#include <ThirdHitPredictionFromCircle.h>

Classes
class	HelixRZ

Public Types
typedef PixelRecoRange< float >	Range

using	Scalar = double

typedef Basic2DVector< Scalar >	Vector2D

typedef Basic2DVector< float >	VectorF2D

Public Member Functions
float	angle (float curvature, float radius) const

Range	curvature (double transverseIP) const

double	curvature (const Vector2D &thirdPoint) const

Range	operator() (Range curvature, float radius) const

float	phi (float curvature, float radius) const

	ThirdHitPredictionFromCircle (const GlobalPoint &P1, const GlobalPoint &P2, float tolerance)

double	transverseIP (const Vector2D &thirdPoint) const

Private Member Functions
Scalar	invCenterOnAxis (const Vector2D &thirdPoint) const

Private Attributes
Vector2D	axis

Vector2D	center

Scalar	delta

Scalar	delta2

Vector2D	p1

float	theTolerance

Friends
class	HelixRZ

Detailed Description

Definition at line 11 of file ThirdHitPredictionFromCircle.h.

Member Typedef Documentation

typedef PixelRecoRange<float> ThirdHitPredictionFromCircle::Range

Definition at line 15 of file ThirdHitPredictionFromCircle.h.

using ThirdHitPredictionFromCircle::Scalar = double

Definition at line 14 of file ThirdHitPredictionFromCircle.h.

typedef Basic2DVector<Scalar> ThirdHitPredictionFromCircle::Vector2D

Definition at line 16 of file ThirdHitPredictionFromCircle.h.

typedef Basic2DVector<float> ThirdHitPredictionFromCircle::VectorF2D

Definition at line 17 of file ThirdHitPredictionFromCircle.h.

Constructor & Destructor Documentation

ThirdHitPredictionFromCircle::ThirdHitPredictionFromCircle	(	const GlobalPoint &	P1,
		const GlobalPoint &	P2,
		float	tolerance
	)

Definition at line 24 of file ThirdHitPredictionFromCircle.cc.

References axis, center, delta, delta2, diffTreeTool::diff, p1, p2, mathSSE::sqrt(), PV3DBase< T, PVType, FrameType >::x(), and PV3DBase< T, PVType, FrameType >::y().

   : p1(P1.x(), P1.y()), theTolerance(tolerance)
 {
   Vector2D p2(P2.x(), P2.y());
   Vector2D diff = 0.5 * (p2 - p1);
   delta2 = diff.mag2();
   delta = std::sqrt(delta2);
   axis = Vector2D(-diff.y(), diff.x()) / delta;
   center = p1 + diff;
 }

Member Function Documentation

float ThirdHitPredictionFromCircle::angle	(	float	curvature,
		float	radius
	)		const

Definition at line 59 of file ThirdHitPredictionFromCircle.cc.

References abs, axis, center, funct::cos(), delta2, alignCSCRings::e, f, Basic2DVector< T >::mag2(), FWPFMaths::sgn(), funct::sin(), funct::sqr(), and unlikely.

Referenced by MatchedHitRZCorrectionFromBending::tibMatchedHitZFixup().

 {
   if (unlikely(std::abs(curvature) < float(1.0e-5))) {
     float sin = (center * axis) / radius;
     return sin / clamped_sqrt(1 - sqr(sin));
   } else {
     float radius2 = sqr(1.0f / curvature);
     float orthog = clamped_sqrt(radius2 - delta2);
     Basic2DVector<float> lcenter = Basic2DVector<float>(center) - sgn(curvature) * orthog * Basic2DVector<float>(axis);
  
     float cos = (radius2 + sqr(radius) - lcenter.mag2()) *
                  curvature / (2 * radius);
     return - cos / clamped_sqrt(1.f - sqr(cos));
  }
 }

ThirdHitPredictionFromCircle::Range ThirdHitPredictionFromCircle::curvature ( double transverseIP ) const

Definition at line 87 of file ThirdHitPredictionFromCircle.cc.

References abs, axis, center, constexpr, delta, delta2, alignCSCRings::e, FWPFMaths::sgn(), SMALL, funct::sqr(), mathSSE::sqrt(), std::swap(), tmp, transverseIP(), unlikely, Basic2DVector< T >::x(), and Basic2DVector< T >::y().

Referenced by ThirdHitPredictionFromCircle::HelixRZ::rAtZ(), and ThirdHitPredictionFromCircle::HelixRZ::zAtR().

 {
   // this is a mess.  Use a CAS and lots of drawings to verify...
 
   transverseIP = std::abs(transverseIP);
   double transverseIP2 = sqr(transverseIP);
   double tip = axis * center;
   double tip2 = sqr(tip);
   double lip = axis.x() * center.y() - axis.y() * center.x();
   double lip2 = sqr(lip);
 
   double origin = std::sqrt(tip2 + lip2);
   double tmp1 = lip2 + tip2 - transverseIP2;
   double tmp2 = 2. * (tip - transverseIP) * (tip + transverseIP);
   double tmp3 = 2. * delta * origin;
   double tmp4 = tmp1 + delta2;
   double tmp5 = 2. * delta * lip;
 
   // I am probably being overly careful here with border cases
   // but you never know what crap you might get fed
   // VI fixed for finiteMath
 
   double u1=0, u2=0;
   constexpr double SMALL = 1.0e-23;
   constexpr double LARGE = 1.0e23;
 
   if (unlikely(tmp4 - tmp5 < 1.0e-15)) {
     u1 = -SMALL;
     u2 = +SMALL;
   } else {
     if (unlikely(std::abs(tmp2) < 1.0e-15)) {
       // the denominator is zero
       // this means that one of the tracks will be straight
       // and the other can be computed from the limit of the equation
       double tmp = lip2 - delta2;
       u1 = LARGE;
       u2 = (sqr(0.5 * tmp) - delta2 * tip2) / (tmp * tip);
       if (tip < 0)
         std::swap(u1, u2);
     } else {
       double tmp6 = (tmp4 - tmp5) * (tmp4 + tmp5);
       if (unlikely(tmp6 < 1.0e-15)) {
         u1 = -SMALL;
         u2 = +SMALL;
       } else {
         double tmp7 = tmp6 > 0 ? (transverseIP * std::sqrt(tmp6) / tmp2) : 0.;
         double tmp8 = tip * (tmp1 - delta2) / tmp2;
         // the two quadratic solutions
         u1 = tmp8 + tmp7;
         u2 = tmp8 - tmp7;
       }
     }
 
     if (tmp4 <= std::abs(tmp3)) {
       if ((tmp3 < 0) == (tip < 0))
         u2 = +SMALL;
       else
         u1 = -SMALL;
     }
   }
 
   return Range(sgn(u1) / std::sqrt(sqr(u1) + delta2),
                sgn(u2) / std::sqrt(sqr(u2) + delta2));
 }

double ThirdHitPredictionFromCircle::curvature ( const Vector2D & thirdPoint ) const

Definition at line 163 of file ThirdHitPredictionFromCircle.cc.

References delta2, invCenterOnAxis(), FWPFMaths::sgn(), funct::sqr(), and mathSSE::sqrt().

 {
   double invDist = invCenterOnAxis(p2);
   double invDist2 = sqr(invDist);
   double curv = std::sqrt(invDist2 / (1. + invDist2 * delta2));
   return sgn(invDist) * curv;
 }

ThirdHitPredictionFromCircle::Scalar ThirdHitPredictionFromCircle::invCenterOnAxis ( const Vector2D & thirdPoint ) const

private

Definition at line 153 of file ThirdHitPredictionFromCircle.cc.

References a, axis, b, center, diffTreeTool::diff, Basic2DVector< T >::mag(), p1, Basic2DVector< T >::x(), and Basic2DVector< T >::y().

Referenced by curvature(), and transverseIP().

 {
   Vector2D del = p2 - p1;
   Vector2D axis2 = Vector2D(-del.y(), del.x()) / del.mag();
   Vector2D diff = p1 + 0.5f * del - center;
   Scalar a = diff.y() * axis2.x() - diff.x() * axis2.y();
   Scalar b = axis.y() * axis2.x() - axis.x() * axis2.y();
   return b / a;
 }

ThirdHitPredictionFromCircle::Range ThirdHitPredictionFromCircle::operator()	(	Range	curvature,
		float	radius
	)		const

Definition at line 76 of file ThirdHitPredictionFromCircle.cc.

References M_PI, phi(), theTolerance, and unlikely.

 {
   float phi1 = phi(curvature.second, radius);
   float phi2 = phi(curvature.first, radius);
 
   while(unlikely(phi2 <  phi1)) phi2 += float(2. * M_PI); 
 
   return Range(phi1 * radius - theTolerance, phi2 * radius + theTolerance);
 }

float ThirdHitPredictionFromCircle::phi	(	float	curvature,
		float	radius
	)		const

Definition at line 36 of file ThirdHitPredictionFromCircle.cc.

References abs, axis, Basic2DVector< T >::barePhi(), center, funct::cos(), delta2, alignCSCRings::e, f, M_PI, Basic2DVector< T >::mag2(), Basic2DVector< T >::phi(), CosmicsPD_Skims::radius, FWPFMaths::sgn(), funct::sqr(), mathSSE::sqrt(), and unlikely.

Referenced by operator()(), and ThirdHitPredictionFromCircle::HelixRZ::rAtZ().

 {
   float phi;
   if (unlikely(std::abs(curvature) < float(1.0e-5))) {
     float cos = (center * axis) / radius;
     phi = axis.phi() - clamped_acos(cos);
   } else {
     float sign = sgn(curvature);
     float radius2 = sqr(1.0f / curvature);
     float orthog = clamped_sqrt(radius2 - delta2);
     Basic2DVector<float> lcenter = Basic2DVector<float>(center) - sign * orthog *  Basic2DVector<float>(axis);
     float rc2 = lcenter.mag2();
     float cos = (rc2 + sqr(radius) - radius2) /
       (2.f *std:: sqrt(rc2) * radius);
     phi = lcenter.barePhi() + sign * clamped_acos(cos);
  }
 
   while(unlikely(phi >= float(M_PI))) phi -= float(2. * M_PI);
   while(unlikely(phi < -float(M_PI))) phi += float(2. * M_PI);
 
   return phi;
 }

double ThirdHitPredictionFromCircle::transverseIP ( const Vector2D & thirdPoint ) const

Definition at line 171 of file ThirdHitPredictionFromCircle.cc.

References abs, axis, center, delta2, alignCSCRings::e, invCenterOnAxis(), mag(), CosmicsPD_Skims::radius, funct::sqr(), mathSSE::sqrt(), and unlikely.

Referenced by curvature().

 {
   double invDist = invCenterOnAxis(p2);
   if (unlikely(std::abs(invDist) < 1.0e-5))
     return std::abs(p2 * axis);
   else {
     double dist = 1.0 / invDist;
     double radius = std::sqrt(sqr(dist) + delta2);
     return std::abs((center + axis * dist).mag() - radius);
   }
 }