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7f572c00 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// Implementation of the AliHelix class
20// Origin: Marian Ivanov, CERN, marian.ivanov@cern.ch
21//-------------------------------------------------------------------------
22
23
24#include "AliHelix.h"
25#include "AliKalmanTrack.h"
51ad6848 26#include "AliExternalTrackParam.h"
7f572c00 27#include "TMath.h"
28ClassImp(AliHelix)
29
30
31//_______________________________________________________________________
32AliHelix::AliHelix()
33{
34 //
35 // Default constructor
36 //
37 for (Int_t i =0;i<9;i++) fHelix[i]=0;
38}
39
40//_______________________________________________________________________
176aff27 41AliHelix::AliHelix(const AliHelix &t):TObject(t){
7f572c00 42 //
43 //
44 for (Int_t i=0;i<9;i++)
45 fHelix[i]=t.fHelix[i];
46}
47
48AliHelix::AliHelix(const AliKalmanTrack &t)
49{
50 //
51 //
52 Double_t alpha,x,cs,sn;
53 t.GetExternalParameters(x,fHelix);
54 alpha=t.GetAlpha();
55 //
56 //circle parameters
57 fHelix[4]=fHelix[4]/t.GetConvConst(); // C
58 cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
59
60 Double_t xc, yc, rc;
61 rc = 1/fHelix[4];
62 xc = x-fHelix[2]*rc;
63 yc = fHelix[0]+TMath::Sqrt(1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4])/fHelix[4];
64
65 fHelix[6] = xc*cs - yc*sn;
66 fHelix[7] = xc*sn + yc*cs;
67 fHelix[8] = TMath::Abs(rc);
68 //
69 //
70 fHelix[5]=x*cs - fHelix[0]*sn; // x0
71 fHelix[0]=x*sn + fHelix[0]*cs; // y0
72 //fHelix[1]= // z0
9be2fe3a 73 fHelix[2]=TMath::ATan2(-(fHelix[5]-fHelix[6]),fHelix[0]-fHelix[7]); // phi0
74 if (fHelix[4]>0) fHelix[2]-=TMath::Pi();
75
7f572c00 76 //fHelix[3]= // tgl
77 //
78 //
79 fHelix[5] = fHelix[6];
80 fHelix[0] = fHelix[7];
7f572c00 81}
82
51ad6848 83
84AliHelix::AliHelix(const AliExternalTrackParam &t)
85{
86 //
87 //
88 Double_t alpha,x,cs,sn;
89 const Double_t *param =t.GetParameter();
90 for (Int_t i=0;i<5;i++) fHelix[i]=param[i];
91 x = t.X();
92 alpha=t.Alpha();
93 //
94 //circle parameters
95 fHelix[4]=fHelix[4]/AliKalmanTrack::GetConvConst(); // C
96 cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
97
98 Double_t xc, yc, rc;
99 rc = 1/fHelix[4];
100 xc = x-fHelix[2]*rc;
101 yc = fHelix[0]+TMath::Sqrt(1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4])/fHelix[4];
102
103 fHelix[6] = xc*cs - yc*sn;
104 fHelix[7] = xc*sn + yc*cs;
105 fHelix[8] = TMath::Abs(rc);
106 //
107 //
108 fHelix[5]=x*cs - fHelix[0]*sn; // x0
109 fHelix[0]=x*sn + fHelix[0]*cs; // y0
110 //fHelix[1]= // z0
111 fHelix[2]=TMath::ASin(fHelix[2]) + alpha; // phi0
112 //fHelix[3]= // tgl
113 //
114 //
115 fHelix[5] = fHelix[6];
116 fHelix[0] = fHelix[7];
51ad6848 117}
118
7f572c00 119AliHelix::AliHelix(Double_t x[3], Double_t p[3], Double_t charge, Double_t conversion)
120{
121 //
122 //
123 //
124 Double_t pt = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]);
125 if (TMath::Abs(conversion)<0.00000001)
126 conversion = AliKalmanTrack::GetConvConst();
127 //
128 //
129 fHelix[4] = charge/(conversion*pt); // C
130 fHelix[3] = p[2]/pt; // tgl
131 //
132 Double_t xc, yc, rc;
133 rc = 1/fHelix[4];
134 xc = x[0] -rc*p[1]/pt;
135 yc = x[1] +rc*p[0]/pt;
136 //
137 fHelix[5] = x[0]; // x0
138 fHelix[0] = x[1]; // y0
139 fHelix[1] = x[2]; // z0
140 //
141 fHelix[6] = xc;
142 fHelix[7] = yc;
143 fHelix[8] = TMath::Abs(rc);
144 //
145 fHelix[5]=xc;
146 fHelix[0]=yc;
147 //
148 if (TMath::Abs(p[1])<TMath::Abs(p[0])){
149 fHelix[2]=TMath::ASin(p[1]/pt);
150 if (charge*yc<charge*x[1]) fHelix[2] = TMath::Pi()-fHelix[2];
151 }
152 else{
153 fHelix[2]=TMath::ACos(p[0]/pt);
154 if (charge*xc>charge*x[0]) fHelix[2] = -fHelix[2];
155 }
156
157}
158
81e97e0d 159void AliHelix::GetMomentum(Double_t phase, Double_t p[4],Double_t conversion, Double_t *xr)
7f572c00 160{
161 // return momentum at given phase
162 Double_t x[3],g[3],gg[3];
163 Evaluate(phase,x,g,gg);
164 if (TMath::Abs(conversion)<0.0001) conversion = AliKalmanTrack::GetConvConst();
165 Double_t mt = TMath::Sqrt(g[0]*g[0]+g[1]*g[1]);
166 p[0] = fHelix[8]*g[0]/(mt*conversion);
167 p[1] = fHelix[8]*g[1]/(mt*conversion);
168 p[2] = fHelix[8]*g[2]/(mt*conversion);
81e97e0d 169 if (xr){
170 xr[0] = x[0]; xr[1] = x[1]; xr[2] = x[2];
171 }
7f572c00 172}
173
174void AliHelix::GetAngle(Double_t t1, AliHelix &h, Double_t t2, Double_t angle[3])
175{
176 //
177 //
178 //
179 Double_t x1[3],g1[3],gg1[3];
180 Double_t x2[3],g2[3],gg2[3];
181 Evaluate(t1,x1,g1,gg1);
182 h.Evaluate(t2,x2,g2,gg2);
183
184 //
185 Double_t norm1r = g1[0]*g1[0]+g1[1]*g1[1];
186 Double_t norm1 = TMath::Sqrt(norm1r+g1[2]*g1[2]);
187 norm1r = TMath::Sqrt(norm1r);
188 //
189 Double_t norm2r = g2[0]*g2[0]+g2[1]*g2[1];
190 Double_t norm2 = TMath::Sqrt(norm2r+g2[2]*g2[2]);
191 norm2r = TMath::Sqrt(norm2r);
192 //
51ad6848 193 angle[0] = (g1[0]*g2[0]+g1[1]*g2[1])/(norm1r*norm2r); // angle in phi projection
194 if (TMath::Abs(angle[0])<1.) angle[0] = TMath::ACos(angle[0]);
9be2fe3a 195 else{
196 if (angle[0]>0) angle[0] = 0;
197 if (angle[0]<0) angle[0] = TMath::Pi();
198 }
51ad6848 199 //
200 angle[1] = ((norm1r*norm2r)+g1[2]*g2[2])/(norm1*norm2); // angle in rz projection
201 if (TMath::Abs(angle[1])<1.) angle[1] = TMath::ACos(angle[1]);
9be2fe3a 202 else
203 angle[1]=0;
51ad6848 204
205 angle[2] = (g1[0]*g2[0]+g1[1]*g2[1]+g1[2]*g2[2])/(norm1*norm2); //3D angle
206 if (TMath::Abs(angle[2])<1.) angle[2] = TMath::ACos(angle[2]);
9be2fe3a 207 else
208 angle[2]=0;
7f572c00 209
51ad6848 210
7f572c00 211
212
213}
214
215
216void AliHelix::Evaluate(Double_t t,
217 Double_t r[3], //radius vector
218 Double_t g[3], //first defivatives
219 Double_t gg[3]) //second derivatives
220{
221 //--------------------------------------------------------------------
222 // Calculate position of a point on a track and some derivatives at given phase
223 //--------------------------------------------------------------------
224 Double_t phase=fHelix[4]*t+fHelix[2];
225 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
226
7f572c00 227 r[0] = fHelix[5] + sn/fHelix[4];
228 r[1] = fHelix[0] - cs/fHelix[4];
229 r[2] = fHelix[1] + fHelix[3]*t;
230
231 g[0] = cs; g[1]=sn; g[2]=fHelix[3];
232
233 gg[0]=-fHelix[4]*sn; gg[1]=fHelix[4]*cs; gg[2]=0.;
234}
235
9be2fe3a 236Int_t AliHelix::GetClosestPhases(AliHelix &h, Double_t phase[2][2])
237{
238 //
239 // get phases to minimize distances
240 //
241 Double_t xyz0[3];
242 Double_t xyz1[3];
243
244 for (Int_t i=0;i<2;i++){
245 Evaluate(phase[i][0] ,xyz0);
246 h.Evaluate(phase[i][1],xyz1);
247 Double_t mindist = TMath::Sqrt((xyz0[0]-xyz1[0])*(xyz0[0]-xyz1[0])+
248 (xyz0[1]-xyz1[1])*(xyz0[1]-xyz1[1])+
249 (xyz0[2]-xyz1[2])*(xyz0[2]-xyz1[2]));
250 Double_t tbest[2]={phase[i][0],phase[i][1]};
251 for (Int_t i0=-1;i0<=1;i0++){
252 Double_t t0 = ((phase[i][0]*fHelix[4])+i0*2.*TMath::Pi())/fHelix[4];
253 Evaluate(t0,xyz0);
254 for (Int_t i1=-1;i1<=1;i1++){
255 Double_t t1 = ((phase[i][1]*h.fHelix[4])+i1*2.*TMath::Pi())/h.fHelix[4];
256 h.Evaluate(t1,xyz1);
257 Double_t dist = TMath::Sqrt((xyz0[0]-xyz1[0])*(xyz0[0]-xyz1[0])+
258 (xyz0[1]-xyz1[1])*(xyz0[1]-xyz1[1])+
259 (xyz0[2]-xyz1[2])*(xyz0[2]-xyz1[2]));
260 if (dist<=mindist){
261 tbest[0] = t0;
262 tbest[1] = t1;
263 mindist=dist;
264 }
265 }
266 }
267 phase[i][0] = tbest[0];
268 phase[i][1] = tbest[1];
269 }
270 return 1;
271}
272
81e97e0d 273Double_t AliHelix::GetPointAngle(AliHelix &h, Double_t phase[2], const Float_t * vertex)
274{
275 //
276 // get point angle bettwen two helixes
277 //
278 Double_t r0[3],p0[4];
279 Double_t r1[3],p1[4];
280 GetMomentum(phase[0],p0,1,r0);
281 h.GetMomentum(phase[1],p1,1,r1);
282 //
283 Double_t r[3] = {(r0[0]+r1[0])*0.5-vertex[0],(r0[1]+r1[1])*0.5-vertex[1],(r0[2]+r1[2])*0.5-vertex[2]};
284 //intersection point - relative to the prim vertex
285 Double_t p[3] = { p0[0]+p1[0], p0[1]+p1[1],p0[2]+p1[2]};
286 // derivation vector
287 Double_t normr = TMath::Sqrt(r[0]*r[0]+r[1]*r[1]+r[2]*r[2]);
288 Double_t normp = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]);
289 Double_t pointAngle = (r[0]*p[0]+r[1]*p[1]+r[2]*p[2])/(normr*normp);
290 return pointAngle;
291}
292
7f572c00 293Double_t AliHelix::GetPhase(Double_t x, Double_t y )
294
295{
296 //
297 //calculate helix param at given x,y point
298 //
9be2fe3a 299 //Double_t phase2 = TMath::ATan2((y-fHelix[0]), (x-fHelix[5]))- TMath::Pi()/2.;
300 Double_t phase2 = TMath::ATan2(-(x-fHelix[5]),(y-fHelix[0]));
301 Int_t sign = (fHelix[4]>0)? 1:-1;
302 if (sign>0) phase2 = phase2-TMath::Pi();
303 //
304 Float_t delta = TMath::Nint((phase2-fHelix[2])/(2.*TMath::Pi()));
305 phase2-= 2*TMath::Pi()*delta;
306 if ( (phase2-fHelix[2])>TMath::Pi()) phase2 -=2.*TMath::Pi();
307 if ( (phase2-fHelix[2])<-TMath::Pi()) phase2+=2.*TMath::Pi();
7f572c00 308
9be2fe3a 309 Double_t t = (phase2-fHelix[2]);
310 t/=fHelix[4];
7f572c00 311 return t;
312}
313
176aff27 314Int_t AliHelix::GetPhase(Double_t /*r0*/, Double_t * /*t[2]*/)
7f572c00 315{
316 //
317 //calculate helix param at given r point - return nearest point ()
318 //
319 // not implemented yet
320
321
322 return 0;
323}
324
325
326Double_t AliHelix::GetPhaseZ(Double_t z0)
327{
328 //
329 //
330 return (z0-fHelix[1])/fHelix[3];
331}
332
333
334Int_t AliHelix::GetRPHIintersections(AliHelix &h, Double_t phase[2][2], Double_t ri[2], Double_t cut)
335{
336 //--------------------------------------------------------------------
337 // This function returns phase vectors with intesection between helix (0, 1 or 2)
338 // in x-y plane projection
339 //--------------------------------------------------------------------
340 //
341 // Double_t * c1 = &fHelix[6];
342 //Double_t * c2 = &(h.fHelix[6]);
343 // Double_t c1[3] = {fHelix[5],fHelix[0],fHelix[8]};
9e8f4343 344
345 // PH initiaziation in case of return
346 phase[0][0]=phase[0][1]=phase[1][0]=phase[1][1]=0;
347 ri[0]=ri[1]=1000000;
348
7f572c00 349 Double_t c1[3] = {0,0,fHelix[8]};
350 Double_t c2[3] = {h.fHelix[5]-fHelix[5],h.fHelix[0]-fHelix[0],h.fHelix[8]};
351
352 Double_t d = TMath::Sqrt(c2[0]*c2[0]+c2[1]*c2[1]);
51ad6848 353 if (d<0.000000000001) return 0;
7f572c00 354 //
355 Double_t x0[2];
356 Double_t y0[2];
357 //
358 if ( d>=(c1[2]+c2[2])){
359 if (d>=(c1[2]+c2[2]+cut)) return 0;
360 x0[0] = (d+c1[2]-c2[2])*c2[0]/(2*d)+ fHelix[5];
361 y0[0] = (d+c1[2]-c2[2])*c2[1]/(2*d)+ fHelix[0];
51ad6848 362 // return 0;
9e8f4343 363 phase[1][0] = phase[0][0] = GetPhase(x0[0],y0[0]);
364 phase[1][1] = phase[0][1] = h.GetPhase(x0[0],y0[0]);
365 ri[1] = ri[0] = x0[0]*x0[0]+y0[0]*y0[0];
51ad6848 366 return 1;
7f572c00 367 }
368 if ( (d+c2[2])<c1[2]){
369 if ( (d+c2[2])+cut<c1[2]) return 0;
370 //
371 Double_t xx = c2[0]+ c2[0]*c2[2]/d+ fHelix[5];
372 Double_t yy = c2[1]+ c2[1]*c2[2]/d+ fHelix[0];
9e8f4343 373 phase[1][1] = phase[0][1] = h.GetPhase(xx,yy);
7f572c00 374 //
375 Double_t xx2 = c2[0]*c1[2]/d+ fHelix[5];
376 Double_t yy2 = c2[1]*c1[2]/d+ fHelix[0];
9e8f4343 377 phase[1][0] = phase[0][0] = GetPhase(xx2,yy2);
378 ri[1] = ri[0] = xx*xx+yy*yy;
7f572c00 379 return 1;
380 }
381
382 if ( (d+c1[2])<c2[2]){
383 if ( (d+c1[2])+cut<c2[2]) return 0;
384 //
385 Double_t xx = -c2[0]*c1[2]/d+ fHelix[5];
386 Double_t yy = -c2[1]*c1[2]/d+ fHelix[0];
9e8f4343 387 phase[1][1] = phase[0][1] = GetPhase(xx,yy);
7f572c00 388 //
389 Double_t xx2 = c2[0]- c2[0]*c2[2]/d+ fHelix[5];
390 Double_t yy2 = c2[1]- c2[1]*c2[2]/d+ fHelix[0];
9e8f4343 391 phase[1][0] = phase[0][0] = h.GetPhase(xx2,yy2);
392 ri[1] = ri[0] = xx*xx+yy*yy;
7f572c00 393 return 1;
394 }
395
396 Double_t d1 = (d*d+c1[2]*c1[2]-c2[2]*c2[2])/(2.*d);
397 Double_t v1 = c1[2]*c1[2]-d1*d1;
398 if (v1<0) return 0;
399 v1 = TMath::Sqrt(v1);
400 //
401 x0[0] = (c2[0]*d1+c2[1]*v1)/d + fHelix[5];
402 y0[0] = (c2[1]*d1-c2[0]*v1)/d + fHelix[0];
403 //
404 x0[1] = (c2[0]*d1-c2[1]*v1)/d + fHelix[5];
405 y0[1] = (c2[1]*d1+c2[0]*v1)/d + fHelix[0];
406 //
407 for (Int_t i=0;i<2;i++){
408 phase[i][0] = GetPhase(x0[i],y0[i]);
409 phase[i][1] = h.GetPhase(x0[i],y0[i]);
410 ri[i] = x0[i]*x0[i]+y0[i]*y0[i];
411 }
412 return 2;
413}
414
7f572c00 415
416
417Int_t AliHelix::LinearDCA(AliHelix &h, Double_t &t1, Double_t &t2,
418 Double_t &R, Double_t &dist)
419{
420 //
421 //
422 // find intersection using linear approximation
423 Double_t r1[3],g1[3],gg1[3];
424 Double_t r2[3],g2[3],gg2[3];
425 //
426 Evaluate(t1,r1,g1,gg1);
427 h.Evaluate(t2,r2,g2,gg2);
428 //
429 Double_t g1_2 = g1[0]*g1[0] +g1[1]*g1[1] +g1[2]*g1[2];
430 Double_t g2_2 = g2[0]*g2[0] +g2[1]*g2[1] +g2[2]*g2[2];
431 Double_t g1x2 = g1[0]*g2[0] +g1[1]*g2[1] +g1[2]*g2[2];
432 Double_t det = g1_2*g2_2 - g1x2*g1x2;
433 //
434 if (TMath::Abs(det)>0){
435 //
436 Double_t r1g1 = r1[0]*g1[0] +r1[1]*g1[1] +r1[2]*g1[2];
437 Double_t r2g1 = r2[0]*g1[0] +r2[1]*g1[1] +r2[2]*g1[2];
438 Double_t r1g2 = r1[0]*g2[0] +r1[1]*g2[1] +r1[2]*g2[2];
439 Double_t r2g2 = r2[0]*g2[0] +r2[1]*g2[1] +r2[2]*g2[2];
440 //
441 Double_t dt = - ( g2_2*(r1g1-r2g1) - g1x2*(r1g2-r2g2)) / det;
442 Double_t dp = - ( g1_2*(r2g2-r1g2) - g1x2*(r2g1-r1g1)) / det;
443 //
444 t1+=dt;
445 t2+=dp;
446 Evaluate(t1,r1);
447 h.Evaluate(t2,r2);
448 //
449 dist = (r1[0]-r2[0])*(r1[0]-r2[0])+
450 (r1[1]-r2[1])*(r1[1]-r2[1])+
451 (r1[2]-r2[2])*(r1[2]-r2[2]);
452 R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4.;
453 }
454 return 0;
455}
456
457
7f572c00 458Int_t AliHelix::ParabolicDCA(AliHelix&h, //helixes
459 Double_t &t1, Double_t &t2,
460 Double_t &R, Double_t &dist, Int_t iter)
461{
462 //
463 //
464 // find intersection using linear fit
465 Double_t r1[3],g1[3],gg1[3];
466 Double_t r2[3],g2[3],gg2[3];
467 //
468 Evaluate(t1,r1,g1,gg1);
469 h.Evaluate(t2,r2,g2,gg2);
470
471 //
472 Double_t dx2=1.;
473 Double_t dy2=1.;
474 Double_t dz2=1.;
475 //
476 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
477 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
478 //
479
480 iter++;
481 while (iter--) {
9be2fe3a 482 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
483 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
484
485 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
486 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
487 (g1[2]*g1[2] - dz*gg1[2])/dz2;
488 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
489 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
490 (g2[2]*g2[2] + dz*gg2[2])/dz2;
491 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
492
493 Double_t det=h11*h22-h12*h12;
494
495 Double_t dt1,dt2;
496 if (TMath::Abs(det)<1.e-33) {
497 //(quasi)singular Hessian
498 dt1=-gt1; dt2=-gt2;
499 } else {
500 dt1=-(gt1*h22 - gt2*h12)/det;
501 dt2=-(h11*gt2 - h12*gt1)/det;
502 }
503
504 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
505
506 //if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
507 // if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
508 // break;
509 // }
510
511 Double_t dd=dm;
512 for (Int_t div=1 ; div<512 ; div*=2) {
513 Evaluate(t1+dt1,r1,g1,gg1);
514 h.Evaluate(t2+dt2,r2,g2,gg2);
515 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
516 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
517 if (dd<dm) break;
518 dt1*=0.5; dt2*=0.5;
519 if (div==0){
520 div =1;
521 }
522 if (div>512) {
523 break;
524 }
525 }
526 dm=dd;
527 t1+=dt1;
528 t2+=dt2;
7f572c00 529 }
7f572c00 530 Evaluate(t1,r1,g1,gg1);
531 h.Evaluate(t2,r2,g2,gg2);
532 //
533 dist = (r1[0]-r2[0])*(r1[0]-r2[0])+
534 (r1[1]-r2[1])*(r1[1]-r2[1])+
535 (r1[2]-r2[2])*(r1[2]-r2[2]);
536
537 R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4;
9be2fe3a 538 return 0;
7f572c00 539
540}
7f572c00 541
542
9be2fe3a 543Int_t AliHelix::ParabolicDCA2(AliHelix&h, //helixes
7f572c00 544 Double_t &t1, Double_t &t2,
9be2fe3a 545 Double_t &R, Double_t &dist, Double_t err[3], Int_t iter)
7f572c00 546{
547 //
548 //
549 // find intersection using linear fit
550 Double_t r1[3],g1[3],gg1[3];
551 Double_t r2[3],g2[3],gg2[3];
552 //
553 Evaluate(t1,r1,g1,gg1);
554 h.Evaluate(t2,r2,g2,gg2);
555
556 //
9be2fe3a 557 Double_t dx2=err[0];
558 Double_t dy2=err[1];
559 Double_t dz2=err[2];
7f572c00 560 //
561 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
562 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
563 //
564
565 iter++;
566 while (iter--) {
567 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
568 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
569
570 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
571 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
572 (g1[2]*g1[2] - dz*gg1[2])/dz2;
573 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
574 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
575 (g2[2]*g2[2] + dz*gg2[2])/dz2;
576 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
577
578 Double_t det=h11*h22-h12*h12;
579
580 Double_t dt1,dt2;
581 if (TMath::Abs(det)<1.e-33) {
582 //(quasi)singular Hessian
583 dt1=-gt1; dt2=-gt2;
584 } else {
585 dt1=-(gt1*h22 - gt2*h12)/det;
586 dt2=-(h11*gt2 - h12*gt1)/det;
587 }
588
589 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
590
591 //if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
592 // if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
593 // break;
594 // }
595
596 Double_t dd=dm;
597 for (Int_t div=1 ; div<512 ; div*=2) {
598 Evaluate(t1+dt1,r1,g1,gg1);
599 h.Evaluate(t2+dt2,r2,g2,gg2);
600 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
601 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
602 if (dd<dm) break;
603 dt1*=0.5; dt2*=0.5;
604 if (div==0){
605 div =1;
606 }
607 if (div>512) {
608 break;
609 }
610 }
611 dm=dd;
612 t1+=dt1;
613 t2+=dt2;
614 }
615 Evaluate(t1,r1,g1,gg1);
616 h.Evaluate(t2,r2,g2,gg2);
617 //
618 dist = (r1[0]-r2[0])*(r1[0]-r2[0])+
619 (r1[1]-r2[1])*(r1[1]-r2[1])+
620 (r1[2]-r2[2])*(r1[2]-r2[2]);
621
622 R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4;
623 return 0;
624
625}
626