { }
 
    Quaternion_(const Quaternion_& q) :  Vec4P(q) {}
 
    Quaternion_& operator=( const Quaternion_& q ) 
    {   Vec4P::operator=(q.asVec4()); return *this; }
    
    Quaternion_( RealP e0, RealP e1, RealP e2, RealP e3 ) : Vec4P(e0,e1,e2,e3) 
    {   normalizeThis(); }
    explicit Quaternion_( const Vec4P& q ) : Vec4P(q) 
    {   normalizeThis(); }
 
    SimTK_SimTKCOMMON_EXPORT explicit Quaternion_(const Rotation_<P>&);
 
    void setQuaternionToZeroRotation()  {Vec4P::operator=( Vec4P(1,0,0,0) );}
    void setQuaternionToNaN()           {Vec4P::setToNaN();}
 
    SimTK_SimTKCOMMON_EXPORT void  setQuaternionFromAngleAxis(const Vec4P& av);
    SimTK_SimTKCOMMON_EXPORT void  setQuaternionFromAngleAxis(const RealP& a, const UnitVec<P,1>& v);
 
    SimTK_SimTKCOMMON_EXPORT Vec4P convertQuaternionToAngleAxis() const;
 
    const Vec4P& asVec4() const  {return *static_cast<const Vec4P*>(this);}
 
    Quaternion_& normalizeThis() { 
        const RealP epsilon = std::numeric_limits<RealP>::epsilon();
        const RealP magnitude = Vec4P::norm();
        if(      magnitude == 0      )  setQuaternionToZeroRotation();
        else if( magnitude < epsilon )  setQuaternionToNaN();
        else (*this) *= (1/magnitude);
        return *this;
    }
 
    friend Quaternion_<P> operator*(const Quaternion_<P>& lhs,
                                    const Quaternion_<P>& rhs) {
        return lhs.multiply(rhs);
    }
 
    Quaternion_<P> multiply(const Quaternion_& q2) const {
        const Quaternion_& q1 = *this;
        const double w1 = q1[0], x1 = q1[1], y1 = q1[2], z1 = q1[3];
        const double w2 = q2[0], x2 = q2[1], y2 = q2[2], z2 = q2[3];
 
        // Compute the Hamilton product 
        const double w = w1 * w2 - x1 * x2 - y1 * y2 - z1 * z2;
        const double x = w1 * x2 + x1 * w2 + y1 * z2 - z1 * y2;
        const double y = w1 * y2 - x1 * z2 + y1 * w2 + z1 * x2;
        const double z = w1 * z2 + x1 * y2 - y1 * x2 + z1 * w2;
 
        return Quaternion_<P>(w, x, y, z);
    }
 
    Quaternion_ normalize() const {return Quaternion_(*this).normalizeThis();}
 
    Quaternion_(const Vec4P& v, bool) : Vec4P(v) {}
 
//----------------------------------------------------------------------------------------------------
// The following code is obsolete - it is here temporarily for backward compatibility (Mitiguy 10/13/2007)
//----------------------------------------------------------------------------------------------------
private:
    Vec4P convertToAngleAxis() const                          { return convertQuaternionToAngleAxis();}
    void setToAngleAxis(const Vec4P& av)                      { setQuaternionFromAngleAxis(av);}
    void setToAngleAxis(const RealP& a, const UnitVec<P,1>& v){ setQuaternionFromAngleAxis(a,v);}
    void setToNaN()                                           { setQuaternionToNaN(); }
    void setToZero()                                          { setQuaternionToZeroRotation();}
 
};
 
 
//------------------------------------------------------------------------------
}  // End of namespace SimTK
 
//--------------------------------------------------------------------------
#endif // SimTK_SimTKCOMMON_QUATERNION_H_
//--------------------------------------------------------------------------