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