RotationZ.h

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// @(#)root/mathcore:$Id$
// Authors: W. Brown, M. Fischler, L. Moneta    2005
 
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2005 , LCG ROOT FNAL MathLib Team                    *
 *                                                                    *
 *                                                                    *
 **********************************************************************/
 
// Header file for class RotationZ representing a rotation about the Z axis
//
// Created by: Mark Fischler Mon July 18  2005
//
// Last update: $Id$
//
#ifndef ROOT_MathX_GenVectorX_RotationZ
#define ROOT_MathX_GenVectorX_RotationZ 1
 
#include "MathX/GenVectorX/Cartesian3D.h"
#include "MathX/GenVectorX/DisplacementVector3D.h"
#include "MathX/GenVectorX/PositionVector3D.h"
#include "MathX/GenVectorX/LorentzVector.h"
#include "MathX/GenVectorX/3DDistances.h"
 
#include "MathX/GenVectorX/RotationZfwd.h"
 
#include "MathX/GenVectorX/AccHeaders.h"
 
#include "MathX/GenVectorX/MathHeaders.h"
 
namespace ROOT {
namespace ROOT_MATH_ARCH {
 
//__________________________________________________________________________________________
/**
   Rotation class representing a 3D rotation about the Z axis by the angle of rotation.
   For efficiency reason, in addition to the angle, the sine and cosine of the angle are held
 
   @ingroup GenVectorX
 
   @see GenVectorX
*/
 
class RotationZ {
 
public:
   typedef double Scalar;
 
   // ========== Constructors and Assignment =====================
 
   /**
      Default constructor (identity rotation)
   */
   RotationZ() : fAngle(0), fSin(0), fCos(1) {}
 
   /**
      Construct from an angle
   */
   explicit RotationZ(Scalar angle) : fAngle(angle), fSin(math_sin(angle)), fCos(math_cos(angle)) { Rectify(); }
 
   // The compiler-generated copy ctor, copy assignment, and destructor are OK.
 
   /**
      Rectify makes sure the angle is in (-pi,pi]
   */
   void Rectify()
   {
      if (math_fabs(fAngle) >= M_PI) {
         double x = fAngle / (2.0 * M_PI);
         fAngle = (2.0 * M_PI) * (x + math_floor(.5 - x));
         fSin = math_sin(fAngle);
         fCos = math_cos(fAngle);
      }
   }
 
   // ======== Components ==============
 
   /**
      Set given the angle.
   */
   void SetAngle(Scalar angle)
   {
      fSin = math_sin(angle);
      fCos = math_cos(angle);
      fAngle = angle;
      Rectify();
   }
   void SetComponents(Scalar angle) { SetAngle(angle); }
 
   /**
      Get the angle
   */
   void GetAngle(Scalar &angle) const { angle = math_atan2(fSin, fCos); }
   void GetComponents(Scalar &angle) const { GetAngle(angle); }
 
   /**
      Angle of rotation
   */
   Scalar Angle() const { return math_atan2(fSin, fCos); }
 
   /**
      Sine or Cosine of the rotation angle
   */
   Scalar SinAngle() const { return fSin; }
   Scalar CosAngle() const { return fCos; }
 
   // =========== operations ==============
 
   //   /**
   //      Rotation operation on a cartesian vector
   //    */
   //   typedef  DisplacementVector3D< Cartesian3D<double> > XYZVector;
   //   XYZVector operator() (const XYZVector & v) const {
   //     return XYZVector
   //       ( fCos*v.x()-fSin*v.y(), fCos*v.y()+fSin*v.x(), v.z() );
   //   }
 
   /**
      Rotation operation on a displacement vector in any coordinate system
   */
   template <class CoordSystem, class U>
   DisplacementVector3D<CoordSystem, U> operator()(const DisplacementVector3D<CoordSystem, U> &v) const
   {
      DisplacementVector3D<Cartesian3D<double>, U> xyz;
      xyz.SetXYZ(fCos * v.x() - fSin * v.y(), fCos * v.y() + fSin * v.x(), v.z());
      return DisplacementVector3D<CoordSystem, U>(xyz);
   }
 
   /**
      Rotation operation on a position vector in any coordinate system
   */
   template <class CoordSystem, class U>
   PositionVector3D<CoordSystem, U> operator()(const PositionVector3D<CoordSystem, U> &v) const
   {
      DisplacementVector3D<Cartesian3D<double>, U> xyz(v);
      DisplacementVector3D<Cartesian3D<double>, U> rxyz = operator()(xyz);
      return PositionVector3D<CoordSystem, U>(rxyz);
   }
 
   /**
      Rotation operation on a Lorentz vector in any 4D coordinate system
   */
   template <class CoordSystem>
   LorentzVector<CoordSystem> operator()(const LorentzVector<CoordSystem> &v) const
   {
      DisplacementVector3D<Cartesian3D<double>> xyz(v.Vect());
      xyz = operator()(xyz);
      LorentzVector<PxPyPzE4D<double>> xyzt(xyz.X(), xyz.Y(), xyz.Z(), v.E());
      return LorentzVector<CoordSystem>(xyzt);
   }
 
   /**
      Rotation operation on an arbitrary vector v.
      Preconditions:  v must implement methods x(), y(), and z()
      and the arbitrary vector type must have a constructor taking (x,y,z)
   */
   template <class ForeignVector>
   ForeignVector operator()(const ForeignVector &v) const
   {
      DisplacementVector3D<Cartesian3D<double>> xyz(v);
      DisplacementVector3D<Cartesian3D<double>> rxyz = operator()(xyz);
      return ForeignVector(rxyz.X(), rxyz.Y(), rxyz.Z());
   }
 
   /**
      Overload operator * for rotation on a vector
   */
   template <class AVector>
   inline AVector operator*(const AVector &v) const
   {
      return operator()(v);
   }
 
   /**
      Invert a rotation in place
   */
   void Invert()
   {
      fAngle = -fAngle;
      fSin = -fSin;
   }
 
   /**
      Return inverse of  a rotation
   */
   RotationZ Inverse() const
   {
      RotationZ t(*this);
      t.Invert();
      return t;
   }
 
   // ========= Multi-Rotation Operations ===============
 
   /**
      Multiply (combine) two rotations
   */
   RotationZ operator*(const RotationZ &r) const
   {
      RotationZ ans;
      double x = (fAngle + r.fAngle) / (2.0 * M_PI);
      ans.fAngle = (2.0 * M_PI) * (x + math_floor(.5 - x));
      ans.fSin = fSin * r.fCos + fCos * r.fSin;
      ans.fCos = fCos * r.fCos - fSin * r.fSin;
      return ans;
   }
 
   /**
      Post-Multiply (on right) by another rotation :  T = T*R
   */
   RotationZ &operator*=(const RotationZ &r) { return *this = (*this) * r; }
 
   /**
      Equality/inequality operators
   */
   bool operator==(const RotationZ &rhs) const
   {
      if (fAngle != rhs.fAngle)
         return false;
      return true;
   }
   bool operator!=(const RotationZ &rhs) const { return !operator==(rhs); }
 
private:
   Scalar fAngle; // rotation angle
   Scalar fSin;   // sine of the rotation angle
   Scalar fCos;   // cosine of the rotation angle
 
}; // RotationZ
 
// ============ Class RotationZ ends here ============
 
/**
   Distance between two rotations
 */
template <class R>
inline typename RotationZ::Scalar Distance(const RotationZ &r1, const R &r2)
{
   return gv_detail::dist(r1, r2);
}
 
/**
   Stream Output and Input
 */
// TODO - I/O should be put in the manipulator form
 
#if !defined(ROOT_MATH_SYCL) && !defined(ROOT_MATH_CUDA)
 
inline std::ostream &operator<<(std::ostream &os, const RotationZ &r)
{
   os << " RotationZ(" << r.Angle() << ") ";
   return os;
}
 
#endif
 
} // namespace ROOT_MATH_ARCH
} // namespace ROOT
 
#endif // ROOT_MathX_GenVectorX_RotationZ