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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" |
28 | ClassImp(AliHelix) | |
29 | ||
30 | ||
31 | //_______________________________________________________________________ | |
32 | AliHelix::AliHelix() | |
33 | { | |
34 | // | |
35 | // Default constructor | |
36 | // | |
37 | for (Int_t i =0;i<9;i++) fHelix[i]=0; | |
38 | } | |
39 | ||
40 | //_______________________________________________________________________ | |
176aff27 | 41 | AliHelix::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 | ||
48 | AliHelix::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 | |
84 | AliHelix::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 | 119 | AliHelix::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 | 159 | void 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 | ||
174 | void 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 | ||
216 | void 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 | 236 | Int_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 | 273 | Double_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 | 293 | Double_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 | 314 | Int_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 | ||
326 | Double_t AliHelix::GetPhaseZ(Double_t z0) | |
327 | { | |
328 | // | |
329 | // | |
330 | return (z0-fHelix[1])/fHelix[3]; | |
331 | } | |
332 | ||
333 | ||
334 | Int_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 | ||
417 | Int_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 | 458 | Int_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 | 543 | Int_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 |