Quaternion.cxx

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// @(#)root/mathcore:$Id$
// Authors: W. Brown, M. Fischler, L. Moneta    2005

 /**********************************************************************
  *                                                                    *
  * Copyright (c) 2005 , LCG ROOT FNAL MathLib Team                    *
  *                                                                    *
  *                                                                    *
  **********************************************************************/

// Implementation file for rotation in 3 dimensions, represented by quaternion
//
// Created by: Mark Fischler Thurs June 9  2005
//
// Last update: $Id$
//
#include "Math/GenVector/Quaternion.h"

#include <cmath>

#include "Math/GenVector/Cartesian3D.h"
#include "Math/GenVector/DisplacementVector3D.h"
#include "Math/GenVector/Quaternion.h"

#include "Math/GenVector/Rotation3Dfwd.h"
#include "Math/GenVector/AxisAnglefwd.h"
#include "Math/GenVector/EulerAnglesfwd.h"

namespace ROOT {

namespace Math {

// ========== Constructors and Assignment =====================

void Quaternion::Rectify()
{

   // The vector should be a unit vector, and the first element should be
   // non-negative (though negative fU quaternions would work just fine,
   // being isomorphic to a quaternion with positive fU).

   if ( fU < 0 ) {
      fU = - fU; fI = - fI; fJ = - fJ; fK = - fK;
   }

   Scalar a = 1.0 / std::sqrt(fU*fU + fI*fI + fJ*fJ + fK*fK);
   fU *= a;
   fI *= a;
   fJ *= a;
   fK *= a;

} // Rectify()


// ========== Operations =====================

// DisplacementVector3D< Cartesian3D<double> >
// Quaternion::operator() (const DisplacementVector3D< Cartesian3D<double> > & v) const
// {
//    // apply to a 3D Vector
// }

// Quaternion Quaternion::operator * (const Quaternion & q) const {
//    // combination of rotations
//    return Quaternion                          (
//                                                fU*q.fU - fI*q.fI - fJ*q.fJ - fK*q.fK
//                                                , fU*q.fI + fI*q.fU + fJ*q.fK - fK*q.fJ
//                                                , fU*q.fJ - fI*q.fK + fJ*q.fU + fK*q.fI
//                                                , fU*q.fK + fI*q.fJ - fJ*q.fI + fK*q.fU  );
//}

Quaternion Quaternion::operator * (const Rotation3D  & r) const {
   // combination of rotations
   return operator* ( Quaternion(r) );
}

Quaternion Quaternion::operator * (const AxisAngle   & a) const {
   // combination of rotations
   return operator* ( Quaternion(a) );
}

Quaternion Quaternion::operator * (const EulerAngles & e) const {
   // combination of rotations
   return operator* ( Quaternion(e) );
}

Quaternion Quaternion::operator * (const RotationZYX & r) const {
   // combination of rotations
   return operator* ( Quaternion(r) );
}

Quaternion::Scalar Quaternion::Distance(const Quaternion & q) const {
   // distance
   Scalar chordLength = std::fabs(fU*q.fU + fI*q.fI + fJ*q.fJ + fK*q.fK);
   if (chordLength > 1) chordLength = 1; // in case roundoff fouls us up
   return acos(chordLength);
}

// ========== I/O =====================

std::ostream & operator<< (std::ostream & os, const Quaternion & q) {
   // TODO - this will need changing for machine-readable issues
   //        and even the human readable form may need formatiing improvements
   os << "\n{" << q.U() << "   " << q.I()
   << "   " << q.J() << "   " << q.K() << "}\n";
   return os;
}


} //namespace Math
} //namespace ROOT