/************************************************************************** * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. * * * * Author: The ALICE Off-line Project. * * Contributors are mentioned in the code where appropriate. * * * * Permission to use, copy, modify and distribute this software and its * * documentation strictly for non-commercial purposes is hereby granted * * without fee, provided that the above copyright notice appears in all * * copies and that both the copyright notice and this permission notice * * appear in the supporting documentation. The authors make no claims * * about the suitability of this software for any purpose. It is * * provided "as is" without express or implied warranty. * **************************************************************************/ /* $Id$ */ //------------------------------------------------------------------------- // Implementation of the AliHelix class // Origin: Marian Ivanov, CERN, marian.ivanov@cern.ch //------------------------------------------------------------------------- #include "AliHelix.h" #include "AliKalmanTrack.h" #include "AliExternalTrackParam.h" #include "TMath.h" ClassImp(AliHelix) //_______________________________________________________________________ AliHelix::AliHelix() { // // Default constructor // for (Int_t i =0;i<9;i++) fHelix[i]=0; } //_______________________________________________________________________ AliHelix::AliHelix(const AliHelix &t):TObject(t){ // // for (Int_t i=0;i<9;i++) fHelix[i]=t.fHelix[i]; } AliHelix::AliHelix(const AliKalmanTrack &t) { // // Double_t alpha,x,cs,sn; t.GetExternalParameters(x,fHelix); alpha=t.GetAlpha(); // //circle parameters fHelix[4]=fHelix[4]/t.GetConvConst(); // C cs=TMath::Cos(alpha); sn=TMath::Sin(alpha); Double_t xc, yc, rc; rc = 1/fHelix[4]; xc = x-fHelix[2]*rc; yc = fHelix[0]+TMath::Sqrt(1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4])/fHelix[4]; fHelix[6] = xc*cs - yc*sn; fHelix[7] = xc*sn + yc*cs; fHelix[8] = TMath::Abs(rc); // // fHelix[5]=x*cs - fHelix[0]*sn; // x0 fHelix[0]=x*sn + fHelix[0]*cs; // y0 //fHelix[1]= // z0 fHelix[2]=TMath::ASin(fHelix[2]) + alpha; // phi0 //fHelix[3]= // tgl // // fHelix[5] = fHelix[6]; fHelix[0] = fHelix[7]; //fHelix[5]-=TMath::Sin(fHelix[2])/fHelix[4]; //fHelix[0]+=TMath::Cos(fHelix[2])/fHelix[4]; } AliHelix::AliHelix(const AliExternalTrackParam &t) { // // Double_t alpha,x,cs,sn; const Double_t *param =t.GetParameter(); for (Int_t i=0;i<5;i++) fHelix[i]=param[i]; x = t.X(); alpha=t.Alpha(); // //circle parameters fHelix[4]=fHelix[4]/AliKalmanTrack::GetConvConst(); // C cs=TMath::Cos(alpha); sn=TMath::Sin(alpha); Double_t xc, yc, rc; rc = 1/fHelix[4]; xc = x-fHelix[2]*rc; yc = fHelix[0]+TMath::Sqrt(1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4])/fHelix[4]; fHelix[6] = xc*cs - yc*sn; fHelix[7] = xc*sn + yc*cs; fHelix[8] = TMath::Abs(rc); // // fHelix[5]=x*cs - fHelix[0]*sn; // x0 fHelix[0]=x*sn + fHelix[0]*cs; // y0 //fHelix[1]= // z0 fHelix[2]=TMath::ASin(fHelix[2]) + alpha; // phi0 //fHelix[3]= // tgl // // fHelix[5] = fHelix[6]; fHelix[0] = fHelix[7]; //fHelix[5]-=TMath::Sin(fHelix[2])/fHelix[4]; //fHelix[0]+=TMath::Cos(fHelix[2])/fHelix[4]; } AliHelix::AliHelix(Double_t x[3], Double_t p[3], Double_t charge, Double_t conversion) { // // // Double_t pt = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]); if (TMath::Abs(conversion)<0.00000001) conversion = AliKalmanTrack::GetConvConst(); // // fHelix[4] = charge/(conversion*pt); // C fHelix[3] = p[2]/pt; // tgl // Double_t xc, yc, rc; rc = 1/fHelix[4]; xc = x[0] -rc*p[1]/pt; yc = x[1] +rc*p[0]/pt; // fHelix[5] = x[0]; // x0 fHelix[0] = x[1]; // y0 fHelix[1] = x[2]; // z0 // fHelix[6] = xc; fHelix[7] = yc; fHelix[8] = TMath::Abs(rc); // fHelix[5]=xc; fHelix[0]=yc; // if (TMath::Abs(p[1])charge*x[0]) fHelix[2] = -fHelix[2]; } } void AliHelix::GetMomentum(Double_t phase, Double_t p[4],Double_t conversion) { // return momentum at given phase Double_t x[3],g[3],gg[3]; Evaluate(phase,x,g,gg); if (TMath::Abs(conversion)<0.0001) conversion = AliKalmanTrack::GetConvConst(); Double_t mt = TMath::Sqrt(g[0]*g[0]+g[1]*g[1]); p[0] = fHelix[8]*g[0]/(mt*conversion); p[1] = fHelix[8]*g[1]/(mt*conversion); p[2] = fHelix[8]*g[2]/(mt*conversion); } void AliHelix::GetAngle(Double_t t1, AliHelix &h, Double_t t2, Double_t angle[3]) { // // // Double_t x1[3],g1[3],gg1[3]; Double_t x2[3],g2[3],gg2[3]; Evaluate(t1,x1,g1,gg1); h.Evaluate(t2,x2,g2,gg2); // Double_t norm1r = g1[0]*g1[0]+g1[1]*g1[1]; Double_t norm1 = TMath::Sqrt(norm1r+g1[2]*g1[2]); norm1r = TMath::Sqrt(norm1r); // Double_t norm2r = g2[0]*g2[0]+g2[1]*g2[1]; Double_t norm2 = TMath::Sqrt(norm2r+g2[2]*g2[2]); norm2r = TMath::Sqrt(norm2r); // angle[0] = (g1[0]*g2[0]+g1[1]*g2[1])/(norm1r*norm2r); // angle in phi projection if (TMath::Abs(angle[0])<1.) angle[0] = TMath::ACos(angle[0]); else angle[0]=0; // angle[1] = ((norm1r*norm2r)+g1[2]*g2[2])/(norm1*norm2); // angle in rz projection if (TMath::Abs(angle[1])<1.) angle[1] = TMath::ACos(angle[1]); else angle[1]=0; angle[2] = (g1[0]*g2[0]+g1[1]*g2[1]+g1[2]*g2[2])/(norm1*norm2); //3D angle if (TMath::Abs(angle[2])<1.) angle[2] = TMath::ACos(angle[2]); else angle[2]=0; } void AliHelix::Evaluate(Double_t t, Double_t r[3], //radius vector Double_t g[3], //first defivatives Double_t gg[3]) //second derivatives { //-------------------------------------------------------------------- // Calculate position of a point on a track and some derivatives at given phase //-------------------------------------------------------------------- Double_t phase=fHelix[4]*t+fHelix[2]; Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); //r[0] = fHelix[5] + (sn - fHelix[6])/fHelix[4]; //r[1] = fHelix[0] - (cs - fHelix[7])/fHelix[4]; r[0] = fHelix[5] + sn/fHelix[4]; r[1] = fHelix[0] - cs/fHelix[4]; r[2] = fHelix[1] + fHelix[3]*t; g[0] = cs; g[1]=sn; g[2]=fHelix[3]; gg[0]=-fHelix[4]*sn; gg[1]=fHelix[4]*cs; gg[2]=0.; } Double_t AliHelix::GetPhase(Double_t x, Double_t y ) { // //calculate helix param at given x,y point // Double_t phase = (x-fHelix[5])*fHelix[4]; if (TMath::Abs(phase)>=1) phase = TMath::Sign(0.99999999999,phase); phase = TMath::ASin(phase); if ( ( ( fHelix[0]-y)*fHelix[4]) < 0.) { if (phase>0) phase = TMath::Pi()-phase; else phase = -(TMath::Pi()+phase); } if ( (phase-fHelix[2])>TMath::Pi()) phase = phase-2.*TMath::Pi(); if ( (phase-fHelix[2])<-TMath::Pi()) phase = phase+2.*TMath::Pi(); Double_t t = (phase-fHelix[2])/fHelix[4]; // Double_t r[3]; //Evaluate(t,r); //if ( (TMath::Abs(r[0]-x)>0.01) || (TMath::Abs(r[1]-y)>0.01)){ // Double_t phase = (x-fHelix[5])*fHelix[4]; // printf("problem\n"); //} return t; } Int_t AliHelix::GetPhase(Double_t /*r0*/, Double_t * /*t[2]*/) { // //calculate helix param at given r point - return nearest point () // // not implemented yet return 0; } Double_t AliHelix::GetPhaseZ(Double_t z0) { // // return (z0-fHelix[1])/fHelix[3]; } Int_t AliHelix::GetRPHIintersections(AliHelix &h, Double_t phase[2][2], Double_t ri[2], Double_t cut) { //-------------------------------------------------------------------- // This function returns phase vectors with intesection between helix (0, 1 or 2) // in x-y plane projection //-------------------------------------------------------------------- // // Double_t * c1 = &fHelix[6]; //Double_t * c2 = &(h.fHelix[6]); // Double_t c1[3] = {fHelix[5],fHelix[0],fHelix[8]}; Double_t c1[3] = {0,0,fHelix[8]}; Double_t c2[3] = {h.fHelix[5]-fHelix[5],h.fHelix[0]-fHelix[0],h.fHelix[8]}; Double_t d = TMath::Sqrt(c2[0]*c2[0]+c2[1]*c2[1]); if (d<0.000000000001) return 0; // Double_t x0[2]; Double_t y0[2]; // if ( d>=(c1[2]+c2[2])){ if (d>=(c1[2]+c2[2]+cut)) return 0; x0[0] = (d+c1[2]-c2[2])*c2[0]/(2*d)+ fHelix[5]; y0[0] = (d+c1[2]-c2[2])*c2[1]/(2*d)+ fHelix[0]; // return 0; phase[0][0] = GetPhase(x0[0],y0[0]); phase[0][1] = h.GetPhase(x0[0],y0[0]); ri[0] = x0[0]*x0[0]+y0[0]*y0[0]; return 1; } if ( (d+c2[2])=(c1[2]+c2[2])){ if (d>=(c1[2]+c2[2]+cut)) return 0; x0[0] = c1[0]+ (d+c1[2]-c2[2])*(c2[0]-c1[0])/(2*d); y0[0] = c1[1]+ (d+c1[2]-c2[2])*(c2[1]-c1[1])/(2*d); return 0; phase[0][0] = GetPhase(x0[0],y0[0]); phase[0][1] = h.GetPhase(x0[0],y0[0]); ri[0] = x0[0]*x0[0]+y0[0]*y0[0]; return 1; } if ( (d+c2[2])cut)||(TMath::Abs(yy2-yy)>cut)){ // printf("problem\n"); //} ri[0] = xx*xx+yy*yy; return 1; } if ( (d+c1[2])cut)||(TMath::Abs(yy2-yy)>cut)){ // printf("problem\n"); //} ri[0] = xx*xx+yy*yy; return 1; } Double_t d1 = (d*d+c1[2]*c1[2]-c2[2]*c2[2])/(2.*d); Double_t v1 = c1[2]*c1[2]-d1*d1; if (v1<0) return 0; v1 = TMath::Sqrt(v1); // x0[0] = c1[0]+ ((c2[0]-c1[0])*d1-(c1[1]-c2[1])*v1)/d; y0[0] = c1[1]+ ((c2[1]-c1[1])*d1+(c1[0]-c2[0])*v1)/d; // x0[1] = c1[0]+ ((c2[0]-c1[0])*d1+(c1[1]-c2[1])*v1)/d; y0[1] = c1[1]+ ((c2[1]-c1[1])*d1-(c1[0]-c2[0])*v1)/d; // for (Int_t i=0;i<2;i++){ phase[i][0] = GetPhase(x0[i],y0[i]); phase[i][1] = h.GetPhase(x0[i],y0[i]); ri[i] = x0[i]*x0[i]+y0[i]*y0[i]; } return 2; } */ Int_t AliHelix::LinearDCA(AliHelix &h, Double_t &t1, Double_t &t2, Double_t &R, Double_t &dist) { // // // find intersection using linear approximation Double_t r1[3],g1[3],gg1[3]; Double_t r2[3],g2[3],gg2[3]; // Evaluate(t1,r1,g1,gg1); h.Evaluate(t2,r2,g2,gg2); // Double_t g1_2 = g1[0]*g1[0] +g1[1]*g1[1] +g1[2]*g1[2]; Double_t g2_2 = g2[0]*g2[0] +g2[1]*g2[1] +g2[2]*g2[2]; Double_t g1x2 = g1[0]*g2[0] +g1[1]*g2[1] +g1[2]*g2[2]; Double_t det = g1_2*g2_2 - g1x2*g1x2; // if (TMath::Abs(det)>0){ // Double_t r1g1 = r1[0]*g1[0] +r1[1]*g1[1] +r1[2]*g1[2]; Double_t r2g1 = r2[0]*g1[0] +r2[1]*g1[1] +r2[2]*g1[2]; Double_t r1g2 = r1[0]*g2[0] +r1[1]*g2[1] +r1[2]*g2[2]; Double_t r2g2 = r2[0]*g2[0] +r2[1]*g2[1] +r2[2]*g2[2]; // Double_t dt = - ( g2_2*(r1g1-r2g1) - g1x2*(r1g2-r2g2)) / det; Double_t dp = - ( g1_2*(r2g2-r1g2) - g1x2*(r2g1-r1g1)) / det; // t1+=dt; t2+=dp; Evaluate(t1,r1); h.Evaluate(t2,r2); // dist = (r1[0]-r2[0])*(r1[0]-r2[0])+ (r1[1]-r2[1])*(r1[1]-r2[1])+ (r1[2]-r2[2])*(r1[2]-r2[2]); R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4.; } return 0; } /* Int_t AliHelix::ParabolicDCA(AliHelix&h, //helixes Double_t &t1, Double_t &t2, Double_t &R, Double_t &dist, Int_t iter) { // // // find intersection using linear fit Double_t r1[3],g1[3],gg1[3]; Double_t r2[3],g2[3],gg2[3]; // Evaluate(t1,r1,g1,gg1); h.Evaluate(t2,r2,g2,gg2); // Double_t dx2=1.; Double_t dy2=1.; Double_t dz2=1.; // Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; // iter++; while (iter--) { Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + (g1[1]*g1[1] - dy*gg1[1])/dy2 + (g1[2]*g1[2] - dz*gg1[2])/dz2; Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + (g2[1]*g2[1] + dy*gg2[1])/dy2 + (g2[2]*g2[2] + dz*gg2[2])/dz2; Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); Double_t det=h11*h22-h12*h12; Double_t dt1,dt2; if (TMath::Abs(det)<1.e-33) { //(quasi)singular Hessian dt1=-gt1; dt2=-gt2; } else { dt1=-(gt1*h22 - gt2*h12)/det; dt2=-(h11*gt2 - h12*gt1)/det; } if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} //check delta(phase1) ? //check delta(phase2) ? if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { //if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2) // Warning("GetDCA"," stopped at not a stationary point !\n"); Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det); if (lmb < 0.) //Warning("GetDCA"," stopped at not a minimum !\n"); break; } Double_t dd=dm; for (Int_t div=1 ; ; div*=2) { Evaluate(t1+dt1,r1,g1,gg1); h.Evaluate(t2+dt2,r2,g2,gg2); dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; if (dd512) { //Warning("GetDCA"," overshoot !\n"); break; } } dm=dd; t1+=dt1; t2+=dt2; } Evaluate(t1,r1,g1,gg1); h.Evaluate(t2,r2,g2,gg2); // dist = (r1[0]-r2[0])*(r1[0]-r2[0])+ (r1[1]-r2[1])*(r1[1]-r2[1])+ (r1[2]-r2[2])*(r1[2]-r2[2]); R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4; } */ Int_t AliHelix::ParabolicDCA(AliHelix&h, //helixes Double_t &t1, Double_t &t2, Double_t &R, Double_t &dist, Int_t iter) { // // // find intersection using linear fit Double_t r1[3],g1[3],gg1[3]; Double_t r2[3],g2[3],gg2[3]; // Evaluate(t1,r1,g1,gg1); h.Evaluate(t2,r2,g2,gg2); // Double_t dx2=1.; Double_t dy2=1.; Double_t dz2=1.; // Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; // iter++; while (iter--) { Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + (g1[1]*g1[1] - dy*gg1[1])/dy2 + (g1[2]*g1[2] - dz*gg1[2])/dz2; Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + (g2[1]*g2[1] + dy*gg2[1])/dy2 + (g2[2]*g2[2] + dz*gg2[2])/dz2; Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); Double_t det=h11*h22-h12*h12; Double_t dt1,dt2; if (TMath::Abs(det)<1.e-33) { //(quasi)singular Hessian dt1=-gt1; dt2=-gt2; } else { dt1=-(gt1*h22 - gt2*h12)/det; dt2=-(h11*gt2 - h12*gt1)/det; } if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} //if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) // if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { // break; // } Double_t dd=dm; for (Int_t div=1 ; div<512 ; div*=2) { Evaluate(t1+dt1,r1,g1,gg1); h.Evaluate(t2+dt2,r2,g2,gg2); dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; if (dd512) { break; } } dm=dd; t1+=dt1; t2+=dt2; } Evaluate(t1,r1,g1,gg1); h.Evaluate(t2,r2,g2,gg2); // dist = (r1[0]-r2[0])*(r1[0]-r2[0])+ (r1[1]-r2[1])*(r1[1]-r2[1])+ (r1[2]-r2[2])*(r1[2]-r2[2]); R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4; return 0; }