--- /dev/null
+/**************************************************************************
+ * 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 "TMath.h"
+ClassImp(AliHelix)
+
+
+//_______________________________________________________________________
+AliHelix::AliHelix()
+{
+ //
+ // Default constructor
+ //
+ for (Int_t i =0;i<9;i++) fHelix[i]=0;
+}
+
+//_______________________________________________________________________
+AliHelix::AliHelix(const AliHelix &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(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])<TMath::Abs(p[0])){
+ fHelix[2]=TMath::ASin(p[1]/pt);
+ if (charge*yc<charge*x[1]) fHelix[2] = TMath::Pi()-fHelix[2];
+ }
+ else{
+ fHelix[2]=TMath::ACos(p[0]/pt);
+ if (charge*xc>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] = TMath::ACos((g1[0]*g2[0]+g1[1]*g2[1])/(norm1r*norm2r)); // angle in phi projection
+ angle[1] = TMath::ACos(((norm1r*norm2r)+g1[2]*g2[2])/(norm1*norm2)); // angle in rz projection
+ angle[2] = TMath::ACos((g1[0]*g2[0]+g1[1]*g2[1]+g1[2]*g2[2])/(norm1*norm2)); //3D angle
+
+
+
+
+}
+
+
+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]);
+ //
+ 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]){
+ if ( (d+c2[2])+cut<c1[2]) return 0;
+ //
+ Double_t xx = c2[0]+ c2[0]*c2[2]/d+ fHelix[5];
+ Double_t yy = c2[1]+ c2[1]*c2[2]/d+ fHelix[0];
+ phase[0][1] = h.GetPhase(xx,yy);
+ //
+ Double_t xx2 = c2[0]*c1[2]/d+ fHelix[5];
+ Double_t yy2 = c2[1]*c1[2]/d+ fHelix[0];
+ phase[0][0] = GetPhase(xx2,yy2);
+ ri[0] = xx*xx+yy*yy;
+ return 1;
+ }
+
+ if ( (d+c1[2])<c2[2]){
+ if ( (d+c1[2])+cut<c2[2]) return 0;
+ //
+ Double_t xx = -c2[0]*c1[2]/d+ fHelix[5];
+ Double_t yy = -c2[1]*c1[2]/d+ fHelix[0];
+ phase[0][1] = GetPhase(xx,yy);
+ //
+ Double_t xx2 = c2[0]- c2[0]*c2[2]/d+ fHelix[5];
+ Double_t yy2 = c2[1]- c2[1]*c2[2]/d+ fHelix[0];
+ phase[0][0] = h.GetPhase(xx2,yy2);
+ 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] = (c2[0]*d1+c2[1]*v1)/d + fHelix[5];
+ y0[0] = (c2[1]*d1-c2[0]*v1)/d + fHelix[0];
+ //
+ x0[1] = (c2[0]*d1-c2[1]*v1)/d + fHelix[5];
+ y0[1] = (c2[1]*d1+c2[0]*v1)/d + fHelix[0];
+ //
+ 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::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 d = TMath::Sqrt((c1[0]-c2[0])*(c1[0]-c2[0])+(c1[1]-c2[1])*(c1[1]-c2[1]));
+ //
+ 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] = 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])<c1[2]){
+ if ( (d+c2[2])+cut<c1[2]) return 0;
+ //
+ Double_t xx = c2[0]+ (c2[0]-c1[0])*c2[2]/d;
+ Double_t yy = c2[1]+ (c2[1]-c1[1])*c2[2]/d;
+ phase[0][1] = h.GetPhase(xx,yy);
+ //
+ Double_t xx2 = c1[0]- (c1[0]-c2[0])*c1[2]/d;
+ Double_t yy2 = c1[1]- (c1[1]-c2[1])*c1[2]/d;
+ phase[0][0] = GetPhase(xx2,yy2);
+ //if ( (TMath::Abs(xx2-xx)>cut)||(TMath::Abs(yy2-yy)>cut)){
+ // printf("problem\n");
+ //}
+ ri[0] = xx*xx+yy*yy;
+ return 1;
+ }
+
+ if ( (d+c1[2])<c2[2]){
+ if ( (d+c1[2])+cut<c2[2]) return 0;
+ //
+ Double_t xx = c1[0]+ (c1[0]-c2[0])*c1[2]/d;
+ Double_t yy = c1[1]+ (c1[1]-c2[1])*c1[2]/d;
+ phase[0][1] = GetPhase(xx,yy);
+ //
+ Double_t xx2 = c2[0]- (c2[0]-c1[0])*c2[2]/d;
+ Double_t yy2 = c2[1]- (c2[1]-c1[1])*c2[2]/d;
+ phase[0][0] = h.GetPhase(xx2,yy2);
+ //if ( (TMath::Abs(xx2-xx)>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 (dd<dm) break;
+ dt1*=0.5; dt2*=0.5;
+ if (div>512) {
+ //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 (dd<dm) break;
+ dt1*=0.5; dt2*=0.5;
+ if (div==0){
+ div =1;
+ }
+ if (div>512) {
+ 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;
+
+}
+