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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" | |
6c94f330 | 26 | #include "AliTracker.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 | |
022ba35d | 57 | //PH Sometimes fP4 and fHelix[4] are very big and the calculation |
58 | //PH of the Sqrt cannot be done. To be investigated... | |
190fc854 | 59 | fHelix[4]=fHelix[4]/(-1000/0.299792458/AliTracker::GetBz()); // C |
7f572c00 | 60 | cs=TMath::Cos(alpha); sn=TMath::Sin(alpha); |
61 | ||
62 | Double_t xc, yc, rc; | |
63 | rc = 1/fHelix[4]; | |
64 | xc = x-fHelix[2]*rc; | |
022ba35d | 65 | Double_t dummy = 1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4]; |
66 | if (dummy<0) { | |
67 | AliError(Form("The argument of the Sqrt is %f => set to 0\n",dummy)); | |
68 | dummy = 0; | |
69 | } | |
70 | yc = fHelix[0]+TMath::Sqrt(dummy)/fHelix[4]; | |
7f572c00 | 71 | |
72 | fHelix[6] = xc*cs - yc*sn; | |
73 | fHelix[7] = xc*sn + yc*cs; | |
74 | fHelix[8] = TMath::Abs(rc); | |
75 | // | |
76 | // | |
77 | fHelix[5]=x*cs - fHelix[0]*sn; // x0 | |
78 | fHelix[0]=x*sn + fHelix[0]*cs; // y0 | |
79 | //fHelix[1]= // z0 | |
9be2fe3a | 80 | fHelix[2]=TMath::ATan2(-(fHelix[5]-fHelix[6]),fHelix[0]-fHelix[7]); // phi0 |
81 | if (fHelix[4]>0) fHelix[2]-=TMath::Pi(); | |
82 | ||
7f572c00 | 83 | //fHelix[3]= // tgl |
84 | // | |
85 | // | |
86 | fHelix[5] = fHelix[6]; | |
87 | fHelix[0] = fHelix[7]; | |
7f572c00 | 88 | } |
89 | ||
51ad6848 | 90 | |
91 | AliHelix::AliHelix(const AliExternalTrackParam &t) | |
92 | { | |
93 | // | |
94 | // | |
95 | Double_t alpha,x,cs,sn; | |
96 | const Double_t *param =t.GetParameter(); | |
97 | for (Int_t i=0;i<5;i++) fHelix[i]=param[i]; | |
c9ec41e8 | 98 | x = t.GetX(); |
99 | alpha=t.GetAlpha(); | |
51ad6848 | 100 | // |
101 | //circle parameters | |
022ba35d | 102 | //PH Sometimes fP4 and fHelix[4] are very big and the calculation |
103 | //PH of the Sqrt cannot be done. To be investigated... | |
190fc854 | 104 | fHelix[4]=fHelix[4]/(-1000/0.299792458/AliTracker::GetBz()); // C |
51ad6848 | 105 | cs=TMath::Cos(alpha); sn=TMath::Sin(alpha); |
106 | ||
107 | Double_t xc, yc, rc; | |
108 | rc = 1/fHelix[4]; | |
109 | xc = x-fHelix[2]*rc; | |
022ba35d | 110 | Double_t dummy = 1-(x-xc)*(x-xc)*fHelix[4]*fHelix[4]; |
111 | if (dummy<0) { | |
112 | AliError(Form("The argument of the Sqrt is %f => set to 0\n",dummy)); | |
113 | dummy = 0; | |
114 | } | |
115 | yc = fHelix[0]+TMath::Sqrt(dummy)/fHelix[4]; | |
51ad6848 | 116 | |
117 | fHelix[6] = xc*cs - yc*sn; | |
118 | fHelix[7] = xc*sn + yc*cs; | |
119 | fHelix[8] = TMath::Abs(rc); | |
120 | // | |
121 | // | |
122 | fHelix[5]=x*cs - fHelix[0]*sn; // x0 | |
123 | fHelix[0]=x*sn + fHelix[0]*cs; // y0 | |
124 | //fHelix[1]= // z0 | |
125 | fHelix[2]=TMath::ASin(fHelix[2]) + alpha; // phi0 | |
126 | //fHelix[3]= // tgl | |
127 | // | |
128 | // | |
129 | fHelix[5] = fHelix[6]; | |
130 | fHelix[0] = fHelix[7]; | |
51ad6848 | 131 | } |
132 | ||
7f572c00 | 133 | AliHelix::AliHelix(Double_t x[3], Double_t p[3], Double_t charge, Double_t conversion) |
134 | { | |
135 | // | |
136 | // | |
137 | // | |
138 | Double_t pt = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]); | |
139 | if (TMath::Abs(conversion)<0.00000001) | |
190fc854 | 140 | conversion = -1000/0.299792458/AliTracker::GetBz(); |
7f572c00 | 141 | // |
142 | // | |
143 | fHelix[4] = charge/(conversion*pt); // C | |
144 | fHelix[3] = p[2]/pt; // tgl | |
145 | // | |
146 | Double_t xc, yc, rc; | |
147 | rc = 1/fHelix[4]; | |
148 | xc = x[0] -rc*p[1]/pt; | |
149 | yc = x[1] +rc*p[0]/pt; | |
150 | // | |
151 | fHelix[5] = x[0]; // x0 | |
152 | fHelix[0] = x[1]; // y0 | |
153 | fHelix[1] = x[2]; // z0 | |
154 | // | |
155 | fHelix[6] = xc; | |
156 | fHelix[7] = yc; | |
157 | fHelix[8] = TMath::Abs(rc); | |
158 | // | |
159 | fHelix[5]=xc; | |
160 | fHelix[0]=yc; | |
161 | // | |
162 | if (TMath::Abs(p[1])<TMath::Abs(p[0])){ | |
163 | fHelix[2]=TMath::ASin(p[1]/pt); | |
164 | if (charge*yc<charge*x[1]) fHelix[2] = TMath::Pi()-fHelix[2]; | |
165 | } | |
166 | else{ | |
167 | fHelix[2]=TMath::ACos(p[0]/pt); | |
168 | if (charge*xc>charge*x[0]) fHelix[2] = -fHelix[2]; | |
169 | } | |
170 | ||
171 | } | |
172 | ||
81e97e0d | 173 | void AliHelix::GetMomentum(Double_t phase, Double_t p[4],Double_t conversion, Double_t *xr) |
7f572c00 | 174 | { |
175 | // return momentum at given phase | |
176 | Double_t x[3],g[3],gg[3]; | |
177 | Evaluate(phase,x,g,gg); | |
549102ce | 178 | // if (TMath::Abs(conversion)<0.0001) conversion = -1000/0.299792458/AliTracker::GetBz(); |
179 | if (TMath::Abs(conversion)<0.0001) conversion = TMath::Abs(1./kB2C/AliTracker::GetBz()); | |
180 | ||
7f572c00 | 181 | Double_t mt = TMath::Sqrt(g[0]*g[0]+g[1]*g[1]); |
182 | p[0] = fHelix[8]*g[0]/(mt*conversion); | |
183 | p[1] = fHelix[8]*g[1]/(mt*conversion); | |
184 | p[2] = fHelix[8]*g[2]/(mt*conversion); | |
81e97e0d | 185 | if (xr){ |
186 | xr[0] = x[0]; xr[1] = x[1]; xr[2] = x[2]; | |
187 | } | |
7f572c00 | 188 | } |
189 | ||
190 | void AliHelix::GetAngle(Double_t t1, AliHelix &h, Double_t t2, Double_t angle[3]) | |
191 | { | |
192 | // | |
193 | // | |
194 | // | |
195 | Double_t x1[3],g1[3],gg1[3]; | |
196 | Double_t x2[3],g2[3],gg2[3]; | |
197 | Evaluate(t1,x1,g1,gg1); | |
198 | h.Evaluate(t2,x2,g2,gg2); | |
199 | ||
200 | // | |
201 | Double_t norm1r = g1[0]*g1[0]+g1[1]*g1[1]; | |
202 | Double_t norm1 = TMath::Sqrt(norm1r+g1[2]*g1[2]); | |
203 | norm1r = TMath::Sqrt(norm1r); | |
204 | // | |
205 | Double_t norm2r = g2[0]*g2[0]+g2[1]*g2[1]; | |
206 | Double_t norm2 = TMath::Sqrt(norm2r+g2[2]*g2[2]); | |
207 | norm2r = TMath::Sqrt(norm2r); | |
208 | // | |
51ad6848 | 209 | angle[0] = (g1[0]*g2[0]+g1[1]*g2[1])/(norm1r*norm2r); // angle in phi projection |
210 | if (TMath::Abs(angle[0])<1.) angle[0] = TMath::ACos(angle[0]); | |
9be2fe3a | 211 | else{ |
212 | if (angle[0]>0) angle[0] = 0; | |
213 | if (angle[0]<0) angle[0] = TMath::Pi(); | |
214 | } | |
51ad6848 | 215 | // |
216 | angle[1] = ((norm1r*norm2r)+g1[2]*g2[2])/(norm1*norm2); // angle in rz projection | |
217 | if (TMath::Abs(angle[1])<1.) angle[1] = TMath::ACos(angle[1]); | |
9be2fe3a | 218 | else |
219 | angle[1]=0; | |
51ad6848 | 220 | |
221 | angle[2] = (g1[0]*g2[0]+g1[1]*g2[1]+g1[2]*g2[2])/(norm1*norm2); //3D angle | |
222 | if (TMath::Abs(angle[2])<1.) angle[2] = TMath::ACos(angle[2]); | |
9be2fe3a | 223 | else |
224 | angle[2]=0; | |
7f572c00 | 225 | |
51ad6848 | 226 | |
7f572c00 | 227 | |
228 | ||
229 | } | |
230 | ||
231 | ||
232 | void AliHelix::Evaluate(Double_t t, | |
233 | Double_t r[3], //radius vector | |
234 | Double_t g[3], //first defivatives | |
235 | Double_t gg[3]) //second derivatives | |
236 | { | |
237 | //-------------------------------------------------------------------- | |
238 | // Calculate position of a point on a track and some derivatives at given phase | |
239 | //-------------------------------------------------------------------- | |
240 | Double_t phase=fHelix[4]*t+fHelix[2]; | |
241 | Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase); | |
242 | ||
7f572c00 | 243 | r[0] = fHelix[5] + sn/fHelix[4]; |
244 | r[1] = fHelix[0] - cs/fHelix[4]; | |
245 | r[2] = fHelix[1] + fHelix[3]*t; | |
246 | ||
247 | g[0] = cs; g[1]=sn; g[2]=fHelix[3]; | |
248 | ||
249 | gg[0]=-fHelix[4]*sn; gg[1]=fHelix[4]*cs; gg[2]=0.; | |
250 | } | |
251 | ||
9be2fe3a | 252 | Int_t AliHelix::GetClosestPhases(AliHelix &h, Double_t phase[2][2]) |
253 | { | |
254 | // | |
255 | // get phases to minimize distances | |
256 | // | |
257 | Double_t xyz0[3]; | |
258 | Double_t xyz1[3]; | |
259 | ||
260 | for (Int_t i=0;i<2;i++){ | |
261 | Evaluate(phase[i][0] ,xyz0); | |
262 | h.Evaluate(phase[i][1],xyz1); | |
263 | Double_t mindist = TMath::Sqrt((xyz0[0]-xyz1[0])*(xyz0[0]-xyz1[0])+ | |
264 | (xyz0[1]-xyz1[1])*(xyz0[1]-xyz1[1])+ | |
265 | (xyz0[2]-xyz1[2])*(xyz0[2]-xyz1[2])); | |
266 | Double_t tbest[2]={phase[i][0],phase[i][1]}; | |
267 | for (Int_t i0=-1;i0<=1;i0++){ | |
268 | Double_t t0 = ((phase[i][0]*fHelix[4])+i0*2.*TMath::Pi())/fHelix[4]; | |
269 | Evaluate(t0,xyz0); | |
270 | for (Int_t i1=-1;i1<=1;i1++){ | |
271 | Double_t t1 = ((phase[i][1]*h.fHelix[4])+i1*2.*TMath::Pi())/h.fHelix[4]; | |
272 | h.Evaluate(t1,xyz1); | |
273 | Double_t dist = TMath::Sqrt((xyz0[0]-xyz1[0])*(xyz0[0]-xyz1[0])+ | |
274 | (xyz0[1]-xyz1[1])*(xyz0[1]-xyz1[1])+ | |
275 | (xyz0[2]-xyz1[2])*(xyz0[2]-xyz1[2])); | |
276 | if (dist<=mindist){ | |
277 | tbest[0] = t0; | |
278 | tbest[1] = t1; | |
279 | mindist=dist; | |
280 | } | |
281 | } | |
282 | } | |
283 | phase[i][0] = tbest[0]; | |
284 | phase[i][1] = tbest[1]; | |
285 | } | |
286 | return 1; | |
287 | } | |
288 | ||
81e97e0d | 289 | Double_t AliHelix::GetPointAngle(AliHelix &h, Double_t phase[2], const Float_t * vertex) |
290 | { | |
291 | // | |
292 | // get point angle bettwen two helixes | |
293 | // | |
294 | Double_t r0[3],p0[4]; | |
295 | Double_t r1[3],p1[4]; | |
296 | GetMomentum(phase[0],p0,1,r0); | |
297 | h.GetMomentum(phase[1],p1,1,r1); | |
298 | // | |
299 | 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]}; | |
300 | //intersection point - relative to the prim vertex | |
301 | Double_t p[3] = { p0[0]+p1[0], p0[1]+p1[1],p0[2]+p1[2]}; | |
302 | // derivation vector | |
303 | Double_t normr = TMath::Sqrt(r[0]*r[0]+r[1]*r[1]+r[2]*r[2]); | |
304 | Double_t normp = TMath::Sqrt(p[0]*p[0]+p[1]*p[1]+p[2]*p[2]); | |
305 | Double_t pointAngle = (r[0]*p[0]+r[1]*p[1]+r[2]*p[2])/(normr*normp); | |
306 | return pointAngle; | |
307 | } | |
308 | ||
7f572c00 | 309 | Double_t AliHelix::GetPhase(Double_t x, Double_t y ) |
310 | ||
311 | { | |
312 | // | |
313 | //calculate helix param at given x,y point | |
314 | // | |
9be2fe3a | 315 | //Double_t phase2 = TMath::ATan2((y-fHelix[0]), (x-fHelix[5]))- TMath::Pi()/2.; |
316 | Double_t phase2 = TMath::ATan2(-(x-fHelix[5]),(y-fHelix[0])); | |
317 | Int_t sign = (fHelix[4]>0)? 1:-1; | |
318 | if (sign>0) phase2 = phase2-TMath::Pi(); | |
319 | // | |
320 | Float_t delta = TMath::Nint((phase2-fHelix[2])/(2.*TMath::Pi())); | |
321 | phase2-= 2*TMath::Pi()*delta; | |
322 | if ( (phase2-fHelix[2])>TMath::Pi()) phase2 -=2.*TMath::Pi(); | |
323 | if ( (phase2-fHelix[2])<-TMath::Pi()) phase2+=2.*TMath::Pi(); | |
7f572c00 | 324 | |
9be2fe3a | 325 | Double_t t = (phase2-fHelix[2]); |
326 | t/=fHelix[4]; | |
7f572c00 | 327 | return t; |
328 | } | |
329 | ||
176aff27 | 330 | Int_t AliHelix::GetPhase(Double_t /*r0*/, Double_t * /*t[2]*/) |
7f572c00 | 331 | { |
332 | // | |
333 | //calculate helix param at given r point - return nearest point () | |
334 | // | |
335 | // not implemented yet | |
336 | ||
337 | ||
338 | return 0; | |
339 | } | |
340 | ||
341 | ||
342 | Double_t AliHelix::GetPhaseZ(Double_t z0) | |
343 | { | |
344 | // | |
345 | // | |
346 | return (z0-fHelix[1])/fHelix[3]; | |
347 | } | |
348 | ||
349 | ||
350 | Int_t AliHelix::GetRPHIintersections(AliHelix &h, Double_t phase[2][2], Double_t ri[2], Double_t cut) | |
351 | { | |
352 | //-------------------------------------------------------------------- | |
353 | // This function returns phase vectors with intesection between helix (0, 1 or 2) | |
354 | // in x-y plane projection | |
355 | //-------------------------------------------------------------------- | |
356 | // | |
357 | // Double_t * c1 = &fHelix[6]; | |
358 | //Double_t * c2 = &(h.fHelix[6]); | |
359 | // Double_t c1[3] = {fHelix[5],fHelix[0],fHelix[8]}; | |
9e8f4343 | 360 | |
361 | // PH initiaziation in case of return | |
362 | phase[0][0]=phase[0][1]=phase[1][0]=phase[1][1]=0; | |
363 | ri[0]=ri[1]=1000000; | |
364 | ||
7f572c00 | 365 | Double_t c1[3] = {0,0,fHelix[8]}; |
366 | Double_t c2[3] = {h.fHelix[5]-fHelix[5],h.fHelix[0]-fHelix[0],h.fHelix[8]}; | |
367 | ||
368 | Double_t d = TMath::Sqrt(c2[0]*c2[0]+c2[1]*c2[1]); | |
51ad6848 | 369 | if (d<0.000000000001) return 0; |
7f572c00 | 370 | // |
371 | Double_t x0[2]; | |
372 | Double_t y0[2]; | |
373 | // | |
374 | if ( d>=(c1[2]+c2[2])){ | |
375 | if (d>=(c1[2]+c2[2]+cut)) return 0; | |
376 | x0[0] = (d+c1[2]-c2[2])*c2[0]/(2*d)+ fHelix[5]; | |
377 | y0[0] = (d+c1[2]-c2[2])*c2[1]/(2*d)+ fHelix[0]; | |
51ad6848 | 378 | // return 0; |
9e8f4343 | 379 | phase[1][0] = phase[0][0] = GetPhase(x0[0],y0[0]); |
380 | phase[1][1] = phase[0][1] = h.GetPhase(x0[0],y0[0]); | |
381 | ri[1] = ri[0] = x0[0]*x0[0]+y0[0]*y0[0]; | |
51ad6848 | 382 | return 1; |
7f572c00 | 383 | } |
384 | if ( (d+c2[2])<c1[2]){ | |
385 | if ( (d+c2[2])+cut<c1[2]) return 0; | |
386 | // | |
387 | Double_t xx = c2[0]+ c2[0]*c2[2]/d+ fHelix[5]; | |
388 | Double_t yy = c2[1]+ c2[1]*c2[2]/d+ fHelix[0]; | |
9e8f4343 | 389 | phase[1][1] = phase[0][1] = h.GetPhase(xx,yy); |
7f572c00 | 390 | // |
391 | Double_t xx2 = c2[0]*c1[2]/d+ fHelix[5]; | |
392 | Double_t yy2 = c2[1]*c1[2]/d+ fHelix[0]; | |
9e8f4343 | 393 | phase[1][0] = phase[0][0] = GetPhase(xx2,yy2); |
394 | ri[1] = ri[0] = xx*xx+yy*yy; | |
7f572c00 | 395 | return 1; |
396 | } | |
397 | ||
398 | if ( (d+c1[2])<c2[2]){ | |
399 | if ( (d+c1[2])+cut<c2[2]) return 0; | |
400 | // | |
401 | Double_t xx = -c2[0]*c1[2]/d+ fHelix[5]; | |
402 | Double_t yy = -c2[1]*c1[2]/d+ fHelix[0]; | |
9e8f4343 | 403 | phase[1][1] = phase[0][1] = GetPhase(xx,yy); |
7f572c00 | 404 | // |
405 | Double_t xx2 = c2[0]- c2[0]*c2[2]/d+ fHelix[5]; | |
406 | Double_t yy2 = c2[1]- c2[1]*c2[2]/d+ fHelix[0]; | |
9e8f4343 | 407 | phase[1][0] = phase[0][0] = h.GetPhase(xx2,yy2); |
408 | ri[1] = ri[0] = xx*xx+yy*yy; | |
7f572c00 | 409 | return 1; |
410 | } | |
411 | ||
412 | Double_t d1 = (d*d+c1[2]*c1[2]-c2[2]*c2[2])/(2.*d); | |
413 | Double_t v1 = c1[2]*c1[2]-d1*d1; | |
414 | if (v1<0) return 0; | |
415 | v1 = TMath::Sqrt(v1); | |
416 | // | |
417 | x0[0] = (c2[0]*d1+c2[1]*v1)/d + fHelix[5]; | |
418 | y0[0] = (c2[1]*d1-c2[0]*v1)/d + fHelix[0]; | |
419 | // | |
420 | x0[1] = (c2[0]*d1-c2[1]*v1)/d + fHelix[5]; | |
421 | y0[1] = (c2[1]*d1+c2[0]*v1)/d + fHelix[0]; | |
422 | // | |
423 | for (Int_t i=0;i<2;i++){ | |
424 | phase[i][0] = GetPhase(x0[i],y0[i]); | |
425 | phase[i][1] = h.GetPhase(x0[i],y0[i]); | |
426 | ri[i] = x0[i]*x0[i]+y0[i]*y0[i]; | |
427 | } | |
428 | return 2; | |
429 | } | |
430 | ||
7f572c00 | 431 | |
432 | ||
433 | Int_t AliHelix::LinearDCA(AliHelix &h, Double_t &t1, Double_t &t2, | |
434 | Double_t &R, Double_t &dist) | |
435 | { | |
436 | // | |
437 | // | |
438 | // find intersection using linear approximation | |
439 | Double_t r1[3],g1[3],gg1[3]; | |
440 | Double_t r2[3],g2[3],gg2[3]; | |
441 | // | |
442 | Evaluate(t1,r1,g1,gg1); | |
443 | h.Evaluate(t2,r2,g2,gg2); | |
444 | // | |
445 | Double_t g1_2 = g1[0]*g1[0] +g1[1]*g1[1] +g1[2]*g1[2]; | |
446 | Double_t g2_2 = g2[0]*g2[0] +g2[1]*g2[1] +g2[2]*g2[2]; | |
447 | Double_t g1x2 = g1[0]*g2[0] +g1[1]*g2[1] +g1[2]*g2[2]; | |
448 | Double_t det = g1_2*g2_2 - g1x2*g1x2; | |
449 | // | |
450 | if (TMath::Abs(det)>0){ | |
451 | // | |
452 | Double_t r1g1 = r1[0]*g1[0] +r1[1]*g1[1] +r1[2]*g1[2]; | |
453 | Double_t r2g1 = r2[0]*g1[0] +r2[1]*g1[1] +r2[2]*g1[2]; | |
454 | Double_t r1g2 = r1[0]*g2[0] +r1[1]*g2[1] +r1[2]*g2[2]; | |
455 | Double_t r2g2 = r2[0]*g2[0] +r2[1]*g2[1] +r2[2]*g2[2]; | |
456 | // | |
457 | Double_t dt = - ( g2_2*(r1g1-r2g1) - g1x2*(r1g2-r2g2)) / det; | |
458 | Double_t dp = - ( g1_2*(r2g2-r1g2) - g1x2*(r2g1-r1g1)) / det; | |
459 | // | |
460 | t1+=dt; | |
461 | t2+=dp; | |
462 | Evaluate(t1,r1); | |
463 | h.Evaluate(t2,r2); | |
464 | // | |
465 | dist = (r1[0]-r2[0])*(r1[0]-r2[0])+ | |
466 | (r1[1]-r2[1])*(r1[1]-r2[1])+ | |
467 | (r1[2]-r2[2])*(r1[2]-r2[2]); | |
468 | R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4.; | |
469 | } | |
470 | return 0; | |
471 | } | |
472 | ||
473 | ||
7f572c00 | 474 | Int_t AliHelix::ParabolicDCA(AliHelix&h, //helixes |
475 | Double_t &t1, Double_t &t2, | |
476 | Double_t &R, Double_t &dist, Int_t iter) | |
477 | { | |
478 | // | |
479 | // | |
480 | // find intersection using linear fit | |
481 | Double_t r1[3],g1[3],gg1[3]; | |
482 | Double_t r2[3],g2[3],gg2[3]; | |
483 | // | |
484 | Evaluate(t1,r1,g1,gg1); | |
485 | h.Evaluate(t2,r2,g2,gg2); | |
486 | ||
487 | // | |
488 | Double_t dx2=1.; | |
489 | Double_t dy2=1.; | |
490 | Double_t dz2=1.; | |
491 | // | |
492 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
493 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
494 | // | |
495 | ||
496 | iter++; | |
497 | while (iter--) { | |
9be2fe3a | 498 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); |
499 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
500 | ||
501 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
502 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
503 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
504 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
505 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
506 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
507 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
508 | ||
509 | Double_t det=h11*h22-h12*h12; | |
510 | ||
511 | Double_t dt1,dt2; | |
512 | if (TMath::Abs(det)<1.e-33) { | |
513 | //(quasi)singular Hessian | |
514 | dt1=-gt1; dt2=-gt2; | |
515 | } else { | |
516 | dt1=-(gt1*h22 - gt2*h12)/det; | |
517 | dt2=-(h11*gt2 - h12*gt1)/det; | |
518 | } | |
519 | ||
520 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
521 | ||
522 | //if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
523 | // if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
524 | // break; | |
525 | // } | |
526 | ||
527 | Double_t dd=dm; | |
528 | for (Int_t div=1 ; div<512 ; div*=2) { | |
529 | Evaluate(t1+dt1,r1,g1,gg1); | |
530 | h.Evaluate(t2+dt2,r2,g2,gg2); | |
531 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
532 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
533 | if (dd<dm) break; | |
534 | dt1*=0.5; dt2*=0.5; | |
535 | if (div==0){ | |
536 | div =1; | |
537 | } | |
538 | if (div>512) { | |
539 | break; | |
540 | } | |
541 | } | |
542 | dm=dd; | |
543 | t1+=dt1; | |
544 | t2+=dt2; | |
7f572c00 | 545 | } |
7f572c00 | 546 | Evaluate(t1,r1,g1,gg1); |
547 | h.Evaluate(t2,r2,g2,gg2); | |
548 | // | |
549 | dist = (r1[0]-r2[0])*(r1[0]-r2[0])+ | |
550 | (r1[1]-r2[1])*(r1[1]-r2[1])+ | |
551 | (r1[2]-r2[2])*(r1[2]-r2[2]); | |
552 | ||
553 | R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4; | |
9be2fe3a | 554 | return 0; |
7f572c00 | 555 | |
556 | } | |
7f572c00 | 557 | |
558 | ||
9be2fe3a | 559 | Int_t AliHelix::ParabolicDCA2(AliHelix&h, //helixes |
7f572c00 | 560 | Double_t &t1, Double_t &t2, |
9be2fe3a | 561 | Double_t &R, Double_t &dist, Double_t err[3], Int_t iter) |
7f572c00 | 562 | { |
563 | // | |
564 | // | |
565 | // find intersection using linear fit | |
566 | Double_t r1[3],g1[3],gg1[3]; | |
567 | Double_t r2[3],g2[3],gg2[3]; | |
568 | // | |
569 | Evaluate(t1,r1,g1,gg1); | |
570 | h.Evaluate(t2,r2,g2,gg2); | |
571 | ||
572 | // | |
9be2fe3a | 573 | Double_t dx2=err[0]; |
574 | Double_t dy2=err[1]; | |
575 | Double_t dz2=err[2]; | |
7f572c00 | 576 | // |
577 | Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2]; | |
578 | Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
579 | // | |
580 | ||
581 | iter++; | |
582 | while (iter--) { | |
583 | Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2); | |
584 | Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2); | |
585 | ||
586 | Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 + | |
587 | (g1[1]*g1[1] - dy*gg1[1])/dy2 + | |
588 | (g1[2]*g1[2] - dz*gg1[2])/dz2; | |
589 | Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 + | |
590 | (g2[1]*g2[1] + dy*gg2[1])/dy2 + | |
591 | (g2[2]*g2[2] + dz*gg2[2])/dz2; | |
592 | Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2); | |
593 | ||
594 | Double_t det=h11*h22-h12*h12; | |
595 | ||
596 | Double_t dt1,dt2; | |
597 | if (TMath::Abs(det)<1.e-33) { | |
598 | //(quasi)singular Hessian | |
599 | dt1=-gt1; dt2=-gt2; | |
600 | } else { | |
601 | dt1=-(gt1*h22 - gt2*h12)/det; | |
602 | dt2=-(h11*gt2 - h12*gt1)/det; | |
603 | } | |
604 | ||
605 | if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;} | |
606 | ||
607 | //if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4) | |
608 | // if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) { | |
609 | // break; | |
610 | // } | |
611 | ||
612 | Double_t dd=dm; | |
613 | for (Int_t div=1 ; div<512 ; div*=2) { | |
614 | Evaluate(t1+dt1,r1,g1,gg1); | |
615 | h.Evaluate(t2+dt2,r2,g2,gg2); | |
616 | dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2]; | |
617 | dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2; | |
618 | if (dd<dm) break; | |
619 | dt1*=0.5; dt2*=0.5; | |
620 | if (div==0){ | |
621 | div =1; | |
622 | } | |
623 | if (div>512) { | |
624 | break; | |
625 | } | |
626 | } | |
627 | dm=dd; | |
628 | t1+=dt1; | |
629 | t2+=dt2; | |
630 | } | |
631 | Evaluate(t1,r1,g1,gg1); | |
632 | h.Evaluate(t2,r2,g2,gg2); | |
633 | // | |
634 | dist = (r1[0]-r2[0])*(r1[0]-r2[0])+ | |
635 | (r1[1]-r2[1])*(r1[1]-r2[1])+ | |
636 | (r1[2]-r2[2])*(r1[2]-r2[2]); | |
637 | ||
638 | R = ((r1[0]+r2[0])*(r1[0]+r2[0])+(r1[1]+r2[1])*(r1[1]+r2[1]))/4; | |
639 | return 0; | |
640 | ||
641 | } | |
642 |