FastHelix.cc

Go to the documentation of this file.

#include "RecoTracker/TkSeedGenerator/interface/FastHelix.h"
#include "RecoTracker/TkSeedGenerator/interface/FastLine.h"
#include "TrackingTools/TrajectoryParametrization/interface/GlobalTrajectoryParameters.h"
#include "TrackingTools/TrajectoryParametrization/interface/CurvilinearTrajectoryError.h"
#include "TrackingTools/TrajectoryParametrization/interface/CartesianTrajectoryError.h"

FreeTrajectoryState FastHelix::stateAtVertex() const {
  
  if(isValid() && (fabs(tesla0) > 1e-3) && theCircle.rho()<maxRho)
    return helixStateAtVertex();
  else 
    return straightLineStateAtVertex();
    
}

FreeTrajectoryState FastHelix::helixStateAtVertex() const {

  // given the above rho>0.
  double rho = theCircle.rho();
  //remember (radius rho in cm):
  //rho = 
  //100. * pt * 
  //(10./(3.*MagneticField::inTesla(GlobalPoint(0., 0., 0.)).z()));
  
  // pt = 0.01 * rho * (0.3*MagneticField::inTesla(GlobalPoint(0.,0.,0.)).z());
  double pt = 0.01 * rho * 0.3*tesla0;

  // verify that rho is not toooo large
  double dcphi = ((theOuterHit.x()-theCircle.x0())*(theMiddleHit.x()-theCircle.x0()) +
          (theOuterHit.y()-theCircle.y0())*(theMiddleHit.y()-theCircle.y0())
          )/(rho*rho);
  if (fabs(dcphi)>=1.) return straightLineStateAtVertex();

  GlobalPoint pMid(theMiddleHit);
  GlobalPoint v(theVertex);
  
  double dydx = 0., dxdy = 0.;
  double px = 0., py = 0.;
  

  // (py/px)|x=v.x() = (dy/dx)|x=v.x()
  //remember:
  //y(x) = +-sqrt(rho^2 - (x-x0)^2) + y0 
  //y(x) =  sqrt(rho^2 - (x-x0)^2) + y0  if y(x) >= y0 
  //y(x) = -sqrt(rho^2 - (x-x0)^2) + y0  if y(x) < y0
  //=> (dy/dx) = -(x-x0)/sqrt(Q)  if y(x) >= y0
  //   (dy/dx) =  (x-x0)/sqrt(Q)  if y(x) < y0
  //with Q = rho^2 - (x-x0)^2
  // Check approximate slope to determine whether to use dydx or dxdy
  // Choose the one that goes to 0 rather than infinity.
  double arg1 = rho*rho - (v.x()-theCircle.x0())*(v.x()-theCircle.x0());
  double arg2 = rho*rho - (v.y()-theCircle.y0())*(v.y()-theCircle.y0());
  if (arg1<0.0 && arg2<0.0) {
    if(fabs(theCircle.n2()) > 0.) {
      dydx = -theCircle.n1()/theCircle.n2(); //else px = 0
      px = pt/sqrt(1. + dydx*dydx);
      py = px*dydx;
    } else {
      px = 0.;
      py = pt;
    }
  } else if ( arg1>arg2 ) {
    if( v.y() > theCircle.y0() )
      dydx = -(v.x() - theCircle.x0()) / sqrt(arg1);
    else
      dydx = (v.x() - theCircle.x0()) / sqrt(arg1);
    px = pt/sqrt(1. + dydx*dydx);
    py = px*dydx;
  } else {
    if( v.x() > theCircle.x0() )
      dxdy = -(v.y() - theCircle.y0()) / sqrt(arg2);
    else
      dxdy = (v.y() - theCircle.y0()) / sqrt(arg2);
    py = pt/sqrt(1. + dxdy*dxdy);
    px = py*dxdy;
  }
  // check sign with scalar product
  if(px*(pMid.x() - v.x()) + py*(pMid.y() - v.y()) < 0.) {
    px *= -1.;
    py *= -1.;
  } 

  //calculate z0, pz
  //(z, R*phi) linear relation in a helix
  //with R, phi defined as radius and angle w.r.t. centre of circle
  //in transverse plane
  //pz = pT*(dz/d(R*phi)))
  

  // VI 23/01/2012
  double dzdrphi = theOuterHit.z() - theMiddleHit.z();
  dzdrphi /= rho*acos(dcphi);
  double pz = pt*dzdrphi;

  /*
  // old crap
  FastLine flfit(theOuterHit, theMiddleHit, theCircle.rho());
  double dzdrphi2 = -flfit.n1()/flfit.n2();

  //  if (fabs(dzdrphi2-dzdrphi)>1.e-5) 
  std::cout << "FastHelix: old,new " << dzdrphi2 <<", " <<  dzdrphi << std::endl; 
  */

  //get sign of particle

  /*
  TrackCharge q = 
    ((theCircle.x0()*py - theCircle.y0()*px) / 
     (magvtx.z()) < 0.) ? 
    -1 : 1;
  */
  TrackCharge q = 1;
  if (theCircle.x0()*py - theCircle.y0()*px < 0) q =-q;
  if (tesla0 < 0.) q =-q;

  //VI
  if ( useBasisVertex ) {
    return FTS(basisVertex, 
           GlobalVector(px, py, pz),
           q, 
           &(*pSetup)
           );
  } else {
    double z_0 =  theMiddleHit.z();
    // assume v is before middleHit (opposite to outer)
    double ds = ( (v.x()-theCircle.x0())*(theMiddleHit.x()-theCircle.x0()) +
          (v.y()-theCircle.y0())*(theMiddleHit.y()-theCircle.y0())
          )/(rho*rho);
    if (fabs(ds)<1.) {
      ds = rho*acos(ds);
      z_0 -= ds*dzdrphi;
    } else { // line????
      z_0 -= std::sqrt((theMiddleHit-v).perp2()/(theOuterHit-theMiddleHit).perp2())*(theOuterHit.z()-theMiddleHit.z());
    }
    
    //double z_old = -flfit.c()/flfit.n2();
    // std::cout << "v:xyz, z,old,new " << v << "   " << z_old << " " << z_0 << std::endl;

    return FTS(GlobalPoint(v.x(),v.y(),z_0), 
           GlobalVector(px, py, pz),
           q, 
           &(*pSetup)
           );
  }
  
}

FreeTrajectoryState FastHelix::straightLineStateAtVertex() const {

  //calculate FTS assuming straight line...

  GlobalPoint pMid(theMiddleHit);
  GlobalPoint v(theVertex);

  double dydx = 0.;
  double pt = 0., px = 0., py = 0.;
  
  if(fabs(theCircle.n1()) > 0. || fabs(theCircle.n2()) > 0.)
    pt = maxPt  ;// 10 TeV //else no pt
  if(fabs(theCircle.n2()) > 0.) {
    dydx = -theCircle.n1()/theCircle.n2(); //else px = 0 
  }
  px = pt/sqrt(1. + dydx*dydx);
  py = px*dydx;
  // check sign with scalar product
  if (px*(pMid.x() - v.x()) + py*(pMid.y() - v.y()) < 0.) {
    px *= -1.;
    py *= -1.;
  } 

  //calculate z_0 and pz at vertex using weighted mean
  //z = z(r) = z0 + (dz/dr)*r
  //tan(theta) = dr/dz = (dz/dr)^-1
  //theta = atan(1./dzdr)
  //p = pt/sin(theta)
  //pz = p*cos(theta) = pt/tan(theta) 

  FastLine flfit(theOuterHit, theMiddleHit);
  double dzdr = -flfit.n1()/flfit.n2();
  double pz = pt*dzdr; 
  
  TrackCharge q = 1;
  //VI

  if ( useBasisVertex ) {
    return FTS(basisVertex, 
           GlobalVector(px, py, pz),
           q, 
           &(*pSetup)
           );
  } else {
  double z_0 = -flfit.c()/flfit.n2();
  return FTS(GlobalPoint(v.x(), v.y(), z_0),
         GlobalVector(px, py, pz),
         q,
         &(*pSetup)
         );
  }
}