extTkRotation.h

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#ifndef Geom_newTkRotation_H
#define Geom_newTkRotation_H

#include "DataFormats/GeometryVector/interface/Basic2DVector.h"
#include "DataFormats/GeometryVector/interface/Basic3DVector.h"
#include "DataFormats/GeometryVector/interface/GlobalVector.h"

#include "DataFormats/Math/interface/ExtVec.h"

#include <iosfwd>

template <class T>
class TkRotation;
template <class T>
class TkRotation2D;

template <class T>
std::ostream& operator<<(std::ostream& s, const TkRotation<T>& r);
template <class T>
std::ostream& operator<<(std::ostream& s, const TkRotation2D<T>& r);

namespace geometryDetails {
  void TkRotationErr1();
  void TkRotationErr2();

}  // namespace geometryDetails

template <class T>
class TkRotation {
public:
  typedef Vector3DBase<T, GlobalTag> GlobalVector;
  typedef Basic3DVector<T> BasicVector;

  TkRotation() {}
  TkRotation(Rot3<T> const& irot) : rot(irot) {}

  TkRotation(T xx, T xy, T xz, T yx, T yy, T yz, T zx, T zy, T zz) : rot(xx, xy, xz, yx, yy, yz, zx, zy, zz) {}

  TkRotation(const T* p) : rot(p[0], p[1], p[2], p[3], p[4], p[5], p[6], p[7], p[8]) {}

  TkRotation(const GlobalVector& aX, const GlobalVector& aY) {
    GlobalVector uX = aX.unit();
    GlobalVector uY = aY.unit();
    GlobalVector uZ(uX.cross(uY));

    rot.axis[0] = uX.basicVector().v;
    rot.axis[1] = uY.basicVector().v;
    rot.axis[2] = uZ.basicVector().v;
  }

  TkRotation(const BasicVector& aX, const BasicVector& aY) {
    BasicVector uX = aX.unit();
    BasicVector uY = aY.unit();
    BasicVector uZ(uX.cross(uY));

    rot.axis[0] = uX.v;
    rot.axis[1] = uY.v;
    rot.axis[2] = uZ.v;
  }

  TkRotation(const GlobalVector& uX, const GlobalVector& uY, const GlobalVector& uZ) {
    rot.axis[0] = uX.basicVector().v;
    rot.axis[1] = uY.basicVector().v;
    rot.axis[2] = uZ.basicVector().v;
  }

  TkRotation(const BasicVector& uX, const BasicVector& uY, const BasicVector& uZ) {
    rot.axis[0] = uX.v;
    rot.axis[1] = uY.v;
    rot.axis[2] = uZ.v;
  }

  TkRotation(const Basic3DVector<T>& axis, T phi) : rot(cos(phi), sin(phi), 0, -sin(phi), cos(phi), 0, 0, 0, 1) {
    //rotation around the z-axis by  phi
    TkRotation tmpRotz(cos(axis.phi()), sin(axis.phi()), 0., -sin(axis.phi()), cos(axis.phi()), 0., 0., 0., 1.);
    //rotation around y-axis by theta
    TkRotation tmpRoty(cos(axis.theta()), 0., -sin(axis.theta()), 0., 1., 0., sin(axis.theta()), 0., cos(axis.theta()));
    (*this) *= tmpRoty;
    (*this) *= tmpRotz;  // =  this * tmpRoty * tmpRotz

    // (tmpRoty * tmpRotz)^-1 * this * tmpRoty * tmpRotz

    *this = (tmpRoty * tmpRotz).multiplyInverse(*this);
  }
  /* this is the same thing...derived from the CLHEP ... it gives the
     same results MODULO the sign of the rotation....  but I don't want
     that... had 
     TkRotation (const Basic3DVector<T>& axis, float phi) {
     T cx = axis.x();
     T cy = axis.y();
     T cz = axis.z();
     
     T ll = axis.mag();
     if (ll == 0) {
     geometryDetails::TkRotationErr1();
     }else{
     
     float cosa = cos(phi), sina = sin(phi);
     cx /= ll; cy /= ll; cz /= ll;   
     
     R11 = cosa + (1-cosa)*cx*cx;
     R12 =        (1-cosa)*cx*cy - sina*cz;
     R13 =        (1-cosa)*cx*cz + sina*cy;
     
     R21 =        (1-cosa)*cy*cx + sina*cz;
     R22 = cosa + (1-cosa)*cy*cy; 
     R23 =        (1-cosa)*cy*cz - sina*cx;
     
     R31 =        (1-cosa)*cz*cx - sina*cy;
     R32 =        (1-cosa)*cz*cy + sina*cx;
     R33 = cosa + (1-cosa)*cz*cz;
     
     }
     
     }
  */

  template <typename U>
  TkRotation(const TkRotation<U>& a) : rot(a.xx(), a.xy(), a.xz(), a.yx(), a.yy(), a.yz(), a.zx(), a.zy(), a.zz()) {}

  TkRotation transposed() const { return rot.transpose(); }

  Basic3DVector<T> rotate(const Basic3DVector<T>& v) const { return rot.rotate(v.v); }

  Basic3DVector<T> rotateBack(const Basic3DVector<T>& v) const { return rot.rotateBack(v.v); }

  Basic3DVector<T> operator*(const Basic3DVector<T>& v) const { return rot.rotate(v.v); }

  Basic3DVector<T> multiplyInverse(const Basic3DVector<T>& v) const { return rot.rotateBack(v.v); }

  template <class Scalar>
  Basic3DVector<Scalar> multiplyInverse(const Basic3DVector<Scalar>& v) const {
    return Basic3DVector<Scalar>(xx() * v.x() + yx() * v.y() + zx() * v.z(),
                                 xy() * v.x() + yy() * v.y() + zy() * v.z(),
                                 xz() * v.x() + yz() * v.y() + zz() * v.z());
  }

  Basic3DVector<T> operator*(const Basic2DVector<T>& v) const {
    return Basic3DVector<T>(xx() * v.x() + xy() * v.y(), yx() * v.x() + yy() * v.y(), zx() * v.x() + zy() * v.y());
  }
  Basic3DVector<T> multiplyInverse(const Basic2DVector<T>& v) const {
    return Basic3DVector<T>(xx() * v.x() + yx() * v.y(), xy() * v.x() + yy() * v.y(), xz() * v.x() + yz() * v.y());
  }

  TkRotation operator*(const TkRotation& b) const { return rot * b.rot; }
  TkRotation multiplyInverse(const TkRotation& b) const { return rot.transpose() * b.rot; }

  TkRotation& operator*=(const TkRotation& b) { return *this = operator*(b); }

  // Note a *= b; <=> a = a * b; while a.transform(b); <=> a = b * a;
  TkRotation& transform(const TkRotation& b) { return *this = b.operator*(*this); }

  TkRotation& rotateAxes(const Basic3DVector<T>& newX, const Basic3DVector<T>& newY, const Basic3DVector<T>& newZ) {
    T del = 0.001;

    if (

        // the check for right-handedness is not needed since
        // we want to change the handedness when it's left in cmsim
        //
        //       fabs(newZ.x()-w.x()) > del ||
        //       fabs(newZ.y()-w.y()) > del ||
        //       fabs(newZ.z()-w.z()) > del ||
        fabs(newX.mag2() - 1.) > del || fabs(newY.mag2() - 1.) > del || fabs(newZ.mag2() - 1.) > del ||
        fabs(newX.dot(newY)) > del || fabs(newY.dot(newZ)) > del || fabs(newZ.dot(newX)) > del) {
      geometryDetails::TkRotationErr2();
      return *this;
    } else {
      return transform(
          TkRotation(newX.x(), newY.x(), newZ.x(), newX.y(), newY.y(), newZ.y(), newX.z(), newY.z(), newZ.z()));
    }
  }

  Basic3DVector<T> x() const { return rot.axis[0]; }
  Basic3DVector<T> y() const { return rot.axis[1]; }
  Basic3DVector<T> z() const { return rot.axis[2]; }

  T xx() const { return rot.axis[0][0]; }
  T xy() const { return rot.axis[0][1]; }
  T xz() const { return rot.axis[0][2]; }
  T yx() const { return rot.axis[1][0]; }
  T yy() const { return rot.axis[1][1]; }
  T yz() const { return rot.axis[1][2]; }
  T zx() const { return rot.axis[2][0]; }
  T zy() const { return rot.axis[2][1]; }
  T zz() const { return rot.axis[2][2]; }

private:
  Rot3<T> rot;
};

template <>
std::ostream& operator<<<float>(std::ostream& s, const TkRotation<float>& r);

template <>
std::ostream& operator<<<double>(std::ostream& s, const TkRotation<double>& r);

template <class T, class U>
inline Basic3DVector<U> operator*(const TkRotation<T>& r, const Basic3DVector<U>& v) {
  return Basic3DVector<U>(r.xx() * v.x() + r.xy() * v.y() + r.xz() * v.z(),
                          r.yx() * v.x() + r.yy() * v.y() + r.yz() * v.z(),
                          r.zx() * v.x() + r.zy() * v.y() + r.zz() * v.z());
}

template <class T, class U>
inline TkRotation<typename PreciseFloatType<T, U>::Type> operator*(const TkRotation<T>& a, const TkRotation<U>& b) {
  typedef TkRotation<typename PreciseFloatType<T, U>::Type> RT;
  return RT(a.xx() * b.xx() + a.xy() * b.yx() + a.xz() * b.zx(),
            a.xx() * b.xy() + a.xy() * b.yy() + a.xz() * b.zy(),
            a.xx() * b.xz() + a.xy() * b.yz() + a.xz() * b.zz(),
            a.yx() * b.xx() + a.yy() * b.yx() + a.yz() * b.zx(),
            a.yx() * b.xy() + a.yy() * b.yy() + a.yz() * b.zy(),
            a.yx() * b.xz() + a.yy() * b.yz() + a.yz() * b.zz(),
            a.zx() * b.xx() + a.zy() * b.yx() + a.zz() * b.zx(),
            a.zx() * b.xy() + a.zy() * b.yy() + a.zz() * b.zy(),
            a.zx() * b.xz() + a.zy() * b.yz() + a.zz() * b.zz());
}

template <class T>
class TkRotation2D {
public:
  typedef Basic2DVector<T> BasicVector;

  TkRotation2D() {}
  TkRotation2D(Rot2<T> const& irot) : rot(irot) {}

  TkRotation2D(T xx, T xy, T yx, T yy) : rot(xx, xy, yx, yy) {}

  TkRotation2D(const T* p) : rot(p[0], p[1], p[2], p[3]) {}

  TkRotation2D(const BasicVector& aX) {
    BasicVector uX = aX.unit();
    BasicVector uY(-uX.y(), uX.x());

    rot.axis[0] = uX.v;
    rot.axis[1] = uY.v;
  }

  TkRotation2D(const BasicVector& uX, const BasicVector& uY) {
    rot.axis[0] = uX.v;
    rot.axis[1] = uY.v;
  }

  BasicVector x() const { return rot.axis[0]; }
  BasicVector y() const { return rot.axis[1]; }

  TkRotation2D transposed() const { return rot.transpose(); }

  BasicVector rotate(const BasicVector& v) const { return rot.rotate(v.v); }

  BasicVector rotateBack(const BasicVector& v) const { return rot.rotateBack(v.v); }

private:
  Rot2<T> rot;
};

template <>
std::ostream& operator<<<float>(std::ostream& s, const TkRotation2D<float>& r);

template <>
std::ostream& operator<<<double>(std::ostream& s, const TkRotation2D<double>& r);

#endif