Translation3D.h

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

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

// Header file for class Translation3D
//
// Created by: Lorenzo Moneta  October 21 2005
//
//
#ifndef ROOT_Math_GenVector_Translation3D
#define ROOT_Math_GenVector_Translation3D  1


#include "Math/GenVector/DisplacementVector3D.h"

#include "Math/GenVector/Plane3D.h"

#include "Math/GenVector/PositionVector3Dfwd.h"

#include "Math/GenVector/LorentzVectorfwd.h"

#include <iostream>
#include <type_traits>

namespace ROOT {

namespace Math {

namespace Impl {

//____________________________________________________________________________________________________
/**
    Class describing a 3 dimensional translation. It can be combined (using the operator *)
    with the ROOT::Math::Rotation3D  classes and ROOT::Math::Transform3D to obtained combined
    transformations and to operate on points and vectors.
    Note that a the translation applied to a Vector object (DisplacementVector3D and LorentzVector classes)
    performes a noop, i.e. it returns the same vector. A translation can be applied only to the Point objects
    (PositionVector3D classes).

    @ingroup GenVector

*/

template <typename T = double>
class Translation3D {

public:
   typedef T Scalar;

   typedef DisplacementVector3D<Cartesian3D<T>, DefaultCoordinateSystemTag> Vector;

   /**
       Default constructor ( zero translation )
   */
   Translation3D() {}

   /**
      Construct given a pair of pointers or iterators defining the
      beginning and end of an array of 3 Scalars representing the z,y,z of the translation vector
   */
   template<class IT>
   Translation3D(IT begin, IT end)
   {
      fVect.SetCoordinates(begin,end);
   }

   /**
      Construct from x,y,z values representing the translation
   */
   Translation3D(T dx, T dy, T dz) : fVect(Vector(dx, dy, dz)) {}

   /**
      Construct from any Displacement vector in ant tag and coordinate system
   */
   template<class CoordSystem, class Tag>
   explicit Translation3D( const DisplacementVector3D<CoordSystem,Tag> & v) :
      fVect(Vector(v.X(),v.Y(),v.Z()))
   { }


   /**
      Construct transformation from one coordinate system defined one point (the origin)
       to a new coordinate system defined by other point (origin )
      @param p1  point defining origin of original reference system
      @param p2  point defining origin of transformed reference system

   */
   template <class CoordSystem, class Tag>
   Translation3D(const PositionVector3D<CoordSystem, Tag> &p1, const PositionVector3D<CoordSystem, Tag> &p2)
      : fVect(p2 - p1)
   { }


   // use compiler generated copy ctor, copy assignmet and dtor


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

   /**
       return a const reference to the underline vector representing the translation
   */
   const Vector & Vect() const { return fVect; }

   /**
      Set the 3  components given an iterator to the start of
      the desired data, and another to the end (3 past start).
   */
   template<class IT>
   void SetComponents(IT begin, IT end) {
      fVect.SetCoordinates(begin,end);
   }

   /**
      Get the 3  components into data specified by an iterator begin
      and another to the end of the desired data (12 past start).
   */
   template<class IT>
   void GetComponents(IT begin, IT end) const {
      fVect.GetCoordinates(begin,end);
   }

   /**
      Get the 3 matrix components into data specified by an iterator begin
   */
   template<class IT>
   void GetComponents(IT begin) const {
      fVect.GetCoordinates(begin);
   }


   /**
      Set the components from 3 scalars
   */
   void SetComponents(T dx, T dy, T dz) { fVect.SetCoordinates(dx, dy, dz); }

   /**
      Get the components into 3 scalars
   */
   void GetComponents(T &dx, T &dy, T &dz) const { fVect.GetCoordinates(dx, dy, dz); }

   /**
      Set the XYZ vector components from 3 scalars
   */
   void SetXYZ(T dx, T dy, T dz) { fVect.SetXYZ(dx, dy, dz); }

   // operations on points and vectors


   /**
      Transformation operation for Position Vector in any coordinate system and default tag
   */
   template<class CoordSystem, class Tag >
   PositionVector3D<CoordSystem,Tag> operator() (const PositionVector3D <CoordSystem,Tag> & p) const {
      return PositionVector3D<CoordSystem, Tag>(p.X() + fVect.X(), p.Y() + fVect.Y(), p.Z() + fVect.Z());
   }
   /**
     Transformation operation
   */
   template <class CoordSystem, class Tag>
   PositionVector3D<CoordSystem, Tag> operator*(const PositionVector3D<CoordSystem, Tag> &v) const
   {
      return operator()(v);
   }

   /**
      Transformation operation for Displacement Vector in any coordinate system and default tag
      For the Displacement Vectors no translation apply so return the vector itself
   */
   template<class CoordSystem, class Tag >
   DisplacementVector3D<CoordSystem,Tag> operator() (const DisplacementVector3D <CoordSystem,Tag> & v) const {
      return  v;
   }
   /**
     Transformation operation
   */
   template <class CoordSystem, class Tag>
   DisplacementVector3D<CoordSystem, Tag> operator*(const DisplacementVector3D<CoordSystem, Tag> &v) const
   {
      return operator()(v);
   }

   /**
      Transformation operation for points between different coordinate system tags
   */
   template<class CoordSystem, class Tag1, class Tag2 >
   void Transform (const PositionVector3D <CoordSystem,Tag1> & p1, PositionVector3D <CoordSystem,Tag2> & p2  ) const {
      PositionVector3D <CoordSystem,Tag2> tmp;
      tmp.SetXYZ( p1.X(), p1.Y(), p1.Z() );
      p2 =  operator()(tmp);
    }

   /**
      Transformation operation for Displacement Vector of different coordinate systems
   */
    template <class CoordSystem, class Tag1, class Tag2>
    void Transform(const DisplacementVector3D<CoordSystem, Tag1> &v1, DisplacementVector3D<CoordSystem, Tag2> &v2) const
    {
       // just copy v1 in v2
       v2.SetXYZ(v1.X(), v1.Y(), v1.Z());
   }

   /**
      Transformation operation for a Lorentz Vector in any  coordinate system
      A LorentzVector contains a displacement vector so no translation applies as well
   */
   template <class CoordSystem>
   LorentzVector<CoordSystem> operator()(const LorentzVector<CoordSystem> &q) const
   {
      return q;
   }
   /**
     Transformation operation
   */
   template <class CoordSystem>
   LorentzVector<CoordSystem> operator*(const LorentzVector<CoordSystem> &q) const
   {
      return operator()(q);
   }

   /**
      Transformation on a 3D plane
   */
   Plane3D<T> operator()(const Plane3D<T> &plane) const
   {
      // transformations on a 3D plane
      const Vector n = plane.Normal();
      // take a point on the plane. Use origin projection on the plane
      // ( -ad, -bd, -cd) if (a**2 + b**2 + c**2 ) = 1
      const T                          d = plane.HesseDistance();
      PositionVector3D<Cartesian3D<T>> p(-d * n.X(), -d * n.Y(), -d * n.Z());
      return PLANE(operator()(n), operator()(p));
   }

   /**
      multiply (combine) with another transformation in place
   */
   Translation3D<T> &operator*=(const Translation3D<T> &t)
   {
      fVect+= t.Vect();
      return *this;
   }

   /**
      multiply (combine) two transformations
   */
   Translation3D<T> operator*(const Translation3D<T> &t) const { return Translation3D<T>(fVect + t.Vect()); }

   /**
       Invert the transformation in place
   */
   void Invert() {
      SetComponents( -fVect.X(), -fVect.Y(),-fVect.Z() );
   }

   /**
      Return the inverse of the transformation.
   */
   Translation3D<T> Inverse() const { return Translation3D<T>(-fVect.X(), -fVect.Y(), -fVect.Z()); }

   /**
      Equality/inequality operators
   */
   bool operator==(const Translation3D<T> &rhs) const
   {
      if( fVect != rhs.fVect )  return false;
      return true;
   }

   bool operator!=(const Translation3D<T> &rhs) const { return !operator==(rhs); }

private:

   Vector fVect;   // internal 3D vector representing the translation

};





// global functions

// TODO - I/O should be put in the manipulator form

template <class T>
std::ostream &operator<<(std::ostream &os, const Translation3D<T> &t)
{
   // TODO - this will need changing for machine-readable issues
   //        and even the human readable form needs formatiing improvements

   T m[3];
   t.GetComponents(m, m + 3);
   return os << "\n" << m[0] << "  " << m[1] << "  " << m[2] << "\n";
}

// need a function Transform = Translation * Rotation ???

} // end namespace Impl

// typedefs for double and float versions
typedef Impl::Translation3D<double> Translation3D;
typedef Impl::Translation3D<float>  Translation3DF;

} // end namespace Math

} // end namespace ROOT


#endif /* ROOT_Math_GenVector_Translation3D */