FrameToFrameDerivative Class Reference

#include <FrameToFrameDerivative.h>

Public Member Functions
AlgebraicMatrix	frameToFrameDerivative (const Alignable *object, const Alignable *composedObject) const
AlgebraicMatrix66	getDerivative (const align::RotationType &objectRot, const align::RotationType &composeRot, const align::GlobalPoint &objectPos, const align::GlobalPoint &composePos) const

Private Member Functions
AlgebraicMatrix	derivativePosPos (const AlgebraicMatrix &RotDet, const AlgebraicMatrix &RotRot) const
	Calculates the derivative DPos/DPos. More...
AlgebraicMatrix	derivativePosRot (const AlgebraicMatrix &RotDet, const AlgebraicMatrix &RotRot, const AlgebraicVector &S) const
	Calculates the derivative DPos/DRot. More...
AlgebraicMatrix	derivativeRotRot (const AlgebraicMatrix &RotDet, const AlgebraicMatrix &RotRot) const
	Calculates the derivative DRot/DRot. More...
AlgebraicMatrix	getDerivative (const align::RotationType &objectRot, const align::RotationType &composeRot, const align::GlobalVector &posVec) const
AlgebraicVector	linearEulerAngles (const AlgebraicMatrix &rotDelta) const
	Gets linear approximated euler Angles. More...

Static Private Member Functions
static AlgebraicMatrix	transform (const align::RotationType &)
	Helper to transform from RotationType to AlgebraicMatrix. More...

Detailed Description

Class for calculating the jacobian d_object/d_composedObject for the rigid body parametrisation of both, i.e. the derivatives expressing the influence of u, v, w, alpha, beta, gamma of the composedObject on u, v, w, alpha, beta, gamma of its component 'object'.

Date

2007/10/08 15:56:00

Revision

1.6

(last update by

Author

cklae

)

Definition at line 20 of file FrameToFrameDerivative.h.

Member Function Documentation

derivativePosPos()

AlgebraicMatrix FrameToFrameDerivative::derivativePosPos ( const AlgebraicMatrix &  RotDet, const AlgebraicMatrix &  RotRot  ) const

private

Calculates the derivative DPos/DPos.

Definition at line 95 of file FrameToFrameDerivative.cc.

                                                                                              {
  return RotDet * RotRot.T();
}

Referenced by getDerivative().

derivativePosRot()

AlgebraicMatrix FrameToFrameDerivative::derivativePosRot ( const AlgebraicMatrix &  RotDet, const AlgebraicMatrix &  RotRot, const AlgebraicVector &  S  ) const

private

Calculates the derivative DPos/DRot.

Definition at line 101 of file FrameToFrameDerivative.cc.

                                                                                         {
  AlgebraicVector dEulerA(3);
  AlgebraicVector dEulerB(3);
  AlgebraicVector dEulerC(3);
  AlgebraicMatrix RotDa(3, 3);
  AlgebraicMatrix RotDb(3, 3);
  AlgebraicMatrix RotDc(3, 3);
 
  RotDa[1][2] = 1;
  RotDa[2][1] = -1;
  RotDb[0][2] = -1;
  RotDb[2][0] = 1;  // New beta sign
  RotDc[0][1] = 1;
  RotDc[1][0] = -1;
 
  dEulerA = RotDet * (RotRot.T() * RotDa * RotRot * S);
  dEulerB = RotDet * (RotRot.T() * RotDb * RotRot * S);
  dEulerC = RotDet * (RotRot.T() * RotDc * RotRot * S);
 
  AlgebraicMatrix eulerDeriv(3, 3);
  eulerDeriv[0][0] = dEulerA[0];
  eulerDeriv[1][0] = dEulerA[1];
  eulerDeriv[2][0] = dEulerA[2];
  eulerDeriv[0][1] = dEulerB[0];
  eulerDeriv[1][1] = dEulerB[1];
  eulerDeriv[2][1] = dEulerB[2];
  eulerDeriv[0][2] = dEulerC[0];
  eulerDeriv[1][2] = dEulerC[1];
  eulerDeriv[2][2] = dEulerC[2];
 
  return eulerDeriv;
}

References S().

Referenced by getDerivative().

derivativeRotRot()

AlgebraicMatrix FrameToFrameDerivative::derivativeRotRot ( const AlgebraicMatrix &  RotDet, const AlgebraicMatrix &  RotRot  ) const

private

Calculates the derivative DRot/DRot.

Definition at line 137 of file FrameToFrameDerivative.cc.

                                                                                              {
  AlgebraicVector dEulerA(3);
  AlgebraicVector dEulerB(3);
  AlgebraicVector dEulerC(3);
  AlgebraicMatrix RotDa(3, 3);
  AlgebraicMatrix RotDb(3, 3);
  AlgebraicMatrix RotDc(3, 3);
 
  RotDa[1][2] = 1;
  RotDa[2][1] = -1;
  RotDb[0][2] = -1;
  RotDb[2][0] = 1;  // New beta sign
  RotDc[0][1] = 1;
  RotDc[1][0] = -1;
 
  dEulerA = linearEulerAngles(RotDet * RotRot.T() * RotDa * RotRot * RotDet.T());
  dEulerB = linearEulerAngles(RotDet * RotRot.T() * RotDb * RotRot * RotDet.T());
  dEulerC = linearEulerAngles(RotDet * RotRot.T() * RotDc * RotRot * RotDet.T());
 
  AlgebraicMatrix eulerDeriv(3, 3);
 
  eulerDeriv[0][0] = dEulerA[0];
  eulerDeriv[1][0] = dEulerA[1];
  eulerDeriv[2][0] = dEulerA[2];
  eulerDeriv[0][1] = dEulerB[0];
  eulerDeriv[1][1] = dEulerB[1];
  eulerDeriv[2][1] = dEulerB[2];
  eulerDeriv[0][2] = dEulerC[0];
  eulerDeriv[1][2] = dEulerC[1];
  eulerDeriv[2][2] = dEulerC[2];
 
  return eulerDeriv;
}

References linearEulerAngles().

Referenced by getDerivative().

frameToFrameDerivative()

AlgebraicMatrix FrameToFrameDerivative::frameToFrameDerivative	(	const Alignable *	object,
		const Alignable *	composedObject
	)		const

Return the derivative DeltaFrame(object)/DeltaFrame(composedObject), i.e. a 6x6 matrix:

/ du/du_c du/dv_c du/dw_c du/da_c du/db_c du/dg_c | | dv/du_c dv/dv_c dv/dw_c dv/da_c dv/db_c dv/dg_c | | dw/du_c dw/dv_c dw/dw_c dw/da_c dw/db_c dw/dg_c | | da/du_c da/dv_c da/dw_c da/da_c da/db_c da/dg_c | | db/du_c db/dv_c db/dw_c db/da_c db/db_c db/dg_c | \ dg/du_c dg/dv_c dg/dw_c dg/da_c dg/db_c dg/dg_c /

where u, v, w, a, b, g are shifts and rotations of the object and u_c, v_c, w_c, a_c, b_c, g_c those of the composed object.

Definition at line 16 of file FrameToFrameDerivative.cc.

                                                                                                      {
  return getDerivative(object->globalRotation(),
                       composedObject->globalRotation(),
                       composedObject->globalPosition() - object->globalPosition());
}

References getDerivative(), Alignable::globalPosition(), Alignable::globalRotation(), and resolutioncreator_cfi::object.

Referenced by RigidBodyAlignmentParameters4D::derivatives(), RigidBodyAlignmentParameters::derivatives(), MillePedeMonitor::fillFrameToFrame(), ParametersToParametersDerivatives::initBowedRigid(), and ParametersToParametersDerivatives::initRigidRigid().

getDerivative() [1/2]

AlgebraicMatrix66 FrameToFrameDerivative::getDerivative	(	const align::RotationType &	objectRot,
		const align::RotationType &	composeRot,
		const align::GlobalPoint &	objectPos,
		const align::GlobalPoint &	composePos
	)		const

Calculates derivatives DeltaFrame(object)/DeltaFrame(composedobject) using their positions and orientations, see method frameToFrameDerivative(..) for definition. As a new method it gets a new interface avoiding CLHEP that should anyway be replaced by SMatrix at some point...

Definition at line 24 of file FrameToFrameDerivative.cc.

                                                                                                  {
  return asSMatrix<6, 6>(this->getDerivative(objectRot, composeRot, composePos - objectPos));
}

Referenced by frameToFrameDerivative().

getDerivative() [2/2]

AlgebraicMatrix FrameToFrameDerivative::getDerivative ( const align::RotationType &  objectRot, const align::RotationType &  composeRot, const align::GlobalVector &  posVec  ) const

private

Calculates derivatives using the orientation Matrixes and the origin difference vector

Definition at line 32 of file FrameToFrameDerivative.cc.

                                                                                             {
  AlgebraicMatrix rotDet = transform(objectRot);
  AlgebraicMatrix rotCompO = transform(composeRot);
 
  AlgebraicVector diffVec(3);
 
  diffVec(1) = posVec.x();
  diffVec(2) = posVec.y();
  diffVec(3) = posVec.z();
 
  AlgebraicMatrix derivative(6, 6);
 
  AlgebraicMatrix derivAA(3, 3);
  AlgebraicMatrix derivAB(3, 3);
  AlgebraicMatrix derivBB(3, 3);
 
  derivAA = derivativePosPos(rotDet, rotCompO);
  derivAB = derivativePosRot(rotDet, rotCompO, diffVec);
  derivBB = derivativeRotRot(rotDet, rotCompO);
 
  derivative[0][0] = derivAA[0][0];
  derivative[0][1] = derivAA[0][1];
  derivative[0][2] = derivAA[0][2];
  derivative[0][3] = derivAB[0][0];
  derivative[0][4] = derivAB[0][1];
  derivative[0][5] = derivAB[0][2];
  derivative[1][0] = derivAA[1][0];
  derivative[1][1] = derivAA[1][1];
  derivative[1][2] = derivAA[1][2];
  derivative[1][3] = derivAB[1][0];
  derivative[1][4] = derivAB[1][1];
  derivative[1][5] = derivAB[1][2];
  derivative[2][0] = derivAA[2][0];
  derivative[2][1] = derivAA[2][1];
  derivative[2][2] = derivAA[2][2];
  derivative[2][3] = derivAB[2][0];
  derivative[2][4] = derivAB[2][1];
  derivative[2][5] = derivAB[2][2];
  derivative[3][0] = 0;
  derivative[3][1] = 0;
  derivative[3][2] = 0;
  derivative[3][3] = derivBB[0][0];
  derivative[3][4] = derivBB[0][1];
  derivative[3][5] = derivBB[0][2];
  derivative[4][0] = 0;
  derivative[4][1] = 0;
  derivative[4][2] = 0;
  derivative[4][3] = derivBB[1][0];
  derivative[4][4] = derivBB[1][1];
  derivative[4][5] = derivBB[1][2];
  derivative[5][0] = 0;
  derivative[5][1] = 0;
  derivative[5][2] = 0;
  derivative[5][3] = derivBB[2][0];
  derivative[5][4] = derivBB[2][1];
  derivative[5][5] = derivBB[2][2];
 
  return derivative;
}

References funct::derivative(), derivativePosPos(), derivativePosRot(), derivativeRotRot(), transform(), PV3DBase< T, PVType, FrameType >::x(), PV3DBase< T, PVType, FrameType >::y(), and PV3DBase< T, PVType, FrameType >::z().

linearEulerAngles()

AlgebraicVector FrameToFrameDerivative::linearEulerAngles ( const AlgebraicMatrix &  rotDelta ) const

private

Gets linear approximated euler Angles.

Definition at line 173 of file FrameToFrameDerivative.cc.

                                                                                               {
  AlgebraicMatrix eulerAB(3, 3);
  AlgebraicVector aB(3);
  eulerAB[0][1] = 1;
  eulerAB[1][0] = -1;  // New beta sign
  aB[2] = 1;
 
  AlgebraicMatrix eulerC(3, 3);
  AlgebraicVector C(3);
  eulerC[2][0] = 1;
  C[1] = 1;
 
  AlgebraicVector eulerAngles(3);
  eulerAngles = eulerAB * rotDelta * aB + eulerC * rotDelta * C;
  return eulerAngles;
}

References gen::C.

Referenced by derivativeRotRot().

transform()

AlgebraicMatrix FrameToFrameDerivative::transform ( const align::RotationType &  rot )

inlinestaticprivate

Helper to transform from RotationType to AlgebraicMatrix.

Definition at line 72 of file FrameToFrameDerivative.h.

                                                                              {
  AlgebraicMatrix R(3, 3);
 
  R(1, 1) = rot.xx();
  R(1, 2) = rot.xy();
  R(1, 3) = rot.xz();
  R(2, 1) = rot.yx();
  R(2, 2) = rot.yy();
  R(2, 3) = rot.yz();
  R(3, 1) = rot.zx();
  R(3, 2) = rot.zy();
  R(3, 3) = rot.zz();
 
  return R;
}

References dttmaxenums::R, and makeMuonMisalignmentScenario::rot.

Referenced by getDerivative().