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#include <HelixExtrapolatorToLine2Order.h>
Public Member Functions | |
| virtual DirectionType | direction (double s) const |
| Direction at pathlength s from the starting point. | |
| DirectionTypeDouble | directionInDouble (double s) const |
| Direction at pathlength s from the starting point in double precision. | |
| HelixExtrapolatorToLine2Order (const double &x0, const double &y0, const double &z0, const double &cosPhi0, const double &sinPhi0, const double &cosTheta, const double &sinTheta, const double &rho, const PropagationDirection propDir=alongMomentum) | |
| Fast constructor (for use by IterativeHelixExtrapolatorToLine). | |
| HelixExtrapolatorToLine2Order (const PositionType &point, const DirectionType &direction, const float curvature, const PropagationDirection propDir=alongMomentum) | |
| Constructor using point, direction and (transverse!) curvature. | |
| virtual std::pair< bool, double > | pathLength (const GlobalPoint &point) const |
| virtual std::pair< bool, double > | pathLength (const Line &line) const |
| virtual PositionType | position (double s) const |
| Position at pathlength s from the starting point. | |
| PositionTypeDouble | positionInDouble (double s) const |
| Position at pathlength s from the starting point in double precision. | |
| virtual | ~HelixExtrapolatorToLine2Order () |
Private Member Functions | |
| virtual std::pair< bool, double > | pathLengthFromCoefficients (const double ceq[4]) const dso_internal |
| common part for propagation to point and line | |
| int | solve2ndOrder (const double ceq[], double sol[]) const dso_internal |
| Solutions of 2nd order equation. | |
| int | solve3rdOrder (const double ceq[], double sol[]) const dso_internal |
| Solutions of 3rd order equation. | |
Private Attributes | |
| DirectionTypeDouble | theDirection |
| const PositionTypeDouble | thePosition |
| const PropagationDirection | thePropDir |
| const double | theRho |
| double | theSinTheta |
Calculates intersections of a helix with planes of any orientation using a parabolic approximation.
Definition at line 11 of file HelixExtrapolatorToLine2Order.h.
| HelixExtrapolatorToLine2Order::HelixExtrapolatorToLine2Order | ( | const PositionType & | point, |
| const DirectionType & | direction, | ||
| const float | curvature, | ||
| const PropagationDirection | propDir = alongMomentum |
||
| ) |
Constructor using point, direction and (transverse!) curvature.
Definition at line 7 of file HelixExtrapolatorToLine2Order.cc.
References AlCaHLTBitMon_ParallelJobs::p, mathSSE::sqrt(), theDirection, theSinTheta, Basic3DVector< T >::x(), Basic3DVector< T >::y(), and Basic3DVector< T >::z().
: thePosition(point), theRho(curvature), thePropDir(propDir) { // // Components of direction vector (with correct normalisation) // double px = direction.x(); double py = direction.y(); double pz = direction.z(); double pt = px*px+py*py; double p = sqrt(pt+pz*pz); pt = sqrt(pt); theDirection = DirectionTypeDouble(px/pt,py/pt,pz/pt); theSinTheta = pt/p; }
| HelixExtrapolatorToLine2Order::HelixExtrapolatorToLine2Order | ( | const double & | x0, |
| const double & | y0, | ||
| const double & | z0, | ||
| const double & | cosPhi0, | ||
| const double & | sinPhi0, | ||
| const double & | cosTheta, | ||
| const double & | sinTheta, | ||
| const double & | rho, | ||
| const PropagationDirection | propDir = alongMomentum |
||
| ) | [inline] |
Fast constructor (for use by IterativeHelixExtrapolatorToLine).
Definition at line 20 of file HelixExtrapolatorToLine2Order.h.
:
thePosition(x0,y0,z0),
theDirection(cosPhi0,sinPhi0,cosTheta/sinTheta),
theSinTheta(sinTheta),
theRho(rho),
thePropDir(propDir) {}
| virtual HelixExtrapolatorToLine2Order::~HelixExtrapolatorToLine2Order | ( | ) | [inline, virtual] |
Definition at line 32 of file HelixExtrapolatorToLine2Order.h.
{}
| HelixLineExtrapolation::DirectionType HelixExtrapolatorToLine2Order::direction | ( | double | s | ) | const [virtual] |
Direction at pathlength s from the starting point.
Implements HelixLineExtrapolation.
Definition at line 226 of file HelixExtrapolatorToLine2Order.cc.
References directionInDouble().
{
// use double precision result
// DirectionTypeDouble dir = directionInDouble(s);
// return DirectionType(dir.x(),dir.y(),dir.z());
return DirectionType(directionInDouble(s));
}
| HelixExtrapolatorToLine2Order::DirectionTypeDouble HelixExtrapolatorToLine2Order::directionInDouble | ( | double | s | ) | const |
Direction at pathlength s from the starting point in double precision.
Definition at line 236 of file HelixExtrapolatorToLine2Order.cc.
References theDirection, theRho, theSinTheta, Basic3DVector< T >::x(), Basic3DVector< T >::y(), and Basic3DVector< T >::z().
Referenced by direction(), and IterativeHelixExtrapolatorToLine::directionInDouble().
{
// based on delta phi
double dph = s*theRho*theSinTheta;
return DirectionTypeDouble(theDirection.x()-(theDirection.y()+0.5*theDirection.x()*dph)*dph,
theDirection.y()+(theDirection.x()-0.5*theDirection.y()*dph)*dph,
theDirection.z());
}
| std::pair< bool, double > HelixExtrapolatorToLine2Order::pathLength | ( | const GlobalPoint & | point | ) | const [virtual] |
Propagation status (true if valid) and (signed) path length along the helix from the starting point to the closest approach to the point. The starting point is given in the constructor.
Implements HelixLineExtrapolation.
Definition at line 32 of file HelixExtrapolatorToLine2Order.cc.
References Basic3DVector< T >::dot(), Basic3DVector< T >::mag2(), pathLengthFromCoefficients(), position(), theDirection, thePosition, theRho, Basic3DVector< T >::x(), and Basic3DVector< T >::y().
Referenced by IterativeHelixExtrapolatorToLine::genericPathLength().
{
//
PositionTypeDouble position(point);
DirectionTypeDouble helix2(-0.5*theRho*theDirection.y(),
0.5*theRho*theDirection.x(),
0.);
DirectionTypeDouble deltaPos(thePosition-position);
//
// coefficients of 3rd order equation
//
double ceq[4];
ceq[3] = 2*helix2.mag2();
// ceq[2] = 3*theDirection.dot(helix2) = 0 since they are orthogonal
ceq[2] = 0.;
ceq[1] = theDirection.mag2()+2*deltaPos.dot(helix2);
ceq[0] = deltaPos.dot(theDirection);
//
return pathLengthFromCoefficients(ceq);
}
| std::pair< bool, double > HelixExtrapolatorToLine2Order::pathLength | ( | const Line & | line | ) | const [virtual] |
Propagation status (true if valid) and (signed) path length along the helix from the starting point to the closest approach to the line. The starting point is given in the constructor.
Implements HelixLineExtrapolation.
Definition at line 56 of file HelixExtrapolatorToLine2Order.cc.
References Line::direction(), Basic3DVector< T >::dot(), pathLengthFromCoefficients(), Line::position(), theDirection, thePosition, theRho, Basic3DVector< T >::x(), and Basic3DVector< T >::y().
{
//
// Auxiliary vectors. Assumes that line.direction().mag()=1 !
//
PositionTypeDouble linePosition(line.position());
DirectionTypeDouble lineDirection(line.direction());
DirectionTypeDouble helix2(-0.5*theRho*theDirection.y(),
0.5*theRho*theDirection.x(),
0.);
DirectionTypeDouble deltaPos(thePosition-linePosition);
DirectionTypeDouble helix1p(theDirection-lineDirection*theDirection.dot(lineDirection));
DirectionTypeDouble helix2p(helix2-lineDirection*helix2.dot(lineDirection));
//
// coefficients of 3rd order equation
//
double ceq[4];
ceq[3] = 2*helix2.dot(helix2p);
// ceq[2] = 3*helix1.dot(helix1p);
// since theDirection.dot(helix2)==0 equivalent to
ceq[2] = 3*theDirection.dot(lineDirection)*helix2.dot(lineDirection);
ceq[1] = theDirection.dot(helix1p)+2*deltaPos.dot(helix2p);
ceq[0] = deltaPos.dot(helix1p);
//
return pathLengthFromCoefficients(ceq);
}
| std::pair< bool, double > HelixExtrapolatorToLine2Order::pathLengthFromCoefficients | ( | const double | ceq[4] | ) | const [private, virtual] |
common part for propagation to point and line
Definition at line 86 of file HelixExtrapolatorToLine2Order.cc.
References alongMomentum, anyDirection, i, oppositeToMomentum, StEvtSolProducer_cfi::solutions, solve3rdOrder(), thePropDir, and theSinTheta.
Referenced by pathLength().
{
//
// Solution of 3rd order equation
//
double solutions[3];
int nRaw = solve3rdOrder(ceq,solutions);
//
// check compatibility with propagation direction
//
int nDir(0);
for ( int i=0; i<nRaw; i++ ) {
if ( thePropDir==anyDirection ||
(solutions[i]>=0&&thePropDir==alongMomentum) ||
(solutions[i]<=0&&thePropDir==oppositeToMomentum) )
solutions[nDir++] = solutions[i];
}
if ( nDir==0 ) return std::make_pair(false,0.);
//
// check 2nd derivative
//
int nMin(0);
for ( int i=0; i<nDir; i++ ) {
double st = solutions[i];
double deri2 = (3*ceq[3]*st+2*ceq[2])*st+ceq[1];
if ( deri2>0. ) solutions[nMin++] = st;
}
if ( nMin==0 ) return std::make_pair(false,0.);
//
// choose smallest path length
//
double dSt = solutions[0];
for ( int i=1; i<nMin; i++ ) {
if ( fabs(solutions[i])<fabs(dSt) ) dSt = solutions[i];
}
return std::make_pair(true,dSt/theSinTheta);
}
| HelixLineExtrapolation::PositionType HelixExtrapolatorToLine2Order::position | ( | double | s | ) | const [virtual] |
Position at pathlength s from the starting point.
Implements HelixLineExtrapolation.
Definition at line 205 of file HelixExtrapolatorToLine2Order.cc.
References positionInDouble().
Referenced by pathLength().
{
// use double precision result
// PositionTypeDouble pos = positionInDouble(s);
// return PositionType(pos.x(),pos.y(),pos.z());
return PositionType(positionInDouble(s));
}
| HelixExtrapolatorToLine2Order::PositionTypeDouble HelixExtrapolatorToLine2Order::positionInDouble | ( | double | s | ) | const |
Position at pathlength s from the starting point in double precision.
Definition at line 215 of file HelixExtrapolatorToLine2Order.cc.
References theDirection, thePosition, theRho, theSinTheta, Basic3DVector< T >::x(), Basic3DVector< T >::y(), and Basic3DVector< T >::z().
Referenced by position(), and IterativeHelixExtrapolatorToLine::positionInDouble().
{
// based on path length in the transverse plane
double st = s*theSinTheta;
return PositionTypeDouble(thePosition.x()+(theDirection.x()-st*0.5*theRho*theDirection.y())*st,
thePosition.y()+(theDirection.y()+st*0.5*theRho*theDirection.x())*st,
thePosition.z()+st*theDirection.z());
}
| int HelixExtrapolatorToLine2Order::solve2ndOrder | ( | const double | ceq[], |
| double | sol[] | ||
| ) | const [private] |
Solutions of 2nd order equation.
Definition at line 172 of file HelixExtrapolatorToLine2Order.cc.
References mathSSE::sqrt().
Referenced by solve3rdOrder().
{
//
double deq1 = coeff[1]*coeff[1];
double deq2 = coeff[2]*coeff[0];
if ( fabs(deq1)<FLT_MIN || fabs(deq2/deq1)>1.e-6 ) {
//
// Standard solution for quadratic equations
//
double deq = deq1+2*deq2;
if ( deq<0. ) return 0;
double ceq = -0.5*(coeff[1]+(coeff[1]>0?1:-1)*sqrt(deq));
solutions[0] = -2*ceq/coeff[2];
solutions[1] = coeff[0]/ceq;
return 2;
}
else {
//
// Solution by expansion of sqrt(1+deq)
//
double ceq = coeff[1]/coeff[2];
double deq = deq2/deq1;
deq *= (1-deq/2);
solutions[0] = -ceq*deq;
solutions[1] = ceq*(2+deq);
return 2;
}
}
| int HelixExtrapolatorToLine2Order::solve3rdOrder | ( | const double | ceq[], |
| double | sol[] | ||
| ) | const [private] |
Solutions of 3rd order equation.
Definition at line 126 of file HelixExtrapolatorToLine2Order.cc.
References a, b, funct::cos(), i, M_PI, phi, funct::pow(), lumiQueryAPI::q, csvReporter::r, query::result, solve2ndOrder(), and mathSSE::sqrt().
Referenced by pathLengthFromCoefficients().
{
//
// Real 3rd order equation? Follow numerical recipes ..
//
if ( fabs(ceq[3])>FLT_MIN ) {
int result(0);
double q = (ceq[2]*ceq[2]-3*ceq[3]*ceq[1]) / (ceq[3]*ceq[3]) / 9.;
double r = (2*ceq[2]*ceq[2]*ceq[2]-9*ceq[3]*ceq[2]*ceq[1]+27*ceq[3]*ceq[3]*ceq[0])
/ (ceq[3]*ceq[3]*ceq[3]) / 54.;
double q3 = q*q*q;
if ( r*r<q3 ) {
double phi = acos(r/sqrt(q3))/3.;
double rootq = sqrt(q);
for ( int i=0; i<3; i++ ) {
solutions[i] = -2*rootq*cos(phi) - ceq[2]/ceq[3]/3.;
phi += 2./3.*M_PI;
}
result = 3;
}
else {
double a = pow(fabs(r)+sqrt(r*r-q3),1./3.);
if ( r>0. ) a *= -1;
double b = fabs(a)>FLT_MIN ? q/a : 0.;
solutions[0] = a + b - ceq[2]/ceq[3]/3.;
result = 1;
}
return result;
}
//
// Second order equation
//
else if ( fabs(ceq[2])>FLT_MIN ) {
return solve2ndOrder(ceq,solutions);
}
else {
//
// Special case: linear equation
//
solutions[0] = -ceq[0]/ceq[1];
return 1;
}
}
Definition at line 68 of file HelixExtrapolatorToLine2Order.h.
Referenced by directionInDouble(), HelixExtrapolatorToLine2Order(), pathLength(), and positionInDouble().
const PositionTypeDouble HelixExtrapolatorToLine2Order::thePosition [private] |
Definition at line 67 of file HelixExtrapolatorToLine2Order.h.
Referenced by pathLength(), and positionInDouble().
const PropagationDirection HelixExtrapolatorToLine2Order::thePropDir [private] |
Definition at line 71 of file HelixExtrapolatorToLine2Order.h.
Referenced by pathLengthFromCoefficients().
const double HelixExtrapolatorToLine2Order::theRho [private] |
Definition at line 70 of file HelixExtrapolatorToLine2Order.h.
Referenced by directionInDouble(), pathLength(), and positionInDouble().
double HelixExtrapolatorToLine2Order::theSinTheta [private] |
Definition at line 69 of file HelixExtrapolatorToLine2Order.h.
Referenced by directionInDouble(), HelixExtrapolatorToLine2Order(), pathLengthFromCoefficients(), and positionInDouble().
1.7.3