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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"
26#include "TMath.h"
27ClassImp(AliHelix)
28
29
30//_______________________________________________________________________
31AliHelix::AliHelix()
32{
33 //
34 // Default constructor
35 //
36 for (Int_t i =0;i<9;i++) fHelix[i]=0;
37}
38
39//_______________________________________________________________________
176aff27 40AliHelix::AliHelix(const AliHelix &t):TObject(t){
7f572c00 41 //
42 //
43 for (Int_t i=0;i<9;i++)
44 fHelix[i]=t.fHelix[i];
45}
46
47AliHelix::AliHelix(const AliKalmanTrack &t)
48{
49 //
50 //
51 Double_t alpha,x,cs,sn;
52 t.GetExternalParameters(x,fHelix);
53 alpha=t.GetAlpha();
54 //
55 //circle parameters
56 fHelix[4]=fHelix[4]/t.GetConvConst(); // C
57 cs=TMath::Cos(alpha); sn=TMath::Sin(alpha);
58
59 Double_t xc, yc, rc;
60 rc = 1/fHelix[4];
61 xc = x-fHelix[2]*rc;
62 yc = fHelix[0]+TMath::Sqrt(1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4])/fHelix[4];
63
64 fHelix[6] = xc*cs - yc*sn;
65 fHelix[7] = xc*sn + yc*cs;
66 fHelix[8] = TMath::Abs(rc);
67 //
68 //
69 fHelix[5]=x*cs - fHelix[0]*sn; // x0
70 fHelix[0]=x*sn + fHelix[0]*cs; // y0
71 //fHelix[1]= // z0
72 fHelix[2]=TMath::ASin(fHelix[2]) + alpha; // phi0
73 //fHelix[3]= // tgl
74 //
75 //
76 fHelix[5] = fHelix[6];
77 fHelix[0] = fHelix[7];
78 //fHelix[5]-=TMath::Sin(fHelix[2])/fHelix[4];
79 //fHelix[0]+=TMath::Cos(fHelix[2])/fHelix[4];
80}
81
82AliHelix::AliHelix(Double_t x[3], Double_t p[3], Double_t charge, Double_t conversion)
83{
84 //
85 //
86 //
87 Double_t pt = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]);
88 if (TMath::Abs(conversion)<0.00000001)
89 conversion = AliKalmanTrack::GetConvConst();
90 //
91 //
92 fHelix[4] = charge/(conversion*pt); // C
93 fHelix[3] = p[2]/pt; // tgl
94 //
95 Double_t xc, yc, rc;
96 rc = 1/fHelix[4];
97 xc = x[0] -rc*p[1]/pt;
98 yc = x[1] +rc*p[0]/pt;
99 //
100 fHelix[5] = x[0]; // x0
101 fHelix[0] = x[1]; // y0
102 fHelix[1] = x[2]; // z0
103 //
104 fHelix[6] = xc;
105 fHelix[7] = yc;
106 fHelix[8] = TMath::Abs(rc);
107 //
108 fHelix[5]=xc;
109 fHelix[0]=yc;
110 //
111 if (TMath::Abs(p[1])<TMath::Abs(p[0])){
112 fHelix[2]=TMath::ASin(p[1]/pt);
113 if (charge*yc<charge*x[1]) fHelix[2] = TMath::Pi()-fHelix[2];
114 }
115 else{
116 fHelix[2]=TMath::ACos(p[0]/pt);
117 if (charge*xc>charge*x[0]) fHelix[2] = -fHelix[2];
118 }
119
120}
121
122void AliHelix::GetMomentum(Double_t phase, Double_t p[4],Double_t conversion)
123{
124 // return momentum at given phase
125 Double_t x[3],g[3],gg[3];
126 Evaluate(phase,x,g,gg);
127 if (TMath::Abs(conversion)<0.0001) conversion = AliKalmanTrack::GetConvConst();
128 Double_t mt = TMath::Sqrt(g[0]*g[0]+g[1]*g[1]);
129 p[0] = fHelix[8]*g[0]/(mt*conversion);
130 p[1] = fHelix[8]*g[1]/(mt*conversion);
131 p[2] = fHelix[8]*g[2]/(mt*conversion);
132}
133
134void AliHelix::GetAngle(Double_t t1, AliHelix &h, Double_t t2, Double_t angle[3])
135{
136 //
137 //
138 //
139 Double_t x1[3],g1[3],gg1[3];
140 Double_t x2[3],g2[3],gg2[3];
141 Evaluate(t1,x1,g1,gg1);
142 h.Evaluate(t2,x2,g2,gg2);
143
144 //
145 Double_t norm1r = g1[0]*g1[0]+g1[1]*g1[1];
146 Double_t norm1 = TMath::Sqrt(norm1r+g1[2]*g1[2]);
147 norm1r = TMath::Sqrt(norm1r);
148 //
149 Double_t norm2r = g2[0]*g2[0]+g2[1]*g2[1];
150 Double_t norm2 = TMath::Sqrt(norm2r+g2[2]*g2[2]);
151 norm2r = TMath::Sqrt(norm2r);
152 //
153 angle[0] = TMath::ACos((g1[0]*g2[0]+g1[1]*g2[1])/(norm1r*norm2r)); // angle in phi projection
154 angle[1] = TMath::ACos(((norm1r*norm2r)+g1[2]*g2[2])/(norm1*norm2)); // angle in rz projection
155 angle[2] = TMath::ACos((g1[0]*g2[0]+g1[1]*g2[1]+g1[2]*g2[2])/(norm1*norm2)); //3D angle
156
157
158
159
160}
161
162
163void AliHelix::Evaluate(Double_t t,
164 Double_t r[3], //radius vector
165 Double_t g[3], //first defivatives
166 Double_t gg[3]) //second derivatives
167{
168 //--------------------------------------------------------------------
169 // Calculate position of a point on a track and some derivatives at given phase
170 //--------------------------------------------------------------------
171 Double_t phase=fHelix[4]*t+fHelix[2];
172 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
173
174 //r[0] = fHelix[5] + (sn - fHelix[6])/fHelix[4];
175 //r[1] = fHelix[0] - (cs - fHelix[7])/fHelix[4];
176 r[0] = fHelix[5] + sn/fHelix[4];
177 r[1] = fHelix[0] - cs/fHelix[4];
178 r[2] = fHelix[1] + fHelix[3]*t;
179
180 g[0] = cs; g[1]=sn; g[2]=fHelix[3];
181
182 gg[0]=-fHelix[4]*sn; gg[1]=fHelix[4]*cs; gg[2]=0.;
183}
184
185Double_t AliHelix::GetPhase(Double_t x, Double_t y )
186
187{
188 //
189 //calculate helix param at given x,y point
190 //
191 Double_t phase = (x-fHelix[5])*fHelix[4];
192 if (TMath::Abs(phase)>=1)
193 phase = TMath::Sign(0.99999999999,phase);
194 phase = TMath::ASin(phase);
195
196 if ( ( ( fHelix[0]-y)*fHelix[4]) < 0.) {
197 if (phase>0)
198 phase = TMath::Pi()-phase;
199 else
200 phase = -(TMath::Pi()+phase);
201 }
202 if ( (phase-fHelix[2])>TMath::Pi()) phase = phase-2.*TMath::Pi();
203 if ( (phase-fHelix[2])<-TMath::Pi()) phase = phase+2.*TMath::Pi();
204
205 Double_t t = (phase-fHelix[2])/fHelix[4];
206
207 // Double_t r[3];
208 //Evaluate(t,r);
209 //if ( (TMath::Abs(r[0]-x)>0.01) || (TMath::Abs(r[1]-y)>0.01)){
210 // Double_t phase = (x-fHelix[5])*fHelix[4];
211 // printf("problem\n");
212 //}
213 return t;
214}
215
176aff27 216Int_t AliHelix::GetPhase(Double_t /*r0*/, Double_t * /*t[2]*/)
7f572c00 217{
218 //
219 //calculate helix param at given r point - return nearest point ()
220 //
221 // not implemented yet
222
223
224 return 0;
225}
226
227
228Double_t AliHelix::GetPhaseZ(Double_t z0)
229{
230 //
231 //
232 return (z0-fHelix[1])/fHelix[3];
233}
234
235
236Int_t AliHelix::GetRPHIintersections(AliHelix &h, Double_t phase[2][2], Double_t ri[2], Double_t cut)
237{
238 //--------------------------------------------------------------------
239 // This function returns phase vectors with intesection between helix (0, 1 or 2)
240 // in x-y plane projection
241 //--------------------------------------------------------------------
242 //
243 // Double_t * c1 = &fHelix[6];
244 //Double_t * c2 = &(h.fHelix[6]);
245 // Double_t c1[3] = {fHelix[5],fHelix[0],fHelix[8]};
246 Double_t c1[3] = {0,0,fHelix[8]};
247 Double_t c2[3] = {h.fHelix[5]-fHelix[5],h.fHelix[0]-fHelix[0],h.fHelix[8]};
248
249 Double_t d = TMath::Sqrt(c2[0]*c2[0]+c2[1]*c2[1]);
250 //
251 Double_t x0[2];
252 Double_t y0[2];
253 //
254 if ( d>=(c1[2]+c2[2])){
255 if (d>=(c1[2]+c2[2]+cut)) return 0;
256 x0[0] = (d+c1[2]-c2[2])*c2[0]/(2*d)+ fHelix[5];
257 y0[0] = (d+c1[2]-c2[2])*c2[1]/(2*d)+ fHelix[0];
258 return 0;
a1b77f90 259// phase[0][0] = GetPhase(x0[0],y0[0]);
260// phase[0][1] = h.GetPhase(x0[0],y0[0]);
261// ri[0] = x0[0]*x0[0]+y0[0]*y0[0];
262// return 1;
7f572c00 263 }
264 if ( (d+c2[2])<c1[2]){
265 if ( (d+c2[2])+cut<c1[2]) return 0;
266 //
267 Double_t xx = c2[0]+ c2[0]*c2[2]/d+ fHelix[5];
268 Double_t yy = c2[1]+ c2[1]*c2[2]/d+ fHelix[0];
269 phase[0][1] = h.GetPhase(xx,yy);
270 //
271 Double_t xx2 = c2[0]*c1[2]/d+ fHelix[5];
272 Double_t yy2 = c2[1]*c1[2]/d+ fHelix[0];
273 phase[0][0] = GetPhase(xx2,yy2);
274 ri[0] = xx*xx+yy*yy;
275 return 1;
276 }
277
278 if ( (d+c1[2])<c2[2]){
279 if ( (d+c1[2])+cut<c2[2]) return 0;
280 //
281 Double_t xx = -c2[0]*c1[2]/d+ fHelix[5];
282 Double_t yy = -c2[1]*c1[2]/d+ fHelix[0];
283 phase[0][1] = GetPhase(xx,yy);
284 //
285 Double_t xx2 = c2[0]- c2[0]*c2[2]/d+ fHelix[5];
286 Double_t yy2 = c2[1]- c2[1]*c2[2]/d+ fHelix[0];
287 phase[0][0] = h.GetPhase(xx2,yy2);
288 ri[0] = xx*xx+yy*yy;
289 return 1;
290 }
291
292 Double_t d1 = (d*d+c1[2]*c1[2]-c2[2]*c2[2])/(2.*d);
293 Double_t v1 = c1[2]*c1[2]-d1*d1;
294 if (v1<0) return 0;
295 v1 = TMath::Sqrt(v1);
296 //
297 x0[0] = (c2[0]*d1+c2[1]*v1)/d + fHelix[5];
298 y0[0] = (c2[1]*d1-c2[0]*v1)/d + fHelix[0];
299 //
300 x0[1] = (c2[0]*d1-c2[1]*v1)/d + fHelix[5];
301 y0[1] = (c2[1]*d1+c2[0]*v1)/d + fHelix[0];
302 //
303 for (Int_t i=0;i<2;i++){
304 phase[i][0] = GetPhase(x0[i],y0[i]);
305 phase[i][1] = h.GetPhase(x0[i],y0[i]);
306 ri[i] = x0[i]*x0[i]+y0[i]*y0[i];
307 }
308 return 2;
309}
310
311/*
312
313Int_t AliHelix::GetRPHIintersections(AliHelix &h, Double_t phase[2][2], Double_t ri[2], Double_t cut)
314{
315 //--------------------------------------------------------------------
316 // This function returns phase vectors with intesection between helix (0, 1 or 2)
317 // in x-y plane projection
318 //--------------------------------------------------------------------
319 //
320 Double_t * c1 = &fHelix[6];
321 Double_t * c2 = &(h.fHelix[6]);
322 Double_t d = TMath::Sqrt((c1[0]-c2[0])*(c1[0]-c2[0])+(c1[1]-c2[1])*(c1[1]-c2[1]));
323 //
324 Double_t x0[2];
325 Double_t y0[2];
326 //
327 if ( d>=(c1[2]+c2[2])){
328 if (d>=(c1[2]+c2[2]+cut)) return 0;
329 x0[0] = c1[0]+ (d+c1[2]-c2[2])*(c2[0]-c1[0])/(2*d);
330 y0[0] = c1[1]+ (d+c1[2]-c2[2])*(c2[1]-c1[1])/(2*d);
331 return 0;
332 phase[0][0] = GetPhase(x0[0],y0[0]);
333 phase[0][1] = h.GetPhase(x0[0],y0[0]);
334 ri[0] = x0[0]*x0[0]+y0[0]*y0[0];
335 return 1;
336 }
337 if ( (d+c2[2])<c1[2]){
338 if ( (d+c2[2])+cut<c1[2]) return 0;
339 //
340 Double_t xx = c2[0]+ (c2[0]-c1[0])*c2[2]/d;
341 Double_t yy = c2[1]+ (c2[1]-c1[1])*c2[2]/d;
342 phase[0][1] = h.GetPhase(xx,yy);
343 //
344 Double_t xx2 = c1[0]- (c1[0]-c2[0])*c1[2]/d;
345 Double_t yy2 = c1[1]- (c1[1]-c2[1])*c1[2]/d;
346 phase[0][0] = GetPhase(xx2,yy2);
347 //if ( (TMath::Abs(xx2-xx)>cut)||(TMath::Abs(yy2-yy)>cut)){
348 // printf("problem\n");
349 //}
350 ri[0] = xx*xx+yy*yy;
351 return 1;
352 }
353
354 if ( (d+c1[2])<c2[2]){
355 if ( (d+c1[2])+cut<c2[2]) return 0;
356 //
357 Double_t xx = c1[0]+ (c1[0]-c2[0])*c1[2]/d;
358 Double_t yy = c1[1]+ (c1[1]-c2[1])*c1[2]/d;
359 phase[0][1] = GetPhase(xx,yy);
360 //
361 Double_t xx2 = c2[0]- (c2[0]-c1[0])*c2[2]/d;
362 Double_t yy2 = c2[1]- (c2[1]-c1[1])*c2[2]/d;
363 phase[0][0] = h.GetPhase(xx2,yy2);
364 //if ( (TMath::Abs(xx2-xx)>cut)||(TMath::Abs(yy2-yy)>cut)){
365 // printf("problem\n");
366 //}
367 ri[0] = xx*xx+yy*yy;
368 return 1;
369 }
370
371 Double_t d1 = (d*d+c1[2]*c1[2]-c2[2]*c2[2])/(2.*d);
372 Double_t v1 = c1[2]*c1[2]-d1*d1;
373 if (v1<0) return 0;
374 v1 = TMath::Sqrt(v1);
375 //
376 x0[0] = c1[0]+ ((c2[0]-c1[0])*d1-(c1[1]-c2[1])*v1)/d;
377 y0[0] = c1[1]+ ((c2[1]-c1[1])*d1+(c1[0]-c2[0])*v1)/d;
378 //
379 x0[1] = c1[0]+ ((c2[0]-c1[0])*d1+(c1[1]-c2[1])*v1)/d;
380 y0[1] = c1[1]+ ((c2[1]-c1[1])*d1-(c1[0]-c2[0])*v1)/d;
381 //
382 for (Int_t i=0;i<2;i++){
383 phase[i][0] = GetPhase(x0[i],y0[i]);
384 phase[i][1] = h.GetPhase(x0[i],y0[i]);
385 ri[i] = x0[i]*x0[i]+y0[i]*y0[i];
386 }
387 return 2;
388}
389*/
390
391
392Int_t AliHelix::LinearDCA(AliHelix &h, Double_t &t1, Double_t &t2,
393 Double_t &R, Double_t &dist)
394{
395 //
396 //
397 // find intersection using linear approximation
398 Double_t r1[3],g1[3],gg1[3];
399 Double_t r2[3],g2[3],gg2[3];
400 //
401 Evaluate(t1,r1,g1,gg1);
402 h.Evaluate(t2,r2,g2,gg2);
403 //
404 Double_t g1_2 = g1[0]*g1[0] +g1[1]*g1[1] +g1[2]*g1[2];
405 Double_t g2_2 = g2[0]*g2[0] +g2[1]*g2[1] +g2[2]*g2[2];
406 Double_t g1x2 = g1[0]*g2[0] +g1[1]*g2[1] +g1[2]*g2[2];
407 Double_t det = g1_2*g2_2 - g1x2*g1x2;
408 //
409 if (TMath::Abs(det)>0){
410 //
411 Double_t r1g1 = r1[0]*g1[0] +r1[1]*g1[1] +r1[2]*g1[2];
412 Double_t r2g1 = r2[0]*g1[0] +r2[1]*g1[1] +r2[2]*g1[2];
413 Double_t r1g2 = r1[0]*g2[0] +r1[1]*g2[1] +r1[2]*g2[2];
414 Double_t r2g2 = r2[0]*g2[0] +r2[1]*g2[1] +r2[2]*g2[2];
415 //
416 Double_t dt = - ( g2_2*(r1g1-r2g1) - g1x2*(r1g2-r2g2)) / det;
417 Double_t dp = - ( g1_2*(r2g2-r1g2) - g1x2*(r2g1-r1g1)) / det;
418 //
419 t1+=dt;
420 t2+=dp;
421 Evaluate(t1,r1);
422 h.Evaluate(t2,r2);
423 //
424 dist = (r1[0]-r2[0])*(r1[0]-r2[0])+
425 (r1[1]-r2[1])*(r1[1]-r2[1])+
426 (r1[2]-r2[2])*(r1[2]-r2[2]);
427 R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4.;
428 }
429 return 0;
430}
431
432
433
434
435/*
436Int_t AliHelix::ParabolicDCA(AliHelix&h, //helixes
437 Double_t &t1, Double_t &t2,
438 Double_t &R, Double_t &dist, Int_t iter)
439{
440 //
441 //
442 // find intersection using linear fit
443 Double_t r1[3],g1[3],gg1[3];
444 Double_t r2[3],g2[3],gg2[3];
445 //
446 Evaluate(t1,r1,g1,gg1);
447 h.Evaluate(t2,r2,g2,gg2);
448
449 //
450 Double_t dx2=1.;
451 Double_t dy2=1.;
452 Double_t dz2=1.;
453 //
454 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
455 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
456 //
457
458 iter++;
459 while (iter--) {
460
461 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
462 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
463 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
464 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
465 (g1[2]*g1[2] - dz*gg1[2])/dz2;
466 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
467 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
468 (g2[2]*g2[2] + dz*gg2[2])/dz2;
469 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
470
471 Double_t det=h11*h22-h12*h12;
472
473 Double_t dt1,dt2;
474 if (TMath::Abs(det)<1.e-33) {
475 //(quasi)singular Hessian
476 dt1=-gt1; dt2=-gt2;
477 } else {
478 dt1=-(gt1*h22 - gt2*h12)/det;
479 dt2=-(h11*gt2 - h12*gt1)/det;
480 }
481
482 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
483
484 //check delta(phase1) ?
485 //check delta(phase2) ?
486
487 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
488 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
489 //if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
490 // Warning("GetDCA"," stopped at not a stationary point !\n");
491 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
492 if (lmb < 0.)
493 //Warning("GetDCA"," stopped at not a minimum !\n");
494 break;
495 }
496
497 Double_t dd=dm;
498 for (Int_t div=1 ; ; div*=2) {
499 Evaluate(t1+dt1,r1,g1,gg1);
500 h.Evaluate(t2+dt2,r2,g2,gg2);
501 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
502 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
503 if (dd<dm) break;
504 dt1*=0.5; dt2*=0.5;
505 if (div>512) {
506 //Warning("GetDCA"," overshoot !\n");
507 break;
508 }
509 }
510 dm=dd;
511
512 t1+=dt1;
513 t2+=dt2;
514
515 }
516
517 Evaluate(t1,r1,g1,gg1);
518 h.Evaluate(t2,r2,g2,gg2);
519 //
520 dist = (r1[0]-r2[0])*(r1[0]-r2[0])+
521 (r1[1]-r2[1])*(r1[1]-r2[1])+
522 (r1[2]-r2[2])*(r1[2]-r2[2]);
523
524 R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4;
525
526}
527*/
528
529
530
531
532
533
534Int_t AliHelix::ParabolicDCA(AliHelix&h, //helixes
535 Double_t &t1, Double_t &t2,
536 Double_t &R, Double_t &dist, Int_t iter)
537{
538 //
539 //
540 // find intersection using linear fit
541 Double_t r1[3],g1[3],gg1[3];
542 Double_t r2[3],g2[3],gg2[3];
543 //
544 Evaluate(t1,r1,g1,gg1);
545 h.Evaluate(t2,r2,g2,gg2);
546
547 //
548 Double_t dx2=1.;
549 Double_t dy2=1.;
550 Double_t dz2=1.;
551 //
552 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
553 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
554 //
555
556 iter++;
557 while (iter--) {
558 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
559 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
560
561 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
562 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
563 (g1[2]*g1[2] - dz*gg1[2])/dz2;
564 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
565 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
566 (g2[2]*g2[2] + dz*gg2[2])/dz2;
567 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
568
569 Double_t det=h11*h22-h12*h12;
570
571 Double_t dt1,dt2;
572 if (TMath::Abs(det)<1.e-33) {
573 //(quasi)singular Hessian
574 dt1=-gt1; dt2=-gt2;
575 } else {
576 dt1=-(gt1*h22 - gt2*h12)/det;
577 dt2=-(h11*gt2 - h12*gt1)/det;
578 }
579
580 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
581
582 //if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
583 // if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
584 // break;
585 // }
586
587 Double_t dd=dm;
588 for (Int_t div=1 ; div<512 ; div*=2) {
589 Evaluate(t1+dt1,r1,g1,gg1);
590 h.Evaluate(t2+dt2,r2,g2,gg2);
591 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
592 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
593 if (dd<dm) break;
594 dt1*=0.5; dt2*=0.5;
595 if (div==0){
596 div =1;
597 }
598 if (div>512) {
599 break;
600 }
601 }
602 dm=dd;
603 t1+=dt1;
604 t2+=dt2;
605 }
606 Evaluate(t1,r1,g1,gg1);
607 h.Evaluate(t2,r2,g2,gg2);
608 //
609 dist = (r1[0]-r2[0])*(r1[0]-r2[0])+
610 (r1[1]-r2[1])*(r1[1]-r2[1])+
611 (r1[2]-r2[2])*(r1[2]-r2[2]);
612
613 R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4;
614 return 0;
615
616}
617