ThirdHitPredictionFromInvParabola.h

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#ifndef ThirdHitPredictionFromInvParabola_H
#define ThirdHitPredictionFromInvParabola_H

#include "DataFormats/GeometryVector/interface/Basic2DVector.h"
#include "DataFormats/GeometryVector/interface/Basic3DVector.h"
#include "DataFormats/GeometrySurface/interface/TkRotation.h"

#include "DataFormats/GeometryVector/interface/GlobalPoint.h"
#include "RecoTracker/TkMSParametrization/interface/PixelRecoRange.h"
#include "FWCore/Utilities/interface/Visibility.h"


class TrackingRegion;
class OrderedHitPair;


class ThirdHitPredictionFromInvParabola {

public:
  using Scalar=double;
  typedef TkRotation2D<Scalar> Rotation;
  typedef PixelRecoRange<float> Range;
  typedef PixelRecoRange<Scalar> RangeD;
  typedef Basic2DVector<Scalar> Point2D;


  ThirdHitPredictionFromInvParabola(){}
  ThirdHitPredictionFromInvParabola(Scalar x1,Scalar y1, Scalar x2,Scalar y2,  Scalar ip, Scalar curv,
                    Scalar tolerance): theTolerance(tolerance)
  {
    init(x1,y1,x2,y2,ip,std::abs(curv));
  }

  ThirdHitPredictionFromInvParabola(const GlobalPoint & P1, const GlobalPoint & P2,
    Scalar ip, Scalar curv, Scalar tolerance);

//  inline Range operator()(Scalar radius, int charge) const { return rangeRPhiSlow(radius,charge,1); } 
  inline Range operator()(Scalar radius, int charge) const { return rangeRPhi(radius,charge); } 

  Range rangeRPhi(Scalar radius, int charge) const __attribute__ ((optimize(3, "fast-math")));
  // Range rangeRPhiSlow(Scalar radius, int charge, int nIter=5) const;

  void init( const GlobalPoint & P1, const GlobalPoint & P2,  Scalar ip, Scalar curv) {
     init( P1.x(), P1.y(), P2.x(),P2.y(),ip,curv);
  }
  void init(Scalar x1,Scalar y1, Scalar x2,Scalar y2,  Scalar ip, Scalar curv);

private:

  inline Scalar coeffA(Scalar impactParameter) const;
  inline Scalar coeffB(Scalar impactParameter) const;
  inline Scalar predV(Scalar u, Scalar  ip) const;
  inline Scalar ipFromCurvature(Scalar  curvature, bool pos) const;

  Point2D transform(Point2D const & p) const {
    return theRotation.rotate(p)/p.mag2();
  }

  Point2D transformBack(Point2D const & p) const {
    return theRotation.rotateBack(p)/p.mag2();
  }

private:

  Rotation theRotation;
  Scalar u1u2, overDu, pv, dv, su;

  // formula is symmetric for (ip,pos) -> (-ip,neg)
  inline void findPointAtCurve(Scalar radius, Scalar ip, Scalar &u, Scalar &v) const;

  RangeD theIpRangePlus, theIpRangeMinus; 
  Scalar theTolerance;

};



ThirdHitPredictionFromInvParabola::Scalar  ThirdHitPredictionFromInvParabola::
    coeffA(Scalar impactParameter) const
{
  auto c = -pv*overDu;
  return c - u1u2*impactParameter;
}

ThirdHitPredictionFromInvParabola::Scalar ThirdHitPredictionFromInvParabola::
    coeffB(Scalar impactParameter) const
{
  auto c = dv*overDu;
  return c - su*impactParameter;
}

ThirdHitPredictionFromInvParabola::Scalar ThirdHitPredictionFromInvParabola::
    ipFromCurvature(Scalar curvature, bool pos) const 
{
  Scalar overU1u2 = 1./u1u2;
  Scalar inInf = -pv*overDu*overU1u2;
  return (pos? inInf : -inInf) -curvature*overU1u2*0.5;
}


ThirdHitPredictionFromInvParabola::Scalar ThirdHitPredictionFromInvParabola::
predV( Scalar u, Scalar ip) const
{
  auto c =  -( coeffA(ip) - coeffB(ip*u) - ip*u*u);
  return c;
}


void ThirdHitPredictionFromInvParabola::findPointAtCurve(Scalar r, Scalar ip, 
                             Scalar & u, Scalar & v) const
{
  //
  // assume u=(1-alpha^2/2)/r v=alpha/r
  // solve qudratic equation neglecting aplha^4 term
  //
  Scalar A = coeffA(ip);
  Scalar B = coeffB(ip);

  // Scalar overR = 1./r;
  Scalar ipOverR = ip/r; // *overR;

  Scalar a = 0.5*B+ipOverR;
  Scalar c = -B+A*r-ipOverR;

  Scalar delta = 1-4*a*c;
  // Scalar sqrtdelta = (delta > 0) ? std::sqrt(delta) : 0.;
  Scalar sqrtdelta = std::sqrt(delta);
  //  Scalar alpha = (-1+sqrtdelta)/(2*a);
  Scalar alpha = (-2*c)/(1+sqrtdelta);

  v = alpha;  // *overR
  Scalar d2 = 1. - v*v;  // overR*overR - v*v
  // u = (d2 > 0) ? std::sqrt(d2) : 0.;
  u = std::sqrt(d2);

  // u,v not rotated! not multiplied by 1/r
}


#endif