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//--------------------------------------------------------------------------------------------------
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// $Id: Helix.h,v 1.3 2009/07/20 03:12:22 loizides Exp $
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//
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// Class Helix
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//
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// Implementation of a general helix class with a set of tools for working with objects like
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// tracks and finding intersections (vertices).
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//
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// Author: C.Paus (stolen and adjusted from CDF implementation of Kurt Rinnert,
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// therefore not all our coding conventions fulfilled)
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//--------------------------------------------------------------------------------------------------
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#ifndef MITCOMMON_MATHTOOLS_HELIX_H
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#define MITCOMMON_MATHTOOLS_HELIX_H
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#include <TVector.h>
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#include <TVector3.h>
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#include "MitCommon/MathTools/interface/Angle.h"
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namespace mithep {
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class Helix {
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public:
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// Constructor
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inline Helix();
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// Construct a helix in various ways
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Helix(const TVector3 &mom, const TVector3 &pos, double q, double Field);
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inline Helix(const Helix &right);
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inline Helix(double cotTheta, double curvature, double z0, double d0, Angle phi0);
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static Helix create(const TVector & v);
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// Destructor
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virtual ~Helix();
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// Operators
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inline const Helix & operator=(const Helix &right);
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bool operator == (const Helix & right) const;
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bool operator != (const Helix & right) const;
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inline void SetParameters(const TVector &p);
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inline const TVector &Parameters() const;
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inline void SetCotTheta(double cotTheta);
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inline void SetCurvature(double curvature);
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inline void SetZ0(double z0);
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inline void SetD0(double d0);
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inline void SetPhi0(Angle phi0);
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virtual TVector3 Position(double s = 0.0) const;
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virtual TVector3 Direction(double s = 0.0) const;
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// the second derivative of the helix vs (three-dimensional) path length
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virtual TVector3 SecondDerivative(double s = 0.0) const;
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// Get pathlength at fixed rho=sqrt(x^2 + y^2)
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virtual double PathLengthAtRhoEquals(double rho) const;
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// Get certain parameters as a function of two-dimensional R.
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Angle PhiAtR(double r) const;
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double ZAtR(double r) const;
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double L2DAtR(double r) const;
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double CosAlphaAtR(double r) const;
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double InverseRadius() const;
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double Radius() const;
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SignedAngle TurningAngle(double s) const; // turning angle as function of path length
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double Curvature() const;
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double Helicity() const; // helicity, positive = counterclockwise
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double CotTheta() const;
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Angle Phi0() const;
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double D0() const;
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double Z0() const;
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double SignLz() const;
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double SinPhi0() const;
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double CosPhi0() const;
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double SinTheta() const;
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double CosTheta() const;
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static unsigned int ParameterSpaceSize() { return 5; }
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//============================================================================================
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// KCDF: analytical computation of helix/plane intersection.
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//
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// What we really compute is the intersection of a line and a circle (projected helix)
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// in the x-y plane.
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//
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// >>>>>>>>>> W A R N I N G W A R N I N G W A R N I N G <<<<<<<<<<
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// > <
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// > We assume the plane to be parallel or perpendicular <
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// > to the z axis (i.e. the B-field), <
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// > since otherwise there is no analytical solution. (One would end up <
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// > with an equation of type cos(alpha) == alpha.) <
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// > Although we know this assumption doesn´t hold exactly, we think it <
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// > is a reasonable first approximation. <
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// > In cases when our assumption has to be dropped, one can use the <
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// > intersection point computed here as a *good* starting point of a <
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// > numerical method, or one uses another analytical method to compute <
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// > the intersection of the tangent line at the point and the plane. <
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// > We plan to use one of these approaches in the near future, but <
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// > this is NOT YET IMPLEMENTED! <
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// > For the time being, we invoke the old numerical <
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// > Trajectory::newIntersectionWith in such circumstances. <
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// > <
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// >>>>>>>>>> W A R N I N G W A R N I N G W A R N I N G <<<<<<<<<<
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//
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// Kurt Rinnert, 08/31/1998
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//============================================================================================
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//Location* newIntersectionWith(const HepPlane3D& plane) const;
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private:
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// This is the Helix
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double fCotTheta;
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double fCurvature;
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double fZ0;
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double fD0;
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Angle fPhi0;
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// This is the cache
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mutable TVector *fVParameters;
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mutable bool fIsStale;
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mutable double fSinPhi0;
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mutable double fCosPhi0;
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mutable double fSinTheta;
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mutable double fCosTheta;
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mutable double fS;
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mutable double fAa;
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mutable double fSs;
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mutable double fCc;
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mutable bool fCenterIsValid; //needed by newIntersectionWith KR
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mutable double fMx;
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mutable double fMy;
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// Needed whenever fSinPhi0, fCosPh0, fSinTheta, or fCosTheta is used.
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inline void fRefreshCache() const;
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// Needed whenever fSs or fCc are used.
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inline void fCacheSinesAndCosines(double s) const;
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ClassDef(Helix, 0) // General helix class
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};
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::fRefreshCache() const
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{
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// Update fSinTheta,fCosTheta,fSinPhi0, and fCosPhi0
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if (fIsStale) {
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fIsStale=false;
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double theta;
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if ( fCotTheta==0.0 ) {
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theta = M_PI/2.0;
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}
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else {
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theta=atan(1.0/fCotTheta);
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if (theta<0.0) theta+=M_PI;
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}
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if (theta==0.0) {
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fSinTheta=0.0;
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fCosTheta=1.0;
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}
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else {
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fCosTheta=cos(theta);
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fSinTheta=sqrt(1-fCosTheta*fCosTheta);
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}
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if (fPhi0==0.0) {
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fSinPhi0=0.0;
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fCosPhi0=1.0;
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}
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else {
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fCosPhi0 = cos(fPhi0);
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fSinPhi0 = sqrt(1.0-fCosPhi0*fCosPhi0);
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if (fPhi0>M_PI) fSinPhi0 = -fSinPhi0;
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}
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}
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::fCacheSinesAndCosines(double s) const
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{
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// Update fS, fAa, fSs, and fCc if the arclength has changed.
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fRefreshCache();
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if (fS!=s){
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fS=s;
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fAa=2.0*fS*fCurvature*fSinTheta;
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if (fAa==0.0) {
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fSs=0.0;
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fCc=1.0;
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}
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else {
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fSs=sin(fAa);
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fCc=cos(fAa);
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}
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}
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}
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//--------------------------------------------------------------------------------------------------
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inline
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mithep::Helix::Helix() :
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fCotTheta(0.0),
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fCurvature(0.0),
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fZ0(0.0),
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fD0(0.0),
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fPhi0(0.0),
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fVParameters(0),
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fIsStale(1),
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fSinPhi0(2),
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fCosPhi0(2),
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fSinTheta(2),
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fCosTheta(2),
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fS(-999.999),
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fAa(2),
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fSs(2),
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fCc(2),
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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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//--------------------------------------------------------------------------------------------------
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inline
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mithep::Helix::Helix(const Helix &right) :
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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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fVParameters(0),
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fIsStale(right.fIsStale),
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fSinPhi0(right.fSinPhi0),
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fCosPhi0(right.fCosPhi0),
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fSinTheta(right.fSinTheta),
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fCosTheta(right.fCosTheta),
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fS(right.fS),
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fAa(right.fAa),
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fSs(right.fSs),
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fCc(right.fCc),
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fCenterIsValid(right.fCenterIsValid),
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fMx(right.fMx),
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fMy(right.fMy)
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{
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if (right.fVParameters)
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fVParameters=new TVector(*(right.fVParameters));
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}
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//--------------------------------------------------------------------------------------------------
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inline
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mithep::Helix::Helix(double cotTheta,double curvature,double z0,double d0, Angle phi0) :
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fCotTheta(cotTheta),
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fCurvature(curvature),
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fZ0(z0),
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fD0(d0),
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fPhi0(phi0),
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fVParameters(0),
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fIsStale(1),
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fSinPhi0(2),
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fCosPhi0(2),
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fSinTheta(2),
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fCosTheta(2),
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fS(-999.999),
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fAa(2),
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fSs(2),
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fCc(2),
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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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//--------------------------------------------------------------------------------------------------
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inline
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const mithep::Helix & mithep::Helix::operator=(const mithep::Helix &right)
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{
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// Assign helix and cache
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if (this != &right) {
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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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fIsStale= right.fIsStale;
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fSinTheta=right.fSinTheta;
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fCosTheta=right.fCosTheta;
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fSinPhi0=right.fSinPhi0;
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fCosPhi0=right.fCosPhi0;
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fS=right.fS;
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fAa=right.fAa;
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fSs=right.fSs;
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fCc=right.fCc;
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if (fVParameters)
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delete fVParameters;
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fVParameters=0;
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if (right.fVParameters)
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fVParameters = new TVector(*(right.fVParameters));
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fCenterIsValid = right.fCenterIsValid;
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fMx = right.fMx;
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fMy = right.fMy;
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}
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return *this;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::SetCotTheta(double cotTheta)
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{
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fCotTheta=cotTheta;
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fIsStale=true;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::SetZ0(double z0)
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{
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fZ0 = z0;
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fIsStale=true;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::SetCurvature(double curvature)
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{
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fCurvature=curvature;
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fIsStale=true;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::SetD0(double d0)
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{
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fD0=d0;
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fIsStale=true;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::SetPhi0(Angle phi0)
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{
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fPhi0=phi0;
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fIsStale=true;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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void mithep::Helix::SetParameters(const TVector &p)
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{
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// Check we're getting a sensible vector.
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if (p.GetNrows() < 5) {
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return;
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}
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SetCotTheta(p[0]);
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SetCurvature(p[1]);
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SetZ0(p[2]);
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SetD0(p[3]);
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SetPhi0(p[4]);
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fIsStale = true;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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const TVector & mithep::Helix::Parameters() const
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{
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if (!fVParameters)
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fVParameters = new TVector(5);
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(*fVParameters)(1)=CotTheta();
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(*fVParameters)(2)=Curvature();
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(*fVParameters)(3)=Z0();
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(*fVParameters)(4)=D0();
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(*fVParameters)(5)=Phi0();
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return *fVParameters;;
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}
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//--------------------------------------------------------------------------------------------------
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inline
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mithep::Helix mithep::Helix::create(const TVector & v)
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{
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return mithep::Helix(v(1),v(2),v(3),v(4),v(5));
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}
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#endif
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