// @(#)root/mathcore:$Name:  $:$Id: RotationZ.h,v 1.3 2005/10/27 18:00:01 moneta Exp $
// 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: RotationZ.h,v 1.3 2005/10/27 18:00:01 moneta Exp $
//
#ifndef ROOT_Math_GenVector_RotationZ 
#define ROOT_Math_GenVector_RotationZ  1


#include "Math/GenVector/Cartesian3D.h"
#include "Math/GenVector/DisplacementVector3D.h"
#include "Math/GenVector/PositionVector3D.h"
#include "Math/GenVector/LorentzVector.h"
#include "Math/GenVector/3DDistances.h"

#include "Math/GenVector/RotationZfwd.h"

#include <cmath>

namespace ROOT {
namespace Math {


  /**
     Rotation class representing a rotation about the Z axis.
     The Rotation is stored by holding the sine and cosine of the angle.

     @ingroup GenVector
  */

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(std::sin(angle)),
                                         fCos(std::cos(angle)) { }

  // The compiler-generated copy ctor, copy assignment, and dtor are OK.

  /**
     Rectify makes sure the angle is in (-pi,pi]
   */
  void Rectify()  {
    if ( std::fabs(fAngle) >= M_PI ) {
      double x = fAngle / (2.0 * M_PI);
      fAngle =  (2.0 * M_PI) * ( x + std::floor(.5-x) );
      fSin = std::sin(fAngle);
      fCos = std::cos(fAngle);
    }
  }

  // ======== Components ==============

  /**
     Set given the angle.
  */
  void SetAngle (Scalar angle) {
    fSin=std::sin(angle);
    fCos=std::cos(angle);
  }
  void SetComponents (Scalar angle) { SetAngle(angle); }

  /**
     Get the angle
  */
  void GetAngle ( Scalar & angle ) const { angle = atan2 (fSin,fCos); }
  void GetComponents ( Scalar & angle ) const { GetAngle(angle); }

  /**
     Angle of rotation
  */
  Scalar Angle () const { return 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>
  DisplacementVector3D<CoordSystem>
  operator() (const DisplacementVector3D<CoordSystem> & v) const {
    DisplacementVector3D< Cartesian3D<double> > xyz(v);
    DisplacementVector3D< Cartesian3D<double> > Rxyz = operator()(xyz);
    return DisplacementVector3D<CoordSystem> ( Rxyz );
  }

  /**
     Rotation operation on a position vector in any coordinate system
   */
  template <class CoordSystem>
  PositionVector3D<CoordSystem>
  operator() (const PositionVector3D<CoordSystem> & v) const {
    DisplacementVector3D< Cartesian3D<double> > xyz(v);
    DisplacementVector3D< Cartesian3D<double> > Rxyz = operator()(xyz);
    return PositionVector3D<CoordSystem> ( 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 + std::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) {
    if( fAngle != rhs.fAngle )  return false;
    return true;
  }
  bool operator != (const RotationZ & rhs) {
    return ! operator==(rhs);
  }

private:

  Scalar fAngle;
  Scalar fSin;
  Scalar fCos;

};  // 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 

inline
std::ostream & operator<< (std::ostream & os, const RotationZ & r) {
  os << " RotationZ(" << r.Angle() << ") ";
  return os;
} 
  

}  // namespace Math
}  // namespace ROOT

#endif // ROOT_Math_GenVector_RotationZ