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// $Id: Helix.cc,v 1.2 2008/09/04 13:55:30 loizides Exp $
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#include "MitCommon/MathTools/interface/Helix.h"
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using namespace mithep;
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Helix::Helix(const TVector3 &MomentumGev, const TVector3 &PositionCm,
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double q, double BFieldTesla)
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{
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double CotTheta,W,Z0,D0;
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Angle Phi0;
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if (BFieldTesla != 0.0 && q != 0.0) {
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double CurvatureConstant
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= 0.0029979;
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double Helicity = -1.0*fabs(BFieldTesla)*fabs(q)/(BFieldTesla*q);
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double Radius = fabs(MomentumGev.Perp()/
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(CurvatureConstant*BFieldTesla*q));
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if (Radius==0.0)
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W = HUGE_VAL;
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else
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W = Helicity/Radius;
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Angle phi1 = MomentumGev.Phi();
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double x = PositionCm.x(),
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y = PositionCm.y(),
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z = PositionCm.z();
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double sinPhi1 = sin(phi1),
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cosPhi1 = cos(phi1);
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double gamma = atan((x*cosPhi1 + y*sinPhi1)/(x*sinPhi1-y*cosPhi1 -1/W));
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Phi0 = phi1+gamma;
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D0 = ((1/W + y*cosPhi1 - x*sinPhi1) /cos(gamma) - 1/W);
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CotTheta = MomentumGev.z()/MomentumGev.Perp();
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Z0 = z + gamma*CotTheta/W;
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}
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// For the special case that we have no Helix, never happens for us .. right?
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else {
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std::cout << "MAJOR ERROR in HELIX !!!! STOP !!!!\n";
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// Line auxLine(PositionCm,MomentumGev.unit());
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// Z0 = auxLine.Z0();
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// Phi0 = auxLine.Phi0();
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// CotTheta = auxLine.CotTheta();
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// D0 = auxLine.D0();
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// W = 0.0;
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//
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// fCotTheta = CotTheta;
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// fCurvature = W/2;
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// fZ0 = Z0;
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// fD0 = D0;
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// fPhi0 = Phi0;
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// fIsStale = 1;
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// fS = -999.999;
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// fAa = -999.999;
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// fSs = -999.999;
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// fCc = -999.999;
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// fSinPhi0 = 1.0;
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// fCosPhi0 = 1.0;
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// fSinTheta = 1.0;
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// fCosTheta = 1.0;
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// fVParameters = 0;
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// fCenterIsValid = false;
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// fMx = 0.0;
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// fMy = 0.0;
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}
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}
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bool Helix::operator == (const Helix &right) const
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{
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return
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fCotTheta == right.fCotTheta &&
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fCurvature == right.fCurvature &&
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fZ0 == right.fZ0 &&
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fD0 == right.fD0 &&
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fPhi0 == right.fPhi0;
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}
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bool Helix::operator != (const Helix & right) const
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{
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return !((*this)==right);
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}
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Helix::~Helix()
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{
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delete fVParameters;
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}
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TVector3 Helix::Position(double s) const
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{
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fCacheSinesAndCosines(s);
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if (s == 0.0 || fCurvature == 0.0) {
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return TVector3(-fD0*fSinPhi0+s*fCosPhi0*fSinTheta,
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fD0*fCosPhi0+s*fSinPhi0*fSinTheta,
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fZ0+s*fCosTheta);
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} else {
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return TVector3((fCosPhi0*fSs-fSinPhi0*(2.0*fCurvature*fD0+1.0-fCc))
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/(2.0*fCurvature),
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(fSinPhi0*fSs+fCosPhi0*(2.0*fCurvature*fD0+1.0-fCc))
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/(2.0*fCurvature),
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fS*fCosTheta + fZ0);
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}
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}
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TVector3 Helix::Direction(double s) const
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{
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fCacheSinesAndCosines(s);
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if (s == 0.0) {
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return TVector3(fCosPhi0*fSinTheta,fSinPhi0*fSinTheta,fCosTheta);
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}
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double xtan = fSinTheta*(fCosPhi0*fCc -fSinPhi0*fSs);
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double ytan = fSinTheta*(fCosPhi0*fSs +fSinPhi0*fCc);
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double ztan = fCosTheta;
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return TVector3(xtan,ytan,ztan);
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}
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double Helix::PathLengthAtRhoEquals(double rho) const
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{
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return (SinTheta()?(L2DAtR(rho)/SinTheta()):0.0);
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}
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double Helix::InverseRadius() const
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{
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return fCurvature*2.0;
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}
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double Helix::Radius() const
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{
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return fabs(1.0/InverseRadius());
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}
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SignedAngle Helix::TurningAngle(double s) const
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{
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return s/Radius();
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}
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double Helix::Curvature() const
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{
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return fCurvature;
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}
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double Helix::Helicity() const
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{
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return fCurvature>0 ? 1.0 : -1.0 ;
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}
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double Helix::CotTheta() const
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{
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return fCotTheta;
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}
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Angle Helix::Phi0() const
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{
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return fPhi0;
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}
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double Helix::D0() const
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{
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return fD0;
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}
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double Helix::SignLz() const
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{
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return (fD0>0) ? -1.0 : 1.0;
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}
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double Helix::Z0() const
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{
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return fZ0;
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}
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TVector3 Helix::SecondDerivative(double s) const
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{
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double phi1 = fPhi0+s*2.0*fCurvature*fSinTheta;
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double sp1 = sin(phi1);
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double xsecond = -fSinTheta*sp1*2.0*fCurvature*fSinTheta;
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double ysecond = fSinTheta*sqrt(1.0-sp1*sp1)*2.0*fCurvature*fSinTheta;
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return TVector3(xsecond,ysecond,0.0);
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}
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double Helix::SinPhi0() const
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{
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fRefreshCache();
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return fSinPhi0;
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}
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double Helix::CosPhi0() const
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{
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fRefreshCache();
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return fCosPhi0;
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}
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double Helix::SinTheta() const
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{
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fRefreshCache();
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return fSinTheta;
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}
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double Helix::CosTheta() const
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{
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fRefreshCache();
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return fCosTheta;
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}
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Angle Helix::PhiAtR(double rho) const
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{
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double c = Curvature();
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double d = D0();
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double a = c/(1.0+2.0*c*d);
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double b = d - a*d*d;
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double arcsin = a*rho+b/rho;
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if (arcsin>1.0 || arcsin<-1.0) {
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return (arcsin > 0.) ? M_PI : -M_PI;
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}
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Angle phi = Phi0() + asin(arcsin);
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return phi;
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}
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double Helix::ZAtR(double rho) const
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{
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return fZ0 + CotTheta()*L2DAtR(rho);
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}
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double Helix::L2DAtR(double rho) const {
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double L2D;
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double c = Curvature();
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double d = D0();
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if (c!=0.0) {
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double rad = (rho*rho-d*d)/(1.0+2.0*c*d);
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double rprime;
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if (rad<0.0)
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rprime = 0.0;
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else
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rprime = sqrt( rad );
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if (c*rprime > 1.0 || c*rprime < -1.0)
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L2D = c*rprime > 0. ? M_PI/c : -M_PI/c;
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else
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L2D = asin(c*rprime)/c;
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}
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else {
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L2D = rho;
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}
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return L2D;
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}
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double Helix::CosAlphaAtR(double rho) const {
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double c = Curvature();
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double d = D0();
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double a = c/(1.0+2.0*c*d);
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double phi = PhiAtR(rho);
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double x = rho*cos(phi);
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double y = rho*sin(phi);
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double dir_x0 = (1.0+2.0*c*d) * (1.0-2.0*a*y);
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double dir_y0 = (1.0+2.0*c*d) * 2.0*a*x;
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double phi0 = Phi0();
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double dir_x = dir_x0*cos(phi0) - dir_y0*sin(phi0);
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double dir_y = dir_x0*sin(phi0) + dir_y0*cos(phi0);
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double cosalpha = (x*dir_x + y*dir_y)/rho;
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return cosalpha;
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}
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//void Helix::Location(Trajectory::Location &loc, double s) const
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//{
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// fCacheSinesAndCosines(s);
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// double cP0sT = fCosPhi0*fSinTheta, sP0sT = fSinPhi0*fSinTheta;
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// if (s && fCurvature) {
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// loc.SetLocation(s,
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// (fCosPhi0*fSs-
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// fSinPhi0*(2.0*fCurvature*fD0+1.0-fCc))
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// /(2.0*fCurvature),
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// (fSinPhi0*fSs+
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// fCosPhi0*(2.0*fCurvature*fD0+1.0-fCc))
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// /(2.0*fCurvature),
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// s*fCosTheta + fZ0,
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// cP0sT*fCc-sP0sT*fSs,
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// cP0sT*fSs+sP0sT*fCc,
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// fCosTheta
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// );
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// }
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// else {
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// loc.SetLocation(s,
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// -fD0*fSinPhi0+s*cP0sT,
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// fD0*fCosPhi0+s*sP0sT,
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// fZ0+s*fCosTheta,
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// cP0sT,sP0sT,fCosTheta
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// );
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// }
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//}
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//Trajectory::Location* Helix::newIntersectionWith (const HepPlane3D& plane) const
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//{
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// if (!SinTheta()) // fastest way out of a screwy situation.
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// return 0;
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//
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// double deltaS=1.0,s=0.0;
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// s = fabs(plane.d())/SinTheta();
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// HepVector3D normal = plane.normal();
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// Trajectory::Location *ploc = new Trajectory::Location ;
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// for (int iteration=0;iteration<100;iteration++) {
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// if (fabs(deltaS)>0.0001){
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// Location(*ploc,s);
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// deltaS = ((-(plane.distance(ploc->position())))
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// /(normal.dot(ploc->direction())));
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// s+=deltaS;
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// }
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// else {
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// if (s>0)
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// return ploc;
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// }
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// }
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// delete ploc;
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// return 0;
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//}
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