CA tracker added to compilation
[u/mrichter/AliRoot.git] / STEER / AliExternalTrackParam.cxx
CommitLineData
51ad6848 1/**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
3 * *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
6 * *
7 * Permission to use, copy, modify and distribute this software and its *
8 * documentation strictly for non-commercial purposes is hereby granted *
9 * without fee, provided that the above copyright notice appears in all *
10 * copies and that both the copyright notice and this permission notice *
11 * appear in the supporting documentation. The authors make no claims *
12 * about the suitability of this software for any purpose. It is *
13 * provided "as is" without express or implied warranty. *
14 **************************************************************************/
15
16/* $Id$ */
17
18///////////////////////////////////////////////////////////////////////////////
19// //
49d13e89 20// Implementation of the external track parameterisation class. //
51ad6848 21// //
49d13e89 22// This parameterisation is used to exchange tracks between the detectors. //
23// A set of functions returning the position and the momentum of tracks //
24// in the global coordinate system as well as the track impact parameters //
25// are implemented.
26// Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
51ad6848 27///////////////////////////////////////////////////////////////////////////////
4b189f98 28#include <TMatrixDSym.h>
d46683db 29#include <TPolyMarker3D.h>
30#include <TVector3.h>
31
51ad6848 32#include "AliExternalTrackParam.h"
58e536c5 33#include "AliVVertex.h"
6c94f330 34#include "AliLog.h"
51ad6848 35
36ClassImp(AliExternalTrackParam)
37
ed5f2849 38Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
39
51ad6848 40//_____________________________________________________________________________
90e48c0c 41AliExternalTrackParam::AliExternalTrackParam() :
4f6e22bd 42 AliVTrack(),
90e48c0c 43 fX(0),
c9ec41e8 44 fAlpha(0)
51ad6848 45{
90e48c0c 46 //
47 // default constructor
48 //
c9ec41e8 49 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
50 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 51}
52
6c94f330 53//_____________________________________________________________________________
54AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
4f6e22bd 55 AliVTrack(track),
6c94f330 56 fX(track.fX),
57 fAlpha(track.fAlpha)
58{
59 //
60 // copy constructor
61 //
62 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
63 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
64}
65
def9660e 66//_____________________________________________________________________________
67AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
68{
69 //
70 // assignment operator
71 //
72
73 if (this!=&trkPar) {
4f6e22bd 74 AliVTrack::operator=(trkPar);
def9660e 75 fX = trkPar.fX;
76 fAlpha = trkPar.fAlpha;
77
78 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
79 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
80 }
81
82 return *this;
83}
84
51ad6848 85//_____________________________________________________________________________
86AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
87 const Double_t param[5],
90e48c0c 88 const Double_t covar[15]) :
4f6e22bd 89 AliVTrack(),
90e48c0c 90 fX(x),
c9ec41e8 91 fAlpha(alpha)
51ad6848 92{
90e48c0c 93 //
94 // create external track parameters from given arguments
95 //
c9ec41e8 96 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
97 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
51ad6848 98}
99
4f6e22bd 100//_____________________________________________________________________________
101AliExternalTrackParam::AliExternalTrackParam(const AliVTrack *vTrack) :
102 AliVTrack(),
103 fX(0.),
104 fAlpha(0.)
105{
106 //
610e3088 107 // Constructor from virtual track,
108 // This is not a copy contructor !
4f6e22bd 109 //
610e3088 110
111 if (vTrack->InheritsFrom("AliExternalTrackParam")) {
112 AliError("This is not a copy constructor. Use AliExternalTrackParam(const AliExternalTrackParam &) !");
113 AliWarning("Calling the default constructor...");
114 AliExternalTrackParam();
115 return;
116 }
117
892be05f 118 Double_t xyz[3],pxpypz[3],cv[21];
119 vTrack->GetXYZ(xyz);
120 pxpypz[0]=vTrack->Px();
121 pxpypz[1]=vTrack->Py();
122 pxpypz[2]=vTrack->Pz();
4f6e22bd 123 vTrack->GetCovarianceXYZPxPyPz(cv);
124 Short_t sign = (Short_t)vTrack->Charge();
125
126 Set(xyz,pxpypz,cv,sign);
127}
128
90e48c0c 129//_____________________________________________________________________________
da4e3deb 130AliExternalTrackParam::AliExternalTrackParam(Double_t xyz[3],Double_t pxpypz[3],
131 Double_t cv[21],Short_t sign) :
4f6e22bd 132 AliVTrack(),
da4e3deb 133 fX(0.),
134 fAlpha(0.)
4f6e22bd 135{
136 //
137 // constructor from the global parameters
138 //
139
140 Set(xyz,pxpypz,cv,sign);
141}
142
143//_____________________________________________________________________________
144void AliExternalTrackParam::Set(Double_t xyz[3],Double_t pxpypz[3],
145 Double_t cv[21],Short_t sign)
da4e3deb 146{
147 //
148 // create external track parameters from the global parameters
149 // x,y,z,px,py,pz and their 6x6 covariance matrix
150 // A.Dainese 10.10.08
151
152 // Calculate alpha: the rotation angle of the corresponding local system
153 fAlpha = TMath::ATan2(pxpypz[1],pxpypz[0]);
154
155 // Get the vertex of origin and the momentum
156 TVector3 ver(xyz[0],xyz[1],xyz[2]);
157 TVector3 mom(pxpypz[0],pxpypz[1],pxpypz[2]);
158
159 // Rotate to the local coordinate system
160 ver.RotateZ(-fAlpha);
161 mom.RotateZ(-fAlpha);
162
163 // x of the reference plane
164 fX = ver.X();
165
166 Double_t charge = (Double_t)sign;
167
168 fP[0] = ver.Y();
169 fP[1] = ver.Z();
170 fP[2] = TMath::Sin(mom.Phi());
171 fP[3] = mom.Pz()/mom.Pt();
172 fP[4] = TMath::Sign(1/mom.Pt(),charge);
173
174 // Covariance matrix (formulas to be simplified)
175
176 Double_t pt=1./TMath::Abs(fP[4]);
177 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
178 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
179
180 Double_t m00=-sn;// m10=cs;
181 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
182 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
183 Double_t m35=pt, m45=-pt*pt*fP[3];
184
185 m43*=GetSign();
186 m44*=GetSign();
187 m45*=GetSign();
188
189 Double_t cv34 = TMath::Sqrt(cv[3 ]*cv[3 ]+cv[4 ]*cv[4 ]);
190 Double_t a1=cv[13]-cv[9]*(m23*m44+m43*m24)/m23/m43;
191 Double_t a2=m23*m24-m23*(m23*m44+m43*m24)/m43;
192 Double_t a3=m43*m44-m43*(m23*m44+m43*m24)/m23;
193 Double_t a4=cv[14]-2.*cv[9]*m24*m44/m23/m43;
194 Double_t a5=m24*m24-2.*m24*m44*m23/m43;
195 Double_t a6=m44*m44-2.*m24*m44*m43/m23;
196
197 fC[0 ] = cv[0 ]+cv[2 ];
198 fC[1 ] = TMath::Sign(cv34,cv[3 ]/m00);
199 fC[2 ] = cv[5 ];
200 fC[3 ] = (cv[10]/m44-cv[6]/m43)/(m24/m44-m23/m43)/m00;
201 fC[10] = (cv[6]/m00-fC[3 ]*m23)/m43;
202 fC[6 ] = (cv[15]/m00-fC[10]*m45)/m35;
203 fC[4 ] = (cv[12]-cv[8]*m44/m43)/(m24-m23*m44/m43);
204 fC[11] = (cv[8]-fC[4]*m23)/m43;
205 fC[7 ] = cv[17]/m35-fC[11]*m45/m35;
206 fC[5 ] = TMath::Abs((a4-a6*a1/a3)/(a5-a6*a2/a3));
207 fC[14] = TMath::Abs(a1/a3-a2*fC[5]/a3);
208 fC[12] = (cv[9]-fC[5]*m23*m23-fC[14]*m43*m43)/m23/m43;
209 Double_t b1=cv[18]-fC[12]*m23*m45-fC[14]*m43*m45;
210 Double_t b2=m23*m35;
211 Double_t b3=m43*m35;
212 Double_t b4=cv[19]-fC[12]*m24*m45-fC[14]*m44*m45;
213 Double_t b5=m24*m35;
214 Double_t b6=m44*m35;
215 fC[8 ] = (b4-b6*b1/b3)/(b5-b6*b2/b3);
216 fC[13] = b1/b3-b2*fC[8]/b3;
217 fC[9 ] = TMath::Abs((cv[20]-fC[14]*(m45*m45)-fC[13]*2.*m35*m45)/(m35*m35));
4f6e22bd 218
219 return;
da4e3deb 220}
221
51ad6848 222//_____________________________________________________________________________
c9ec41e8 223void AliExternalTrackParam::Reset() {
1530f89c 224 //
225 // Resets all the parameters to 0
226 //
c9ec41e8 227 fX=fAlpha=0.;
228 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
229 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
51ad6848 230}
231
3775b0ca 232//_____________________________________________________________________________
233void AliExternalTrackParam::AddCovariance(const Double_t c[15]) {
234 //
235 // Add "something" to the track covarince matrix.
236 // May be needed to account for unknown mis-calibration/mis-alignment
237 //
238 fC[0] +=c[0];
239 fC[1] +=c[1]; fC[2] +=c[2];
240 fC[3] +=c[3]; fC[4] +=c[4]; fC[5] +=c[5];
241 fC[6] +=c[6]; fC[7] +=c[7]; fC[8] +=c[8]; fC[9] +=c[9];
242 fC[10]+=c[10]; fC[11]+=c[11]; fC[12]+=c[12]; fC[13]+=c[13]; fC[14]+=c[14];
243}
244
245
c9ec41e8 246Double_t AliExternalTrackParam::GetP() const {
247 //---------------------------------------------------------------------
248 // This function returns the track momentum
249 // Results for (nearly) straight tracks are meaningless !
250 //---------------------------------------------------------------------
06fb4a2f 251 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
c9ec41e8 252 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
51ad6848 253}
254
1d99986f 255Double_t AliExternalTrackParam::Get1P() const {
256 //---------------------------------------------------------------------
257 // This function returns the 1/(track momentum)
258 //---------------------------------------------------------------------
259 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
260}
261
c9ec41e8 262//_______________________________________________________________________
c7bafca9 263Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
c9ec41e8 264 //------------------------------------------------------------------
265 // This function calculates the transverse impact parameter
266 // with respect to a point with global coordinates (x,y)
267 // in the magnetic field "b" (kG)
268 //------------------------------------------------------------------
5773defd 269 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
1530f89c 270 Double_t rp4=GetC(b);
c9ec41e8 271
272 Double_t xt=fX, yt=fP[0];
273
274 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
275 Double_t a = x*cs + y*sn;
276 y = -x*sn + y*cs; x=a;
277 xt-=x; yt-=y;
278
279 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
280 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
1530f89c 281 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
282}
283
284//_______________________________________________________________________
285void AliExternalTrackParam::
286GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
287 //------------------------------------------------------------------
288 // This function calculates the transverse and longitudinal impact parameters
289 // with respect to a point with global coordinates (x,y)
290 // in the magnetic field "b" (kG)
291 //------------------------------------------------------------------
292 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
293 Double_t xt=fX, yt=fP[0];
294 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
295 Double_t a = x*cs + y*sn;
296 y = -x*sn + y*cs; x=a;
297 xt-=x; yt-=y;
298
299 Double_t rp4=GetC(b);
300 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
301 dz[0] = -(xt*f1 - yt*r1);
302 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
303 return;
304 }
305
306 sn=rp4*xt - f1; cs=rp4*yt + r1;
307 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
308 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
309 dz[0] = -a/(1 + rr);
310 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
311 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
51ad6848 312}
313
49d13e89 314//_______________________________________________________________________
315Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
316 //------------------------------------------------------------------
317 // This function calculates the transverse impact parameter
318 // with respect to a point with global coordinates (xv,yv)
319 // neglecting the track curvature.
320 //------------------------------------------------------------------
321 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
322 Double_t x= xv*cs + yv*sn;
323 Double_t y=-xv*sn + yv*cs;
324
325 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
326
1530f89c 327 return -d;
49d13e89 328}
329
116b445b 330Bool_t AliExternalTrackParam::CorrectForMeanMaterial
7dded1d5 331(Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
332 Double_t (*Bethe)(Double_t)) {
116b445b 333 //------------------------------------------------------------------
334 // This function corrects the track parameters for the crossed material.
335 // "xOverX0" - X/X0, the thickness in units of the radiation length.
336 // "xTimesRho" - is the product length*density (g/cm^2).
337 // "mass" - the mass of this particle (GeV/c^2).
338 //------------------------------------------------------------------
339 Double_t &fP2=fP[2];
340 Double_t &fP3=fP[3];
341 Double_t &fP4=fP[4];
342
343 Double_t &fC22=fC[5];
344 Double_t &fC33=fC[9];
345 Double_t &fC43=fC[13];
346 Double_t &fC44=fC[14];
347
7dded1d5 348 //Apply angle correction, if requested
349 if(anglecorr) {
350 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
351 xOverX0 *=angle;
352 xTimesRho *=angle;
353 }
354
116b445b 355 Double_t p=GetP();
356 Double_t p2=p*p;
357 Double_t beta2=p2/(p2 + mass*mass);
116b445b 358
359 //Multiple scattering******************
360 if (xOverX0 != 0) {
361 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
9a53dcc6 362 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
116b445b 363 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
364 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
365 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
366 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
367 fC44 += theta2*fP3*fP4*fP3*fP4;
368 }
369
370 //Energy losses************************
371 if ((xTimesRho != 0.) && (beta2 < 1.)) {
d46683db 372 Double_t dE=Bethe(p/mass)*xTimesRho;
116b445b 373 Double_t e=TMath::Sqrt(p2 + mass*mass);
374 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
375 fP4*=(1.- e/p2*dE);
4b2fa3ce 376 if (TMath::Abs(fP4)>100.) return kFALSE; // Do not track below 10 MeV/c
377
116b445b 378
379 // Approximate energy loss fluctuation (M.Ivanov)
380 const Double_t knst=0.07; // To be tuned.
381 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
382 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
383
384 }
385
386 return kTRUE;
387}
388
389
ee5dba5e 390Bool_t AliExternalTrackParam::CorrectForMaterial
391(Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
c7bafca9 392 //------------------------------------------------------------------
116b445b 393 // Deprecated function !
394 // Better use CorrectForMeanMaterial instead of it.
395 //
c7bafca9 396 // This function corrects the track parameters for the crossed material
397 // "d" - the thickness (fraction of the radiation length)
398 // "x0" - the radiation length (g/cm^2)
399 // "mass" - the mass of this particle (GeV/c^2)
400 //------------------------------------------------------------------
401 Double_t &fP2=fP[2];
402 Double_t &fP3=fP[3];
403 Double_t &fP4=fP[4];
404
405 Double_t &fC22=fC[5];
406 Double_t &fC33=fC[9];
407 Double_t &fC43=fC[13];
408 Double_t &fC44=fC[14];
409
7b5ef2e6 410 Double_t p=GetP();
411 Double_t p2=p*p;
c7bafca9 412 Double_t beta2=p2/(p2 + mass*mass);
413 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
414
415 //Multiple scattering******************
416 if (d!=0) {
417 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
9a53dcc6 418 if(theta2>TMath::Pi()*TMath::Pi()) return kFALSE;
c7bafca9 419 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
420 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
421 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
422 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
423 fC44 += theta2*fP3*fP4*fP3*fP4;
424 }
425
426 //Energy losses************************
8fc1985d 427 if (x0!=0. && beta2<1) {
c7bafca9 428 d*=x0;
d46683db 429 Double_t dE=Bethe(p/mass)*d;
ee5dba5e 430 Double_t e=TMath::Sqrt(p2 + mass*mass);
ae666100 431 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
ee5dba5e 432 fP4*=(1.- e/p2*dE);
433
434 // Approximate energy loss fluctuation (M.Ivanov)
ed5f2849 435 const Double_t knst=0.07; // To be tuned.
436 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
ee5dba5e 437 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
438
c7bafca9 439 }
440
441 return kTRUE;
442}
443
9c56b409 444Double_t AliExternalTrackParam::BetheBlochAleph(Double_t bg,
445 Double_t kp1,
446 Double_t kp2,
447 Double_t kp3,
448 Double_t kp4,
449 Double_t kp5) {
450 //
451 // This is the empirical ALEPH parameterization of the Bethe-Bloch formula.
452 // It is normalized to 1 at the minimum.
453 //
454 // bg - beta*gamma
455 //
456 // The default values for the kp* parameters are for ALICE TPC.
457 // The returned value is in MIP units
458 //
459
460 Double_t beta = bg/TMath::Sqrt(1.+ bg*bg);
461
462 Double_t aa = TMath::Power(beta,kp4);
463 Double_t bb = TMath::Power(1./bg,kp5);
464
465 bb=TMath::Log(kp3+bb);
466
467 return (kp2-aa-bb)*kp1/aa;
468}
469
470Double_t AliExternalTrackParam::BetheBlochGeant(Double_t bg,
471 Double_t kp0,
472 Double_t kp1,
473 Double_t kp2,
474 Double_t kp3,
475 Double_t kp4) {
476 //
477 // This is the parameterization of the Bethe-Bloch formula inspired by Geant.
478 //
479 // bg - beta*gamma
480 // kp0 - density [g/cm^3]
481 // kp1 - density effect first junction point
482 // kp2 - density effect second junction point
483 // kp3 - mean excitation energy [GeV]
484 // kp4 - mean Z/A
485 //
486 // The default values for the kp* parameters are for silicon.
487 // The returned value is in [GeV/(g/cm^2)].
488 //
489
490 const Double_t mK = 0.307075e-3; // [GeV*cm^2/g]
491 const Double_t me = 0.511e-3; // [GeV/c^2]
492 const Double_t rho = kp0;
493 const Double_t x0 = kp1*2.303;
494 const Double_t x1 = kp2*2.303;
495 const Double_t mI = kp3;
496 const Double_t mZA = kp4;
497 const Double_t bg2 = bg*bg;
498 const Double_t maxT= 2*me*bg2; // neglecting the electron mass
499
500 //*** Density effect
501 Double_t d2=0.;
502 const Double_t x=TMath::Log(bg);
503 const Double_t lhwI=TMath::Log(28.816*1e-9*TMath::Sqrt(rho*mZA)/mI);
504 if (x > x1) {
505 d2 = lhwI + x - 0.5;
506 } else if (x > x0) {
507 const Double_t r=(x1-x)/(x1-x0);
508 d2 = lhwI + x - 0.5 + (0.5 - lhwI - x0)*r*r*r;
509 }
510
511 return mK*mZA*(1+bg2)/bg2*
512 (0.5*TMath::Log(2*me*bg2*maxT/(mI*mI)) - bg2/(1+bg2) - d2);
513}
514
d46683db 515Double_t AliExternalTrackParam::BetheBlochSolid(Double_t bg) {
ee5dba5e 516 //------------------------------------------------------------------
d46683db 517 // This is an approximation of the Bethe-Bloch formula,
518 // reasonable for solid materials.
519 // All the parameters are, in fact, for Si.
520 // The returned value is in [GeV]
ee5dba5e 521 //------------------------------------------------------------------
a821848c 522
9c56b409 523 return BetheBlochGeant(bg);
d46683db 524}
ee5dba5e 525
d46683db 526Double_t AliExternalTrackParam::BetheBlochGas(Double_t bg) {
527 //------------------------------------------------------------------
528 // This is an approximation of the Bethe-Bloch formula,
529 // reasonable for gas materials.
530 // All the parameters are, in fact, for Ne.
531 // The returned value is in [GeV]
532 //------------------------------------------------------------------
533
534 const Double_t rho = 0.9e-3;
535 const Double_t x0 = 2.;
536 const Double_t x1 = 4.;
537 const Double_t mI = 140.e-9;
538 const Double_t mZA = 0.49555;
539
9c56b409 540 return BetheBlochGeant(bg,rho,x0,x1,mI,mZA);
ee5dba5e 541}
542
49d13e89 543Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
544 //------------------------------------------------------------------
545 // Transform this track to the local coord. system rotated
546 // by angle "alpha" (rad) with respect to the global coord. system.
547 //------------------------------------------------------------------
dfcef74c 548 if (TMath::Abs(fP[2]) >= kAlmost1) {
549 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
550 return kFALSE;
551 }
552
49d13e89 553 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
554 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
555
556 Double_t &fP0=fP[0];
557 Double_t &fP2=fP[2];
558 Double_t &fC00=fC[0];
559 Double_t &fC10=fC[1];
560 Double_t &fC20=fC[3];
561 Double_t &fC21=fC[4];
562 Double_t &fC22=fC[5];
563 Double_t &fC30=fC[6];
564 Double_t &fC32=fC[8];
565 Double_t &fC40=fC[10];
566 Double_t &fC42=fC[12];
567
568 Double_t x=fX;
569 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
570 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
571
dfcef74c 572 Double_t tmp=sf*ca - cf*sa;
573 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
574
49d13e89 575 fAlpha = alpha;
576 fX = x*ca + fP0*sa;
577 fP0= -x*sa + fP0*ca;
dfcef74c 578 fP2= tmp;
49d13e89 579
06fb4a2f 580 if (TMath::Abs(cf)<kAlmost0) {
581 AliError(Form("Too small cosine value %f",cf));
582 cf = kAlmost0;
583 }
584
49d13e89 585 Double_t rr=(ca+sf/cf*sa);
586
587 fC00 *= (ca*ca);
588 fC10 *= ca;
589 fC20 *= ca*rr;
590 fC21 *= rr;
591 fC22 *= rr*rr;
592 fC30 *= ca;
593 fC32 *= rr;
594 fC40 *= ca;
595 fC42 *= rr;
596
597 return kTRUE;
598}
599
600Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
601 //----------------------------------------------------------------
602 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
603 //----------------------------------------------------------------
49d13e89 604 Double_t dx=xk-fX;
e421f556 605 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
18ebc5ef 606
1530f89c 607 Double_t crv=GetC(b);
5773defd 608 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
609
49d13e89 610 Double_t f1=fP[2], f2=f1 + crv*dx;
bbefa4c4 611 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 612 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
613
614 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
615 Double_t
616 &fC00=fC[0],
617 &fC10=fC[1], &fC11=fC[2],
618 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
619 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
620 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
621
622 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
623
624 fX=xk;
625 fP0 += dx*(f1+f2)/(r1+r2);
18ebc5ef 626 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
49d13e89 627 fP2 += dx*crv;
628
629 //f = F - 1
630
631 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
632 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
633 Double_t f12= dx*fP3*f1/(r1*r1*r1);
634 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
635 Double_t f13= dx/r1;
636 Double_t f24= dx; f24*=cc;
637
638 //b = C*ft
639 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
640 Double_t b02=f24*fC40;
641 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
642 Double_t b12=f24*fC41;
643 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
644 Double_t b22=f24*fC42;
645 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
646 Double_t b42=f24*fC44;
647 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
648 Double_t b32=f24*fC43;
649
650 //a = f*b = f*C*ft
651 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
652 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
653 Double_t a22=f24*b42;
654
655 //F*C*Ft = C + (b + bt + a)
656 fC00 += b00 + b00 + a00;
657 fC10 += b10 + b01 + a01;
658 fC20 += b20 + b02 + a02;
659 fC30 += b30;
660 fC40 += b40;
661 fC11 += b11 + b11 + a11;
662 fC21 += b21 + b12 + a12;
663 fC31 += b31;
664 fC41 += b41;
665 fC22 += b22 + b22 + a22;
666 fC32 += b32;
667 fC42 += b42;
668
669 return kTRUE;
670}
671
052daaff 672void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
673Double_t p[3], Double_t bz) const {
674 //+++++++++++++++++++++++++++++++++++++++++
675 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
676 // Extrapolate track along simple helix in magnetic field
677 // Arguments: len -distance alogn helix, [cm]
678 // bz - mag field, [kGaus]
679 // Returns: x and p contain extrapolated positon and momentum
680 // The momentum returned for straight-line tracks is meaningless !
681 //+++++++++++++++++++++++++++++++++++++++++
682 GetXYZ(x);
683
2258e165 684 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field || GetC(bz) < kAlmost0){ //straight-line tracks
052daaff 685 Double_t unit[3]; GetDirection(unit);
686 x[0]+=unit[0]*len;
687 x[1]+=unit[1]*len;
688 x[2]+=unit[2]*len;
689
690 p[0]=unit[0]/kAlmost0;
691 p[1]=unit[1]/kAlmost0;
692 p[2]=unit[2]/kAlmost0;
693 } else {
694 GetPxPyPz(p);
695 Double_t pp=GetP();
696 Double_t a = -kB2C*bz*GetSign();
697 Double_t rho = a/pp;
698 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
699 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
700 x[2] += p[2]*len/pp;
701
702 Double_t p0=p[0];
703 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
704 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
705 }
706}
707
708Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
709Double_t bz) const {
710 //+++++++++++++++++++++++++++++++++++++++++
711 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
712 // Finds point of intersection (if exists) of the helix with the plane.
713 // Stores result in fX and fP.
714 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
715 // and vector, normal to the plane
716 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
717 //+++++++++++++++++++++++++++++++++++++++++
718 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
719
720 //estimates initial helix length up to plane
721 Double_t s=
722 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
723 Double_t dist=99999,distPrev=dist;
724 Double_t x[3],p[3];
725 while(TMath::Abs(dist)>0.00001){
726 //calculates helix at the distance s from x0 ALONG the helix
727 Propagate(s,x,p,bz);
728
729 //distance between current helix position and plane
730 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
731
732 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
733 distPrev=dist;
734 s-=dist;
735 }
736 //on exit pnt is intersection point,norm is track vector at that point,
737 //all in MARS
738 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
739 return kTRUE;
740}
741
49d13e89 742Double_t
743AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
744 //----------------------------------------------------------------
745 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
746 //----------------------------------------------------------------
747 Double_t sdd = fC[0] + cov[0];
748 Double_t sdz = fC[1] + cov[1];
749 Double_t szz = fC[2] + cov[2];
750 Double_t det = sdd*szz - sdz*sdz;
751
752 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
753
754 Double_t d = fP[0] - p[0];
755 Double_t z = fP[1] - p[1];
756
757 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
758}
759
4b189f98 760Double_t AliExternalTrackParam::
761GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
762 //----------------------------------------------------------------
763 // Estimate the chi2 of the 3D space point "p" and
1e023a36 764 // the full covariance matrix "covyz" and "covxyz"
4b189f98 765 //
766 // Cov(x,x) ... : covxyz[0]
767 // Cov(y,x) ... : covxyz[1] covyz[0]
768 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
769 //----------------------------------------------------------------
770
771 Double_t res[3] = {
772 GetX() - p[0],
773 GetY() - p[1],
774 GetZ() - p[2]
775 };
776
777 Double_t f=GetSnp();
778 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
779 Double_t r=TMath::Sqrt(1.- f*f);
780 Double_t a=f/r, b=GetTgl()/r;
781
782 Double_t s2=333.*333.; //something reasonably big (cm^2)
783
784 TMatrixDSym v(3);
785 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
786 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
787 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
788
789 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
790 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
791 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
792
793 v.Invert();
794 if (!v.IsValid()) return kVeryBig;
795
796 Double_t chi2=0.;
797 for (Int_t i = 0; i < 3; i++)
798 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
799
800 return chi2;
801
802
803}
804
1e023a36 805Bool_t AliExternalTrackParam::
806PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
807 //----------------------------------------------------------------
808 // Propagate this track to the plane
809 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
810 // belongs to.
811 // The magnetic field is "bz" (kG)
812 //
813 // The track curvature and the change of the covariance matrix
814 // of the track parameters are negleted !
815 // (So the "step" should be small compared with 1/curvature)
816 //----------------------------------------------------------------
817
818 Double_t f=GetSnp();
819 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
820 Double_t r=TMath::Sqrt(1.- f*f);
821 Double_t a=f/r, b=GetTgl()/r;
822
823 Double_t s2=333.*333.; //something reasonably big (cm^2)
824
825 TMatrixDSym tV(3);
826 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
827 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
828 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
829
830 TMatrixDSym pV(3);
831 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
832 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
833 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
834
835 TMatrixDSym tpV(tV);
836 tpV+=pV;
837 tpV.Invert();
838 if (!tpV.IsValid()) return kFALSE;
839
840 TMatrixDSym pW(3),tW(3);
841 for (Int_t i=0; i<3; i++)
842 for (Int_t j=0; j<3; j++) {
843 pW(i,j)=tW(i,j)=0.;
844 for (Int_t k=0; k<3; k++) {
845 pW(i,j) += tV(i,k)*tpV(k,j);
846 tW(i,j) += pV(i,k)*tpV(k,j);
847 }
848 }
849
850 Double_t t[3] = {GetX(), GetY(), GetZ()};
851
852 Double_t x=0.;
853 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
854 Double_t crv=GetC(bz);
855 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
856 f += crv*(x-fX);
857 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
858 fX=x;
859
860 fP[0]=0.;
861 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
862 fP[1]=0.;
863 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
864
865 return kTRUE;
866}
867
e23a38cb 868Double_t *AliExternalTrackParam::GetResiduals(
869Double_t *p,Double_t *cov,Bool_t updated) const {
870 //------------------------------------------------------------------
871 // Returns the track residuals with the space point "p" having
872 // the covariance matrix "cov".
873 // If "updated" is kTRUE, the track parameters expected to be updated,
874 // otherwise they must be predicted.
875 //------------------------------------------------------------------
876 static Double_t res[2];
877
878 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
879 if (updated) {
880 r00-=fC[0]; r01-=fC[1]; r11-=fC[2];
881 } else {
882 r00+=fC[0]; r01+=fC[1]; r11+=fC[2];
883 }
884 Double_t det=r00*r11 - r01*r01;
885
886 if (TMath::Abs(det) < kAlmost0) return 0;
887
888 Double_t tmp=r00; r00=r11/det; r11=tmp/det;
f0fbf964 889
890 if (r00 < 0.) return 0;
891 if (r11 < 0.) return 0;
892
e23a38cb 893 Double_t dy = fP[0] - p[0];
894 Double_t dz = fP[1] - p[1];
895
896 res[0]=dy*TMath::Sqrt(r00);
897 res[1]=dz*TMath::Sqrt(r11);
898
899 return res;
900}
901
49d13e89 902Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
903 //------------------------------------------------------------------
904 // Update the track parameters with the space point "p" having
905 // the covariance matrix "cov"
906 //------------------------------------------------------------------
907 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
908 Double_t
909 &fC00=fC[0],
910 &fC10=fC[1], &fC11=fC[2],
911 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
912 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
913 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
914
915 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
916 r00+=fC00; r01+=fC10; r11+=fC11;
917 Double_t det=r00*r11 - r01*r01;
918
919 if (TMath::Abs(det) < kAlmost0) return kFALSE;
920
921
922 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
923
924 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
925 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
926 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
927 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
928 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
929
930 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
931 Double_t sf=fP2 + k20*dy + k21*dz;
932 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
933
934 fP0 += k00*dy + k01*dz;
935 fP1 += k10*dy + k11*dz;
936 fP2 = sf;
937 fP3 += k30*dy + k31*dz;
938 fP4 += k40*dy + k41*dz;
939
940 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
941 Double_t c12=fC21, c13=fC31, c14=fC41;
942
943 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
944 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
945 fC40-=k00*c04+k01*c14;
946
947 fC11-=k10*c01+k11*fC11;
948 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
949 fC41-=k10*c04+k11*c14;
950
951 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
952 fC42-=k20*c04+k21*c14;
953
954 fC33-=k30*c03+k31*c13;
955 fC43-=k30*c04+k31*c14;
956
957 fC44-=k40*c04+k41*c14;
958
959 return kTRUE;
960}
961
c7bafca9 962void
963AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
964 //--------------------------------------------------------------------
965 // External track parameters -> helix parameters
966 // "b" - magnetic field (kG)
967 //--------------------------------------------------------------------
968 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
969
1530f89c 970 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
c7bafca9 971
972 hlx[5]=fX*cs - hlx[0]*sn; // x0
973 hlx[0]=fX*sn + hlx[0]*cs; // y0
974//hlx[1]= // z0
975 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
976//hlx[3]= // tgl
1530f89c 977 hlx[4]=GetC(b); // C
c7bafca9 978}
979
980
981static void Evaluate(const Double_t *h, Double_t t,
982 Double_t r[3], //radius vector
983 Double_t g[3], //first defivatives
984 Double_t gg[3]) //second derivatives
985{
986 //--------------------------------------------------------------------
987 // Calculate position of a point on a track and some derivatives
988 //--------------------------------------------------------------------
989 Double_t phase=h[4]*t+h[2];
990 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
991
992 r[0] = h[5] + (sn - h[6])/h[4];
993 r[1] = h[0] - (cs - h[7])/h[4];
994 r[2] = h[1] + h[3]*t;
995
996 g[0] = cs; g[1]=sn; g[2]=h[3];
997
998 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
999}
1000
1001Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
1002Double_t b, Double_t &xthis, Double_t &xp) const {
1003 //------------------------------------------------------------
1004 // Returns the (weighed !) distance of closest approach between
1005 // this track and the track "p".
1006 // Other returned values:
1007 // xthis, xt - coordinates of tracks' reference planes at the DCA
1008 //-----------------------------------------------------------
1009 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
1010 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
1011 Double_t dx2=dy2;
1012
c7bafca9 1013 Double_t p1[8]; GetHelixParameters(p1,b);
1014 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
1015 Double_t p2[8]; p->GetHelixParameters(p2,b);
1016 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
1017
1018
1019 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
1020 Evaluate(p1,t1,r1,g1,gg1);
1021 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
1022 Evaluate(p2,t2,r2,g2,gg2);
1023
1024 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
1025 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1026
1027 Int_t max=27;
1028 while (max--) {
1029 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
1030 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
1031 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
1032 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
1033 (g1[2]*g1[2] - dz*gg1[2])/dz2;
1034 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
1035 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
1036 (g2[2]*g2[2] + dz*gg2[2])/dz2;
1037 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
1038
1039 Double_t det=h11*h22-h12*h12;
1040
1041 Double_t dt1,dt2;
1042 if (TMath::Abs(det)<1.e-33) {
1043 //(quasi)singular Hessian
1044 dt1=-gt1; dt2=-gt2;
1045 } else {
1046 dt1=-(gt1*h22 - gt2*h12)/det;
1047 dt2=-(h11*gt2 - h12*gt1)/det;
1048 }
1049
1050 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
1051
1052 //check delta(phase1) ?
1053 //check delta(phase2) ?
1054
1055 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
1056 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
1057 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
358f16ae 1058 AliDebug(1," stopped at not a stationary point !");
c7bafca9 1059 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
1060 if (lmb < 0.)
358f16ae 1061 AliDebug(1," stopped at not a minimum !");
c7bafca9 1062 break;
1063 }
1064
1065 Double_t dd=dm;
1066 for (Int_t div=1 ; ; div*=2) {
1067 Evaluate(p1,t1+dt1,r1,g1,gg1);
1068 Evaluate(p2,t2+dt2,r2,g2,gg2);
1069 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
1070 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
1071 if (dd<dm) break;
1072 dt1*=0.5; dt2*=0.5;
1073 if (div>512) {
358f16ae 1074 AliDebug(1," overshoot !"); break;
c7bafca9 1075 }
1076 }
1077 dm=dd;
1078
1079 t1+=dt1;
1080 t2+=dt2;
1081
1082 }
1083
358f16ae 1084 if (max<=0) AliDebug(1," too many iterations !");
c7bafca9 1085
1086 Double_t cs=TMath::Cos(GetAlpha());
1087 Double_t sn=TMath::Sin(GetAlpha());
1088 xthis=r1[0]*cs + r1[1]*sn;
1089
1090 cs=TMath::Cos(p->GetAlpha());
1091 sn=TMath::Sin(p->GetAlpha());
1092 xp=r2[0]*cs + r2[1]*sn;
1093
1094 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
1095}
1096
1097Double_t AliExternalTrackParam::
1098PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
1099 //--------------------------------------------------------------
1100 // Propagates this track and the argument track to the position of the
1101 // distance of closest approach.
1102 // Returns the (weighed !) distance of closest approach.
1103 //--------------------------------------------------------------
1104 Double_t xthis,xp;
1105 Double_t dca=GetDCA(p,b,xthis,xp);
1106
1107 if (!PropagateTo(xthis,b)) {
1108 //AliWarning(" propagation failed !");
1109 return 1e+33;
1110 }
1111
1112 if (!p->PropagateTo(xp,b)) {
1113 //AliWarning(" propagation failed !";
1114 return 1e+33;
1115 }
1116
1117 return dca;
1118}
1119
1120
58e536c5 1121Bool_t AliExternalTrackParam::PropagateToDCA(const AliVVertex *vtx,
e99a34df 1122Double_t b, Double_t maxd, Double_t dz[2], Double_t covar[3]) {
f76701bf 1123 //
e99a34df 1124 // Propagate this track to the DCA to vertex "vtx",
f76701bf 1125 // if the (rough) transverse impact parameter is not bigger then "maxd".
1126 // Magnetic field is "b" (kG).
1127 //
1128 // a) The track gets extapolated to the DCA to the vertex.
1129 // b) The impact parameters and their covariance matrix are calculated.
1130 //
1131 // In the case of success, the returned value is kTRUE
1132 // (otherwise, it's kFALSE)
1133 //
1134 Double_t alpha=GetAlpha();
1135 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
1136 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
58e536c5 1137 Double_t xv= vtx->GetX()*cs + vtx->GetY()*sn;
1138 Double_t yv=-vtx->GetX()*sn + vtx->GetY()*cs, zv=vtx->GetZ();
f76701bf 1139 x-=xv; y-=yv;
1140
1141 //Estimate the impact parameter neglecting the track curvature
1142 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
1143 if (d > maxd) return kFALSE;
1144
1145 //Propagate to the DCA
2258e165 1146 Double_t crv=GetC(b);
e99a34df 1147 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1148
f76701bf 1149 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
1150 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
e99a34df 1151 if (TMath::Abs(tgfv)>0.) cs = sn/tgfv;
1152 else cs=1.;
f76701bf 1153
1154 x = xv*cs + yv*sn;
1155 yv=-xv*sn + yv*cs; xv=x;
1156
1157 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
e99a34df 1158
1159 if (dz==0) return kTRUE;
1160 dz[0] = GetParameter()[0] - yv;
1161 dz[1] = GetParameter()[1] - zv;
1162
1163 if (covar==0) return kTRUE;
58e536c5 1164 Double_t cov[6]; vtx->GetCovarianceMatrix(cov);
e99a34df 1165
1166 //***** Improvements by A.Dainese
1167 alpha=GetAlpha(); sn=TMath::Sin(alpha); cs=TMath::Cos(alpha);
1168 Double_t s2ylocvtx = cov[0]*sn*sn + cov[2]*cs*cs - 2.*cov[1]*cs*sn;
1169 covar[0] = GetCovariance()[0] + s2ylocvtx; // neglecting correlations
1170 covar[1] = GetCovariance()[1]; // between (x,y) and z
1171 covar[2] = GetCovariance()[2] + cov[5]; // in vertex's covariance matrix
1172 //*****
1173
29fbcc93 1174 return kTRUE;
f76701bf 1175}
1176
1177
b1149664 1178void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
1179 //----------------------------------------------------------------
1180 // This function returns a unit vector along the track direction
1181 // in the global coordinate system.
1182 //----------------------------------------------------------------
1183 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1184 Double_t snp=fP[2];
92934324 1185 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
b1149664 1186 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
1187 d[0]=(csp*cs - snp*sn)/norm;
1188 d[1]=(snp*cs + csp*sn)/norm;
1189 d[2]=fP[3]/norm;
1190}
1191
c683ddc2 1192Bool_t AliExternalTrackParam::GetPxPyPz(Double_t p[3]) const {
c9ec41e8 1193 //---------------------------------------------------------------------
1194 // This function returns the global track momentum components
1195 // Results for (nearly) straight tracks are meaningless !
1196 //---------------------------------------------------------------------
1197 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
1198 return Local2GlobalMomentum(p,fAlpha);
1199}
a5e407e9 1200
def9660e 1201Double_t AliExternalTrackParam::Px() const {
957fb479 1202 //---------------------------------------------------------------------
1203 // Returns x-component of momentum
1204 // Result for (nearly) straight tracks is meaningless !
1205 //---------------------------------------------------------------------
def9660e 1206
957fb479 1207 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1208 GetPxPyPz(p);
1209
1210 return p[0];
1211}
1212
1213Double_t AliExternalTrackParam::Py() const {
957fb479 1214 //---------------------------------------------------------------------
1215 // Returns y-component of momentum
1216 // Result for (nearly) straight tracks is meaningless !
1217 //---------------------------------------------------------------------
def9660e 1218
957fb479 1219 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1220 GetPxPyPz(p);
1221
1222 return p[1];
1223}
1224
1225Double_t AliExternalTrackParam::Pz() const {
957fb479 1226 //---------------------------------------------------------------------
1227 // Returns z-component of momentum
1228 // Result for (nearly) straight tracks is meaningless !
1229 //---------------------------------------------------------------------
def9660e 1230
957fb479 1231 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
def9660e 1232 GetPxPyPz(p);
1233
1234 return p[2];
1235}
1236
c683ddc2 1237Double_t AliExternalTrackParam::Xv() const {
1238 //---------------------------------------------------------------------
1239 // Returns x-component of first track point
1240 //---------------------------------------------------------------------
1241
1242 Double_t r[3]={0.,0.,0.};
1243 GetXYZ(r);
1244
1245 return r[0];
1246}
1247
1248Double_t AliExternalTrackParam::Yv() const {
1249 //---------------------------------------------------------------------
1250 // Returns y-component of first track point
1251 //---------------------------------------------------------------------
1252
1253 Double_t r[3]={0.,0.,0.};
1254 GetXYZ(r);
1255
1256 return r[1];
1257}
1258
1259Double_t AliExternalTrackParam::Zv() const {
1260 //---------------------------------------------------------------------
1261 // Returns z-component of first track point
1262 //---------------------------------------------------------------------
1263
1264 Double_t r[3]={0.,0.,0.};
1265 GetXYZ(r);
1266
1267 return r[2];
1268}
1269
def9660e 1270Double_t AliExternalTrackParam::Theta() const {
1271 // return theta angle of momentum
1272
7cdd0c20 1273 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
def9660e 1274}
1275
1276Double_t AliExternalTrackParam::Phi() const {
957fb479 1277 //---------------------------------------------------------------------
1278 // Returns the azimuthal angle of momentum
1279 // 0 <= phi < 2*pi
1280 //---------------------------------------------------------------------
def9660e 1281
957fb479 1282 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1283 if (phi<0.) phi+=2.*TMath::Pi();
1284 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1285
1286 return phi;
def9660e 1287}
1288
1289Double_t AliExternalTrackParam::M() const {
1290 // return particle mass
1291
1292 // No mass information available so far.
1293 // Redifine in derived class!
1294
1295 return -999.;
1296}
1297
1298Double_t AliExternalTrackParam::E() const {
1299 // return particle energy
1300
1301 // No PID information available so far.
1302 // Redifine in derived class!
1303
1304 return -999.;
1305}
1306
1307Double_t AliExternalTrackParam::Eta() const {
1308 // return pseudorapidity
1309
1310 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1311}
1312
1313Double_t AliExternalTrackParam::Y() const {
1314 // return rapidity
1315
1316 // No PID information available so far.
1317 // Redifine in derived class!
1318
1319 return -999.;
1320}
1321
c9ec41e8 1322Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1323 //---------------------------------------------------------------------
1324 // This function returns the global track position
1325 //---------------------------------------------------------------------
1326 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1327 return Local2GlobalPosition(r,fAlpha);
51ad6848 1328}
1329
c9ec41e8 1330Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1331 //---------------------------------------------------------------------
1332 // This function returns the global covariance matrix of the track params
1333 //
1334 // Cov(x,x) ... : cv[0]
1335 // Cov(y,x) ... : cv[1] cv[2]
1336 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1337 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1338 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1339 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
a5e407e9 1340 //
c9ec41e8 1341 // Results for (nearly) straight tracks are meaningless !
1342 //---------------------------------------------------------------------
e421f556 1343 if (TMath::Abs(fP[4])<=kAlmost0) {
c9ec41e8 1344 for (Int_t i=0; i<21; i++) cv[i]=0.;
1345 return kFALSE;
a5e407e9 1346 }
49d13e89 1347 if (TMath::Abs(fP[2]) > kAlmost1) {
c9ec41e8 1348 for (Int_t i=0; i<21; i++) cv[i]=0.;
1349 return kFALSE;
1350 }
1351 Double_t pt=1./TMath::Abs(fP[4]);
1352 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
92934324 1353 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
c9ec41e8 1354
1355 Double_t m00=-sn, m10=cs;
1356 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1357 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1358 Double_t m35=pt, m45=-pt*pt*fP[3];
1359
854d5d49 1360 m43*=GetSign();
1361 m44*=GetSign();
1362 m45*=GetSign();
1363
c9ec41e8 1364 cv[0 ] = fC[0]*m00*m00;
1365 cv[1 ] = fC[0]*m00*m10;
1366 cv[2 ] = fC[0]*m10*m10;
1367 cv[3 ] = fC[1]*m00;
1368 cv[4 ] = fC[1]*m10;
1369 cv[5 ] = fC[2];
1370 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1371 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1372 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1373 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1374 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1375 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1376 cv[12] = fC[4]*m24 + fC[11]*m44;
1377 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1378 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1379 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1380 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1381 cv[17] = fC[7]*m35 + fC[11]*m45;
1382 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1383 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1384 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
51ad6848 1385
c9ec41e8 1386 return kTRUE;
51ad6848 1387}
1388
51ad6848 1389
c9ec41e8 1390Bool_t
1391AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1392 //---------------------------------------------------------------------
1393 // This function returns the global track momentum extrapolated to
1394 // the radial position "x" (cm) in the magnetic field "b" (kG)
1395 //---------------------------------------------------------------------
c9ec41e8 1396 p[0]=fP[4];
1530f89c 1397 p[1]=fP[2]+(x-fX)*GetC(b);
c9ec41e8 1398 p[2]=fP[3];
1399 return Local2GlobalMomentum(p,fAlpha);
51ad6848 1400}
1401
7cf7bb6c 1402Bool_t
1403AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1404 //---------------------------------------------------------------------
1405 // This function returns the local Y-coordinate of the intersection
1406 // point between this track and the reference plane "x" (cm).
1407 // Magnetic field "b" (kG)
1408 //---------------------------------------------------------------------
1409 Double_t dx=x-fX;
1410 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1411
1530f89c 1412 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
7cf7bb6c 1413
1414 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1415 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1416
1417 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1418 y = fP[0] + dx*(f1+f2)/(r1+r2);
1419 return kTRUE;
1420}
1421
6c94f330 1422Bool_t
1423AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1424 //---------------------------------------------------------------------
1425 // This function returns the local Z-coordinate of the intersection
1426 // point between this track and the reference plane "x" (cm).
1427 // Magnetic field "b" (kG)
1428 //---------------------------------------------------------------------
1429 Double_t dx=x-fX;
1430 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1431
2258e165 1432 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
6c94f330 1433
1434 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1435 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1436
1437 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1438 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1439 return kTRUE;
1440}
1441
c9ec41e8 1442Bool_t
1443AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1444 //---------------------------------------------------------------------
1445 // This function returns the global track position extrapolated to
1446 // the radial position "x" (cm) in the magnetic field "b" (kG)
1447 //---------------------------------------------------------------------
c9ec41e8 1448 Double_t dx=x-fX;
e421f556 1449 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1450
1530f89c 1451 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
c9ec41e8 1452
e421f556 1453 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
49d13e89 1454 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
c9ec41e8 1455
1456 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1457 r[0] = x;
1458 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
f90a11c9 1459 r[2] = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3];//Thanks to Andrea & Peter
1460
c9ec41e8 1461 return Local2GlobalPosition(r,fAlpha);
51ad6848 1462}
1463
51ad6848 1464//_____________________________________________________________________________
1465void AliExternalTrackParam::Print(Option_t* /*option*/) const
1466{
1467// print the parameters and the covariance matrix
1468
1469 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1470 printf(" parameters: %12g %12g %12g %12g %12g\n",
c9ec41e8 1471 fP[0], fP[1], fP[2], fP[3], fP[4]);
1472 printf(" covariance: %12g\n", fC[0]);
1473 printf(" %12g %12g\n", fC[1], fC[2]);
1474 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
51ad6848 1475 printf(" %12g %12g %12g %12g\n",
c9ec41e8 1476 fC[6], fC[7], fC[8], fC[9]);
51ad6848 1477 printf(" %12g %12g %12g %12g %12g\n",
c9ec41e8 1478 fC[10], fC[11], fC[12], fC[13], fC[14]);
51ad6848 1479}
5b77d93c 1480
c194ba83 1481Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1482 //
1483 // Get sinus at given x
1484 //
1530f89c 1485 Double_t crv=GetC(b);
c194ba83 1486 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1487 Double_t dx = x-fX;
1488 Double_t res = fP[2]+dx*crv;
1489 return res;
1490}
bf00ebb8 1491
1492Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1493 //------------------------------------------------------------------------
1494 // Get the distance between two tracks at the local position x
1495 // working in the local frame of this track.
1496 // Origin : Marian.Ivanov@cern.ch
1497 //-----------------------------------------------------------------------
1498 Double_t xyz[3];
1499 Double_t xyz2[3];
1500 xyz[0]=x;
1501 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1502 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1503 //
1504 //
1505 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1506 xyz2[0]=x;
1507 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1508 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1509 }else{
1510 //
1511 Double_t xyz1[3];
1512 Double_t dfi = param2->GetAlpha()-GetAlpha();
1513 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1514 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1515 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1516 //
1517 xyz1[0]=xyz2[0];
1518 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1519 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1520 //
1521 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1522 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1523 xyz2[2] = xyz1[2];
1524 }
1525 dist[0] = xyz[0]-xyz2[0];
1526 dist[1] = xyz[1]-xyz2[1];
1527 dist[2] = xyz[2]-xyz2[2];
1528
1529 return kTRUE;
1530}
0c19adf7 1531
1532
1533//
1534// Draw functionality.
1535// Origin: Marian Ivanov, Marian.Ivanov@cern.ch
1536//
1537
1538void AliExternalTrackParam::DrawTrack(Float_t magf, Float_t minR, Float_t maxR, Float_t stepR){
1539 //
1540 // Draw track line
1541 //
1542 if (minR>maxR) return ;
1543 if (stepR<=0) return ;
1544 Int_t npoints = TMath::Nint((maxR-minR)/stepR)+1;
1545 if (npoints<1) return;
1546 TPolyMarker3D *polymarker = new TPolyMarker3D(npoints);
1547 FillPolymarker(polymarker, magf,minR,maxR,stepR);
1548 polymarker->Draw();
1549}
1550
1551//
1552void AliExternalTrackParam::FillPolymarker(TPolyMarker3D *pol, Float_t magF, Float_t minR, Float_t maxR, Float_t stepR){
1553 //
1554 // Fill points in the polymarker
1555 //
1556 Int_t counter=0;
1557 for (Double_t r=minR; r<maxR; r+=stepR){
1558 Double_t point[3];
1559 GetXYZAt(r,magF,point);
1560 pol->SetPoint(counter,point[0],point[1], point[2]);
1561 printf("xyz\t%f\t%f\t%f\n",point[0], point[1],point[2]);
1562 counter++;
1563 }
1564}
0e8460af 1565
1566Int_t AliExternalTrackParam::GetIndex(Int_t i, Int_t j) const {
1567 //
1568 Int_t min = TMath::Min(i,j);
1569 Int_t max = TMath::Max(i,j);
1570
1571 return min+(max+1)*max/2;
1572}