TRotation.h

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// @(#)root/physics:$Id$
// Author: Peter Malzacher   19/06/99

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/
#ifndef ROOT_TRotation
#define ROOT_TRotation

#include "TObject.h"

#include "TVector3.h"

class TQuaternion;

class TRotation : public TObject {

public:

class TRotationRow {
public:
   inline TRotationRow(const TRotation &, int);
   inline TRotationRow(const TRotationRow &);
   inline TRotationRow & operator=(const TRotationRow &);
   inline Double_t operator [] (int) const;
private:
   const TRotation * fRR;
   //    const TRotation & fRR;
   int fII;
};
   // Helper class for implemention of C-style subscripting r[i][j]

   TRotation();
   // Default constructor. Gives a unit matrix.

   TRotation(const TRotation &);
   TRotation(const TQuaternion &);
   // Copy constructor.

   virtual ~TRotation() {;};

   inline Double_t XX() const;
   inline Double_t XY() const;
   inline Double_t XZ() const;
   inline Double_t YX() const;
   inline Double_t YY() const;
   inline Double_t YZ() const;
   inline Double_t ZX() const;
   inline Double_t ZY() const;
   inline Double_t ZZ() const;
   // Elements of the rotation matrix (Geant4).

   inline TRotationRow operator [] (int) const;
   // Returns object of the helper class for C-style subscripting r[i][j]

   Double_t operator () (int, int) const;
   // Fortran-style subscripting: returns (i,j) element of the rotation matrix.

   inline TRotation & operator = (const TRotation &);
   // Assignment.

   inline Bool_t operator == (const TRotation &) const;
   inline Bool_t operator != (const TRotation &) const;
   // Comparisons (Geant4).

   inline Bool_t IsIdentity() const;
   // Returns true if the identity matrix (Geant4).

   inline TVector3 operator * (const TVector3 &) const;
   // Multiplication with a TVector3.

   TRotation operator * (const TRotation &) const;
   inline TRotation & operator *= (const TRotation &);
   inline TRotation & Transform(const TRotation &);
   // Matrix multiplication.
   // Note a *= b; <=> a = a * b; while a.transform(b); <=> a = b * a;

   inline TRotation Inverse() const;
   // Returns the inverse.

   inline TRotation & Invert();
   // Inverts the Rotation matrix.

   TRotation & RotateX(Double_t);
   // Rotation around the x-axis.

   TRotation & RotateY(Double_t);
   // Rotation around the y-axis.

   TRotation & RotateZ(Double_t);
   // Rotation around the z-axis.

   TRotation & Rotate(Double_t, const TVector3 &);
   inline TRotation & Rotate(Double_t, const TVector3 *);
   // Rotation around a specified vector.

   TRotation & RotateAxes(const TVector3 & newX,
                          const TVector3 & newY,
                          const TVector3 & newZ);
   // Rotation of local axes (Geant4).

   Double_t PhiX() const;
   Double_t PhiY() const;
   Double_t PhiZ() const;
   Double_t ThetaX() const;
   Double_t ThetaY() const;
   Double_t ThetaZ() const;
   // Return angles (RADS) made by rotated axes against original axes (Geant4).

   void AngleAxis(Double_t &, TVector3 &) const;
   // Returns the rotation angle and rotation axis (Geant4).

   inline TRotation & SetToIdentity();
   // Set equal to the identity rotation.

   TRotation & SetXEulerAngles(Double_t phi, Double_t theta, Double_t psi);
   void SetXPhi(Double_t);
   void SetXTheta(Double_t);
   void SetXPsi(Double_t);
   // Set the euler angles of the rotation.  The angles are defined using the
   // y-convention which rotates around the Z axis, around the new X axis, and
   // then around the new Z axis.  The x-convention is used Goldstein, Landau
   // and Lifshitz, and other common physics texts.  Contrast this with
   // SetYEulerAngles.

   TRotation & RotateXEulerAngles(Double_t phi, Double_t theta, Double_t psi);
   // Adds a rotation of the local axes defined by the Euler angle to the
   // current rotation.  See SetXEulerAngles for a note about conventions.

   Double_t GetXPhi(void) const;
   Double_t GetXTheta(void) const;
   Double_t GetXPsi(void) const;
   // Return the euler angles of the rotation.  See SetYEulerAngles for a
   // note about conventions.

   TRotation & SetYEulerAngles(Double_t phi, Double_t theta, Double_t psi);
   void SetYPhi(Double_t);
   void SetYTheta(Double_t);
   void SetYPsi(Double_t);
   // Set the euler angles of the rotation.  The angles are defined using the
   // y-convention which rotates around the Z axis, around the new Y axis, and
   // then around the new Z axis.  The x-convention is used Goldstein, Landau
   // and Lifshitz, and other common physics texts and is a rotation around the
   // Z axis, around the new X axis, and then around the new Z axis.

   TRotation & RotateYEulerAngles(Double_t phi, Double_t theta, Double_t psi);
   // Adds a rotation of the local axes defined by the Euler angle to the
   // current rotation.  See SetYEulerAngles for a note about conventions.

   Double_t GetYPhi(void) const;
   Double_t GetYTheta(void) const;
   Double_t GetYPsi(void) const;
   // Return the euler angles of the rotation.  See SetYEulerAngles for a
   // note about conventions.

   TRotation & SetXAxis(const TVector3& axis);
   TRotation & SetXAxis(const TVector3& axis, const TVector3& xyPlane);
   TRotation & SetYAxis(const TVector3& axis);
   TRotation & SetYAxis(const TVector3& axis, const TVector3& yzPlane);
   TRotation & SetZAxis(const TVector3& axis);
   TRotation & SetZAxis(const TVector3& axis, const TVector3& zxPlane);
   // Create a rotation with the axis vector parallel to the rotated coordinate
   // system.  If a second vector is provided it defines a plane passing
   // through the axis.

   void MakeBasis(TVector3& xAxis, TVector3& yAxis, TVector3& zAxis) const;
   // Take two input vectors (in xAxis, and zAxis) and turn them into an
   // orthogonal basis.  This is an internal helper function used to implement
   // the Set?Axis functions, but is exposed because the functionality is
   // often useful.

protected:

   TRotation(Double_t, Double_t, Double_t, Double_t, Double_t,
             Double_t, Double_t, Double_t, Double_t);
   // Protected constructor.

   Double_t fxx, fxy, fxz, fyx, fyy, fyz, fzx, fzy, fzz;
   // The matrix elements.

   ClassDef(TRotation,1) // Rotations of TVector3 objects

};


inline Double_t TRotation::XX() const { return fxx; }
inline Double_t TRotation::XY() const { return fxy; }
inline Double_t TRotation::XZ() const { return fxz; }
inline Double_t TRotation::YX() const { return fyx; }
inline Double_t TRotation::YY() const { return fyy; }
inline Double_t TRotation::YZ() const { return fyz; }
inline Double_t TRotation::ZX() const { return fzx; }
inline Double_t TRotation::ZY() const { return fzy; }
inline Double_t TRotation::ZZ() const { return fzz; }

inline TRotation::TRotationRow::TRotationRow
(const TRotation & r, int i) : fRR(&r), fII(i) {}

inline TRotation::TRotationRow::TRotationRow
(const TRotationRow & rr) : fRR(rr.fRR), fII(rr.fII) {}

inline TRotation::TRotationRow & TRotation::TRotationRow::operator = (const TRotation::TRotationRow & rr) {
   fRR = rr.fRR;
   fII = rr.fII;
   return *this;
}

inline Double_t TRotation::TRotationRow::operator [] (int jj) const {
   return fRR->operator()(fII,jj);
}

inline TRotation::TRotationRow TRotation::operator [] (int i) const {
   return TRotationRow(*this, i);
}

inline TRotation & TRotation::operator = (const TRotation & m) {
   fxx = m.fxx;
   fxy = m.fxy;
   fxz = m.fxz;
   fyx = m.fyx;
   fyy = m.fyy;
   fyz = m.fyz;
   fzx = m.fzx;
   fzy = m.fzy;
   fzz = m.fzz;
   return *this;
}

inline Bool_t TRotation::operator == (const TRotation& m) const {
   return (fxx == m.fxx && fxy == m.fxy && fxz == m.fxz &&
           fyx == m.fyx && fyy == m.fyy && fyz == m.fyz &&
           fzx == m.fzx && fzy == m.fzy && fzz == m.fzz) ? kTRUE : kFALSE;
}

inline Bool_t TRotation::operator != (const TRotation &m) const {
   return (fxx != m.fxx || fxy != m.fxy || fxz != m.fxz ||
           fyx != m.fyx || fyy != m.fyy || fyz != m.fyz ||
           fzx != m.fzx || fzy != m.fzy || fzz != m.fzz) ? kTRUE : kFALSE;
}

inline Bool_t TRotation::IsIdentity() const {
   return  (fxx == 1.0 && fxy == 0.0 && fxz == 0.0 &&
            fyx == 0.0 && fyy == 1.0 && fyz == 0.0 &&
            fzx == 0.0 && fzy == 0.0 && fzz == 1.0) ? kTRUE : kFALSE;
}

inline TRotation & TRotation::SetToIdentity() {
   fxx = fyy = fzz = 1.0;
   fxy = fxz = fyx = fyz = fzx = fzy = 0.0;
   return *this;
}

inline TVector3 TRotation::operator * (const TVector3 & p) const {
   return TVector3(fxx*p.X() + fxy*p.Y() + fxz*p.Z(),
                   fyx*p.X() + fyy*p.Y() + fyz*p.Z(),
                   fzx*p.X() + fzy*p.Y() + fzz*p.Z());
}

inline TRotation & TRotation::operator *= (const TRotation & m) {
   return *this = operator * (m);
}

inline TRotation & TRotation::Transform(const TRotation & m) {
   return *this = m.operator * (*this);
}

inline TRotation TRotation::Inverse() const {
   return TRotation(fxx, fyx, fzx, fxy, fyy, fzy, fxz, fyz, fzz);
}

inline TRotation & TRotation::Invert() {
   return *this=Inverse();
}

inline TRotation & TRotation::Rotate(Double_t psi, const TVector3 * p) {
   return Rotate(psi, *p);
}



#endif