1 /**************************************************************************
2 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
4 * Author: The ALICE Off-line Project. *
5 * Contributors are mentioned in the code where appropriate. *
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 **************************************************************************/
18 ///////////////////////////////////////////////////////////////////////////////
20 // Implementation of the external track parameterisation class. //
22 // This parameterisation is used to exchange tracks between the detectors. //
23 // A set of functions returning the position and the momentum of tracks //
24 // in the global coordinate system as well as the track impact parameters //
26 // Origin: I.Belikov, CERN, Jouri.Belikov@cern.ch //
27 ///////////////////////////////////////////////////////////////////////////////
28 #include <TMatrixDSym.h>
29 #include "AliExternalTrackParam.h"
30 #include "AliESDVertex.h"
33 ClassImp(AliExternalTrackParam)
35 Double32_t AliExternalTrackParam::fgMostProbablePt=kMostProbablePt;
37 //_____________________________________________________________________________
38 AliExternalTrackParam::AliExternalTrackParam() :
44 // default constructor
46 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
47 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
50 //_____________________________________________________________________________
51 AliExternalTrackParam::AliExternalTrackParam(const AliExternalTrackParam &track):
59 for (Int_t i = 0; i < 5; i++) fP[i] = track.fP[i];
60 for (Int_t i = 0; i < 15; i++) fC[i] = track.fC[i];
63 //_____________________________________________________________________________
64 AliExternalTrackParam& AliExternalTrackParam::operator=(const AliExternalTrackParam &trkPar)
67 // assignment operator
71 AliVParticle::operator=(trkPar);
73 fAlpha = trkPar.fAlpha;
75 for (Int_t i = 0; i < 5; i++) fP[i] = trkPar.fP[i];
76 for (Int_t i = 0; i < 15; i++) fC[i] = trkPar.fC[i];
82 //_____________________________________________________________________________
83 AliExternalTrackParam::AliExternalTrackParam(Double_t x, Double_t alpha,
84 const Double_t param[5],
85 const Double_t covar[15]) :
91 // create external track parameters from given arguments
93 for (Int_t i = 0; i < 5; i++) fP[i] = param[i];
94 for (Int_t i = 0; i < 15; i++) fC[i] = covar[i];
97 //_____________________________________________________________________________
98 void AliExternalTrackParam::Set(Double_t x, Double_t alpha,
99 const Double_t p[5], const Double_t cov[15]) {
101 // Sets the parameters
105 for (Int_t i = 0; i < 5; i++) fP[i] = p[i];
106 for (Int_t i = 0; i < 15; i++) fC[i] = cov[i];
109 //_____________________________________________________________________________
110 void AliExternalTrackParam::Reset() {
112 // Resets all the parameters to 0
115 for (Int_t i = 0; i < 5; i++) fP[i] = 0;
116 for (Int_t i = 0; i < 15; i++) fC[i] = 0;
119 Double_t AliExternalTrackParam::GetP() const {
120 //---------------------------------------------------------------------
121 // This function returns the track momentum
122 // Results for (nearly) straight tracks are meaningless !
123 //---------------------------------------------------------------------
124 if (TMath::Abs(fP[4])<=kAlmost0) return kVeryBig;
125 return TMath::Sqrt(1.+ fP[3]*fP[3])/TMath::Abs(fP[4]);
128 Double_t AliExternalTrackParam::Get1P() const {
129 //---------------------------------------------------------------------
130 // This function returns the 1/(track momentum)
131 //---------------------------------------------------------------------
132 return TMath::Abs(fP[4])/TMath::Sqrt(1.+ fP[3]*fP[3]);
135 //_______________________________________________________________________
136 Double_t AliExternalTrackParam::GetD(Double_t x,Double_t y,Double_t b) const {
137 //------------------------------------------------------------------
138 // This function calculates the transverse impact parameter
139 // with respect to a point with global coordinates (x,y)
140 // in the magnetic field "b" (kG)
141 //------------------------------------------------------------------
142 if (TMath::Abs(b) < kAlmost0Field) return GetLinearD(x,y);
143 Double_t rp4=GetC(b);
145 Double_t xt=fX, yt=fP[0];
147 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
148 Double_t a = x*cs + y*sn;
149 y = -x*sn + y*cs; x=a;
152 sn=rp4*xt - fP[2]; cs=rp4*yt + TMath::Sqrt(1.- fP[2]*fP[2]);
153 a=2*(xt*fP[2] - yt*TMath::Sqrt(1.- fP[2]*fP[2]))-rp4*(xt*xt + yt*yt);
154 return -a/(1 + TMath::Sqrt(sn*sn + cs*cs));
157 //_______________________________________________________________________
158 void AliExternalTrackParam::
159 GetDZ(Double_t x, Double_t y, Double_t z, Double_t b, Float_t dz[2]) const {
160 //------------------------------------------------------------------
161 // This function calculates the transverse and longitudinal impact parameters
162 // with respect to a point with global coordinates (x,y)
163 // in the magnetic field "b" (kG)
164 //------------------------------------------------------------------
165 Double_t f1 = fP[2], r1 = TMath::Sqrt(1. - f1*f1);
166 Double_t xt=fX, yt=fP[0];
167 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
168 Double_t a = x*cs + y*sn;
169 y = -x*sn + y*cs; x=a;
172 Double_t rp4=GetC(b);
173 if ((TMath::Abs(b) < kAlmost0Field) || (TMath::Abs(rp4) < kAlmost0)) {
174 dz[0] = -(xt*f1 - yt*r1);
175 dz[1] = fP[1] + (dz[0]*f1 - xt)/r1*fP[3] - z;
179 sn=rp4*xt - f1; cs=rp4*yt + r1;
180 a=2*(xt*f1 - yt*r1)-rp4*(xt*xt + yt*yt);
181 Double_t rr=TMath::Sqrt(sn*sn + cs*cs);
183 Double_t f2 = -sn/rr, r2 = TMath::Sqrt(1. - f2*f2);
184 dz[1] = fP[1] + fP[3]/rp4*TMath::ASin(f2*r1 - f1*r2) - z;
187 //_______________________________________________________________________
188 Double_t AliExternalTrackParam::GetLinearD(Double_t xv,Double_t yv) const {
189 //------------------------------------------------------------------
190 // This function calculates the transverse impact parameter
191 // with respect to a point with global coordinates (xv,yv)
192 // neglecting the track curvature.
193 //------------------------------------------------------------------
194 Double_t sn=TMath::Sin(fAlpha), cs=TMath::Cos(fAlpha);
195 Double_t x= xv*cs + yv*sn;
196 Double_t y=-xv*sn + yv*cs;
198 Double_t d = (fX-x)*fP[2] - (fP[0]-y)*TMath::Sqrt(1.- fP[2]*fP[2]);
203 Bool_t AliExternalTrackParam::CorrectForMeanMaterial
204 (Double_t xOverX0, Double_t xTimesRho, Double_t mass, Bool_t anglecorr,
205 Double_t (*Bethe)(Double_t)) {
206 //------------------------------------------------------------------
207 // This function corrects the track parameters for the crossed material.
208 // "xOverX0" - X/X0, the thickness in units of the radiation length.
209 // "xTimesRho" - is the product length*density (g/cm^2).
210 // "mass" - the mass of this particle (GeV/c^2).
211 //------------------------------------------------------------------
216 Double_t &fC22=fC[5];
217 Double_t &fC33=fC[9];
218 Double_t &fC43=fC[13];
219 Double_t &fC44=fC[14];
221 //Apply angle correction, if requested
223 Double_t angle=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
230 Double_t beta2=p2/(p2 + mass*mass);
232 //Multiple scattering******************
234 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(xOverX0);
235 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
236 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
237 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
238 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
239 fC44 += theta2*fP3*fP4*fP3*fP4;
242 //Energy losses************************
243 if ((xTimesRho != 0.) && (beta2 < 1.)) {
244 Double_t dE=Bethe(beta2)*xTimesRho;
245 Double_t e=TMath::Sqrt(p2 + mass*mass);
246 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
249 // Approximate energy loss fluctuation (M.Ivanov)
250 const Double_t knst=0.07; // To be tuned.
251 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
252 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
260 Bool_t AliExternalTrackParam::CorrectForMaterial
261 (Double_t d, Double_t x0, Double_t mass, Double_t (*Bethe)(Double_t)) {
262 //------------------------------------------------------------------
263 // Deprecated function !
264 // Better use CorrectForMeanMaterial instead of it.
266 // This function corrects the track parameters for the crossed material
267 // "d" - the thickness (fraction of the radiation length)
268 // "x0" - the radiation length (g/cm^2)
269 // "mass" - the mass of this particle (GeV/c^2)
270 //------------------------------------------------------------------
275 Double_t &fC22=fC[5];
276 Double_t &fC33=fC[9];
277 Double_t &fC43=fC[13];
278 Double_t &fC44=fC[14];
282 Double_t beta2=p2/(p2 + mass*mass);
283 d*=TMath::Sqrt((1.+ fP3*fP3)/(1.- fP2*fP2));
285 //Multiple scattering******************
287 Double_t theta2=14.1*14.1/(beta2*p2*1e6)*TMath::Abs(d);
288 //Double_t theta2=1.0259e-6*14*14/28/(beta2*p2)*TMath::Abs(d)*9.36*2.33;
289 fC22 += theta2*(1.- fP2*fP2)*(1. + fP3*fP3);
290 fC33 += theta2*(1. + fP3*fP3)*(1. + fP3*fP3);
291 fC43 += theta2*fP3*fP4*(1. + fP3*fP3);
292 fC44 += theta2*fP3*fP4*fP3*fP4;
295 //Energy losses************************
296 if (x0!=0. && beta2<1) {
298 Double_t dE=Bethe(beta2)*d;
299 Double_t e=TMath::Sqrt(p2 + mass*mass);
300 if ( TMath::Abs(dE) > 0.3*e ) return kFALSE; //30% energy loss is too much!
303 // Approximate energy loss fluctuation (M.Ivanov)
304 const Double_t knst=0.07; // To be tuned.
305 Double_t sigmadE=knst*TMath::Sqrt(TMath::Abs(dE));
306 fC44+=((sigmadE*e/p2*fP4)*(sigmadE*e/p2*fP4));
313 Double_t ApproximateBetheBloch(Double_t beta2) {
314 //------------------------------------------------------------------
315 // This is an approximation of the Bethe-Bloch formula with
316 // the density effect taken into account at beta*gamma > 3.5
317 // (the approximation is reasonable only for solid materials)
318 //------------------------------------------------------------------
319 if (beta2/(1-beta2)>3.5*3.5)
320 return 0.153e-3/beta2*(log(3.5*5940)+0.5*log(beta2/(1-beta2)) - beta2);
322 return 0.153e-3/beta2*(log(5940*beta2/(1-beta2)) - beta2);
325 Bool_t AliExternalTrackParam::Rotate(Double_t alpha) {
326 //------------------------------------------------------------------
327 // Transform this track to the local coord. system rotated
328 // by angle "alpha" (rad) with respect to the global coord. system.
329 //------------------------------------------------------------------
330 if (TMath::Abs(fP[2]) >= kAlmost1) {
331 AliError(Form("Precondition is not satisfied: |sin(phi)|>1 ! %f",fP[2]));
335 if (alpha < -TMath::Pi()) alpha += 2*TMath::Pi();
336 else if (alpha >= TMath::Pi()) alpha -= 2*TMath::Pi();
340 Double_t &fC00=fC[0];
341 Double_t &fC10=fC[1];
342 Double_t &fC20=fC[3];
343 Double_t &fC21=fC[4];
344 Double_t &fC22=fC[5];
345 Double_t &fC30=fC[6];
346 Double_t &fC32=fC[8];
347 Double_t &fC40=fC[10];
348 Double_t &fC42=fC[12];
351 Double_t ca=TMath::Cos(alpha-fAlpha), sa=TMath::Sin(alpha-fAlpha);
352 Double_t sf=fP2, cf=TMath::Sqrt(1.- fP2*fP2);
354 Double_t tmp=sf*ca - cf*sa;
355 if (TMath::Abs(tmp) >= kAlmost1) return kFALSE;
362 if (TMath::Abs(cf)<kAlmost0) {
363 AliError(Form("Too small cosine value %f",cf));
367 Double_t rr=(ca+sf/cf*sa);
382 Bool_t AliExternalTrackParam::PropagateTo(Double_t xk, Double_t b) {
383 //----------------------------------------------------------------
384 // Propagate this track to the plane X=xk (cm) in the field "b" (kG)
385 //----------------------------------------------------------------
387 if (TMath::Abs(dx)<=kAlmost0) return kTRUE;
389 Double_t crv=GetC(b);
390 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
392 Double_t f1=fP[2], f2=f1 + crv*dx;
393 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
394 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
396 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
399 &fC10=fC[1], &fC11=fC[2],
400 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
401 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
402 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
404 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
407 fP0 += dx*(f1+f2)/(r1+r2);
408 fP1 += dx*(r2 + f2*(f1+f2)/(r1+r2))*fP3; // Many thanks to P.Hristov !
413 Double_t f02= dx/(r1*r1*r1); Double_t cc=crv/fP4;
414 Double_t f04=0.5*dx*dx/(r1*r1*r1); f04*=cc;
415 Double_t f12= dx*fP3*f1/(r1*r1*r1);
416 Double_t f14=0.5*dx*dx*fP3*f1/(r1*r1*r1); f14*=cc;
418 Double_t f24= dx; f24*=cc;
421 Double_t b00=f02*fC20 + f04*fC40, b01=f12*fC20 + f14*fC40 + f13*fC30;
422 Double_t b02=f24*fC40;
423 Double_t b10=f02*fC21 + f04*fC41, b11=f12*fC21 + f14*fC41 + f13*fC31;
424 Double_t b12=f24*fC41;
425 Double_t b20=f02*fC22 + f04*fC42, b21=f12*fC22 + f14*fC42 + f13*fC32;
426 Double_t b22=f24*fC42;
427 Double_t b40=f02*fC42 + f04*fC44, b41=f12*fC42 + f14*fC44 + f13*fC43;
428 Double_t b42=f24*fC44;
429 Double_t b30=f02*fC32 + f04*fC43, b31=f12*fC32 + f14*fC43 + f13*fC33;
430 Double_t b32=f24*fC43;
433 Double_t a00=f02*b20+f04*b40,a01=f02*b21+f04*b41,a02=f02*b22+f04*b42;
434 Double_t a11=f12*b21+f14*b41+f13*b31,a12=f12*b22+f14*b42+f13*b32;
435 Double_t a22=f24*b42;
437 //F*C*Ft = C + (b + bt + a)
438 fC00 += b00 + b00 + a00;
439 fC10 += b10 + b01 + a01;
440 fC20 += b20 + b02 + a02;
443 fC11 += b11 + b11 + a11;
444 fC21 += b21 + b12 + a12;
447 fC22 += b22 + b22 + a22;
454 void AliExternalTrackParam::Propagate(Double_t len, Double_t x[3],
455 Double_t p[3], Double_t bz) const {
456 //+++++++++++++++++++++++++++++++++++++++++
457 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
458 // Extrapolate track along simple helix in magnetic field
459 // Arguments: len -distance alogn helix, [cm]
460 // bz - mag field, [kGaus]
461 // Returns: x and p contain extrapolated positon and momentum
462 // The momentum returned for straight-line tracks is meaningless !
463 //+++++++++++++++++++++++++++++++++++++++++
466 if (OneOverPt() < kAlmost0 || TMath::Abs(bz) < kAlmost0Field ){ //straight-line tracks
467 Double_t unit[3]; GetDirection(unit);
472 p[0]=unit[0]/kAlmost0;
473 p[1]=unit[1]/kAlmost0;
474 p[2]=unit[2]/kAlmost0;
478 Double_t a = -kB2C*bz*GetSign();
480 x[0] += p[0]*TMath::Sin(rho*len)/a - p[1]*(1-TMath::Cos(rho*len))/a;
481 x[1] += p[1]*TMath::Sin(rho*len)/a + p[0]*(1-TMath::Cos(rho*len))/a;
485 p[0] = p0 *TMath::Cos(rho*len) - p[1]*TMath::Sin(rho*len);
486 p[1] = p[1]*TMath::Cos(rho*len) + p0 *TMath::Sin(rho*len);
490 Bool_t AliExternalTrackParam::Intersect(Double_t pnt[3], Double_t norm[3],
492 //+++++++++++++++++++++++++++++++++++++++++
493 // Origin: K. Shileev (Kirill.Shileev@cern.ch)
494 // Finds point of intersection (if exists) of the helix with the plane.
495 // Stores result in fX and fP.
496 // Arguments: planePoint,planeNorm - the plane defined by any plane's point
497 // and vector, normal to the plane
498 // Returns: kTrue if helix intersects the plane, kFALSE otherwise.
499 //+++++++++++++++++++++++++++++++++++++++++
500 Double_t x0[3]; GetXYZ(x0); //get track position in MARS
502 //estimates initial helix length up to plane
504 (pnt[0]-x0[0])*norm[0] + (pnt[1]-x0[1])*norm[1] + (pnt[2]-x0[2])*norm[2];
505 Double_t dist=99999,distPrev=dist;
507 while(TMath::Abs(dist)>0.00001){
508 //calculates helix at the distance s from x0 ALONG the helix
511 //distance between current helix position and plane
512 dist=(x[0]-pnt[0])*norm[0]+(x[1]-pnt[1])*norm[1]+(x[2]-pnt[2])*norm[2];
514 if(TMath::Abs(dist) >= TMath::Abs(distPrev)) {return kFALSE;}
518 //on exit pnt is intersection point,norm is track vector at that point,
520 for (Int_t i=0; i<3; i++) {pnt[i]=x[i]; norm[i]=p[i];}
525 AliExternalTrackParam::GetPredictedChi2(Double_t p[2],Double_t cov[3]) const {
526 //----------------------------------------------------------------
527 // Estimate the chi2 of the space point "p" with the cov. matrix "cov"
528 //----------------------------------------------------------------
529 Double_t sdd = fC[0] + cov[0];
530 Double_t sdz = fC[1] + cov[1];
531 Double_t szz = fC[2] + cov[2];
532 Double_t det = sdd*szz - sdz*sdz;
534 if (TMath::Abs(det) < kAlmost0) return kVeryBig;
536 Double_t d = fP[0] - p[0];
537 Double_t z = fP[1] - p[1];
539 return (d*szz*d - 2*d*sdz*z + z*sdd*z)/det;
542 Double_t AliExternalTrackParam::
543 GetPredictedChi2(Double_t p[3],Double_t covyz[3],Double_t covxyz[3]) const {
544 //----------------------------------------------------------------
545 // Estimate the chi2 of the 3D space point "p" and
546 // the full covariance matrix "covyz" and "covxyz"
548 // Cov(x,x) ... : covxyz[0]
549 // Cov(y,x) ... : covxyz[1] covyz[0]
550 // Cov(z,x) ... : covxyz[2] covyz[1] covyz[2]
551 //----------------------------------------------------------------
560 if (TMath::Abs(f) >= kAlmost1) return kVeryBig;
561 Double_t r=TMath::Sqrt(1.- f*f);
562 Double_t a=f/r, b=GetTgl()/r;
564 Double_t s2=333.*333.; //something reasonably big (cm^2)
567 v(0,0)= s2; v(0,1)= a*s2; v(0,2)= b*s2;;
568 v(1,0)=a*s2; v(1,1)=a*a*s2 + GetSigmaY2(); v(1,2)=a*b*s2 + GetSigmaZY();
569 v(2,0)=b*s2; v(2,1)=a*b*s2 + GetSigmaZY(); v(2,2)=b*b*s2 + GetSigmaZ2();
571 v(0,0)+=covxyz[0]; v(0,1)+=covxyz[1]; v(0,2)+=covxyz[2];
572 v(1,0)+=covxyz[1]; v(1,1)+=covyz[0]; v(1,2)+=covyz[1];
573 v(2,0)+=covxyz[2]; v(2,1)+=covyz[1]; v(2,2)+=covyz[2];
576 if (!v.IsValid()) return kVeryBig;
579 for (Int_t i = 0; i < 3; i++)
580 for (Int_t j = 0; j < 3; j++) chi2 += res[i]*res[j]*v(i,j);
587 Bool_t AliExternalTrackParam::
588 PropagateTo(Double_t p[3],Double_t covyz[3],Double_t covxyz[3],Double_t bz) {
589 //----------------------------------------------------------------
590 // Propagate this track to the plane
591 // the 3D space point "p" (with the covariance matrix "covyz" and "covxyz")
593 // The magnetic field is "bz" (kG)
595 // The track curvature and the change of the covariance matrix
596 // of the track parameters are negleted !
597 // (So the "step" should be small compared with 1/curvature)
598 //----------------------------------------------------------------
601 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
602 Double_t r=TMath::Sqrt(1.- f*f);
603 Double_t a=f/r, b=GetTgl()/r;
605 Double_t s2=333.*333.; //something reasonably big (cm^2)
608 tV(0,0)= s2; tV(0,1)= a*s2; tV(0,2)= b*s2;
609 tV(1,0)=a*s2; tV(1,1)=a*a*s2; tV(1,2)=a*b*s2;
610 tV(2,0)=b*s2; tV(2,1)=a*b*s2; tV(2,2)=b*b*s2;
613 pV(0,0)=covxyz[0]; pV(0,1)=covxyz[1]; pV(0,2)=covxyz[2];
614 pV(1,0)=covxyz[1]; pV(1,1)=covyz[0]; pV(1,2)=covyz[1];
615 pV(2,0)=covxyz[2]; pV(2,1)=covyz[1]; pV(2,2)=covyz[2];
620 if (!tpV.IsValid()) return kFALSE;
622 TMatrixDSym pW(3),tW(3);
623 for (Int_t i=0; i<3; i++)
624 for (Int_t j=0; j<3; j++) {
626 for (Int_t k=0; k<3; k++) {
627 pW(i,j) += tV(i,k)*tpV(k,j);
628 tW(i,j) += pV(i,k)*tpV(k,j);
632 Double_t t[3] = {GetX(), GetY(), GetZ()};
635 for (Int_t i=0; i<3; i++) x += (tW(0,i)*t[i] + pW(0,i)*p[i]);
636 Double_t crv=GetC(bz);
637 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
639 if (TMath::Abs(f) >= kAlmost1) return kFALSE;
643 for (Int_t i=0; i<3; i++) fP[0] += (tW(1,i)*t[i] + pW(1,i)*p[i]);
645 for (Int_t i=0; i<3; i++) fP[1] += (tW(2,i)*t[i] + pW(2,i)*p[i]);
650 Bool_t AliExternalTrackParam::Update(Double_t p[2], Double_t cov[3]) {
651 //------------------------------------------------------------------
652 // Update the track parameters with the space point "p" having
653 // the covariance matrix "cov"
654 //------------------------------------------------------------------
655 Double_t &fP0=fP[0], &fP1=fP[1], &fP2=fP[2], &fP3=fP[3], &fP4=fP[4];
658 &fC10=fC[1], &fC11=fC[2],
659 &fC20=fC[3], &fC21=fC[4], &fC22=fC[5],
660 &fC30=fC[6], &fC31=fC[7], &fC32=fC[8], &fC33=fC[9],
661 &fC40=fC[10], &fC41=fC[11], &fC42=fC[12], &fC43=fC[13], &fC44=fC[14];
663 Double_t r00=cov[0], r01=cov[1], r11=cov[2];
664 r00+=fC00; r01+=fC10; r11+=fC11;
665 Double_t det=r00*r11 - r01*r01;
667 if (TMath::Abs(det) < kAlmost0) return kFALSE;
670 Double_t tmp=r00; r00=r11/det; r11=tmp/det; r01=-r01/det;
672 Double_t k00=fC00*r00+fC10*r01, k01=fC00*r01+fC10*r11;
673 Double_t k10=fC10*r00+fC11*r01, k11=fC10*r01+fC11*r11;
674 Double_t k20=fC20*r00+fC21*r01, k21=fC20*r01+fC21*r11;
675 Double_t k30=fC30*r00+fC31*r01, k31=fC30*r01+fC31*r11;
676 Double_t k40=fC40*r00+fC41*r01, k41=fC40*r01+fC41*r11;
678 Double_t dy=p[0] - fP0, dz=p[1] - fP1;
679 Double_t sf=fP2 + k20*dy + k21*dz;
680 if (TMath::Abs(sf) > kAlmost1) return kFALSE;
682 fP0 += k00*dy + k01*dz;
683 fP1 += k10*dy + k11*dz;
685 fP3 += k30*dy + k31*dz;
686 fP4 += k40*dy + k41*dz;
688 Double_t c01=fC10, c02=fC20, c03=fC30, c04=fC40;
689 Double_t c12=fC21, c13=fC31, c14=fC41;
691 fC00-=k00*fC00+k01*fC10; fC10-=k00*c01+k01*fC11;
692 fC20-=k00*c02+k01*c12; fC30-=k00*c03+k01*c13;
693 fC40-=k00*c04+k01*c14;
695 fC11-=k10*c01+k11*fC11;
696 fC21-=k10*c02+k11*c12; fC31-=k10*c03+k11*c13;
697 fC41-=k10*c04+k11*c14;
699 fC22-=k20*c02+k21*c12; fC32-=k20*c03+k21*c13;
700 fC42-=k20*c04+k21*c14;
702 fC33-=k30*c03+k31*c13;
703 fC43-=k30*c04+k31*c14;
705 fC44-=k40*c04+k41*c14;
711 AliExternalTrackParam::GetHelixParameters(Double_t hlx[6], Double_t b) const {
712 //--------------------------------------------------------------------
713 // External track parameters -> helix parameters
714 // "b" - magnetic field (kG)
715 //--------------------------------------------------------------------
716 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
718 hlx[0]=fP[0]; hlx[1]=fP[1]; hlx[2]=fP[2]; hlx[3]=fP[3];
720 hlx[5]=fX*cs - hlx[0]*sn; // x0
721 hlx[0]=fX*sn + hlx[0]*cs; // y0
723 hlx[2]=TMath::ASin(hlx[2]) + fAlpha; // phi0
729 static void Evaluate(const Double_t *h, Double_t t,
730 Double_t r[3], //radius vector
731 Double_t g[3], //first defivatives
732 Double_t gg[3]) //second derivatives
734 //--------------------------------------------------------------------
735 // Calculate position of a point on a track and some derivatives
736 //--------------------------------------------------------------------
737 Double_t phase=h[4]*t+h[2];
738 Double_t sn=TMath::Sin(phase), cs=TMath::Cos(phase);
740 r[0] = h[5] + (sn - h[6])/h[4];
741 r[1] = h[0] - (cs - h[7])/h[4];
742 r[2] = h[1] + h[3]*t;
744 g[0] = cs; g[1]=sn; g[2]=h[3];
746 gg[0]=-h[4]*sn; gg[1]=h[4]*cs; gg[2]=0.;
749 Double_t AliExternalTrackParam::GetDCA(const AliExternalTrackParam *p,
750 Double_t b, Double_t &xthis, Double_t &xp) const {
751 //------------------------------------------------------------
752 // Returns the (weighed !) distance of closest approach between
753 // this track and the track "p".
754 // Other returned values:
755 // xthis, xt - coordinates of tracks' reference planes at the DCA
756 //-----------------------------------------------------------
757 Double_t dy2=GetSigmaY2() + p->GetSigmaY2();
758 Double_t dz2=GetSigmaZ2() + p->GetSigmaZ2();
763 Double_t p1[8]; GetHelixParameters(p1,b);
764 p1[6]=TMath::Sin(p1[2]); p1[7]=TMath::Cos(p1[2]);
765 Double_t p2[8]; p->GetHelixParameters(p2,b);
766 p2[6]=TMath::Sin(p2[2]); p2[7]=TMath::Cos(p2[2]);
769 Double_t r1[3],g1[3],gg1[3]; Double_t t1=0.;
770 Evaluate(p1,t1,r1,g1,gg1);
771 Double_t r2[3],g2[3],gg2[3]; Double_t t2=0.;
772 Evaluate(p2,t2,r2,g2,gg2);
774 Double_t dx=r2[0]-r1[0], dy=r2[1]-r1[1], dz=r2[2]-r1[2];
775 Double_t dm=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
779 Double_t gt1=-(dx*g1[0]/dx2 + dy*g1[1]/dy2 + dz*g1[2]/dz2);
780 Double_t gt2=+(dx*g2[0]/dx2 + dy*g2[1]/dy2 + dz*g2[2]/dz2);
781 Double_t h11=(g1[0]*g1[0] - dx*gg1[0])/dx2 +
782 (g1[1]*g1[1] - dy*gg1[1])/dy2 +
783 (g1[2]*g1[2] - dz*gg1[2])/dz2;
784 Double_t h22=(g2[0]*g2[0] + dx*gg2[0])/dx2 +
785 (g2[1]*g2[1] + dy*gg2[1])/dy2 +
786 (g2[2]*g2[2] + dz*gg2[2])/dz2;
787 Double_t h12=-(g1[0]*g2[0]/dx2 + g1[1]*g2[1]/dy2 + g1[2]*g2[2]/dz2);
789 Double_t det=h11*h22-h12*h12;
792 if (TMath::Abs(det)<1.e-33) {
793 //(quasi)singular Hessian
796 dt1=-(gt1*h22 - gt2*h12)/det;
797 dt2=-(h11*gt2 - h12*gt1)/det;
800 if ((dt1*gt1+dt2*gt2)>0) {dt1=-dt1; dt2=-dt2;}
802 //check delta(phase1) ?
803 //check delta(phase2) ?
805 if (TMath::Abs(dt1)/(TMath::Abs(t1)+1.e-3) < 1.e-4)
806 if (TMath::Abs(dt2)/(TMath::Abs(t2)+1.e-3) < 1.e-4) {
807 if ((gt1*gt1+gt2*gt2) > 1.e-4/dy2/dy2)
808 AliWarning(" stopped at not a stationary point !");
809 Double_t lmb=h11+h22; lmb=lmb-TMath::Sqrt(lmb*lmb-4*det);
811 AliWarning(" stopped at not a minimum !");
816 for (Int_t div=1 ; ; div*=2) {
817 Evaluate(p1,t1+dt1,r1,g1,gg1);
818 Evaluate(p2,t2+dt2,r2,g2,gg2);
819 dx=r2[0]-r1[0]; dy=r2[1]-r1[1]; dz=r2[2]-r1[2];
820 dd=dx*dx/dx2 + dy*dy/dy2 + dz*dz/dz2;
824 AliWarning(" overshoot !"); break;
834 if (max<=0) AliWarning(" too many iterations !");
836 Double_t cs=TMath::Cos(GetAlpha());
837 Double_t sn=TMath::Sin(GetAlpha());
838 xthis=r1[0]*cs + r1[1]*sn;
840 cs=TMath::Cos(p->GetAlpha());
841 sn=TMath::Sin(p->GetAlpha());
842 xp=r2[0]*cs + r2[1]*sn;
844 return TMath::Sqrt(dm*TMath::Sqrt(dy2*dz2));
847 Double_t AliExternalTrackParam::
848 PropagateToDCA(AliExternalTrackParam *p, Double_t b) {
849 //--------------------------------------------------------------
850 // Propagates this track and the argument track to the position of the
851 // distance of closest approach.
852 // Returns the (weighed !) distance of closest approach.
853 //--------------------------------------------------------------
855 Double_t dca=GetDCA(p,b,xthis,xp);
857 if (!PropagateTo(xthis,b)) {
858 //AliWarning(" propagation failed !");
862 if (!p->PropagateTo(xp,b)) {
863 //AliWarning(" propagation failed !";
873 Bool_t AliExternalTrackParam::PropagateToDCA(const AliESDVertex *vtx, Double_t b, Double_t maxd){
875 // Try to relate this track to the vertex "vtx",
876 // if the (rough) transverse impact parameter is not bigger then "maxd".
877 // Magnetic field is "b" (kG).
879 // a) The track gets extapolated to the DCA to the vertex.
880 // b) The impact parameters and their covariance matrix are calculated.
882 // In the case of success, the returned value is kTRUE
883 // (otherwise, it's kFALSE)
885 Double_t alpha=GetAlpha();
886 Double_t sn=TMath::Sin(alpha), cs=TMath::Cos(alpha);
887 Double_t x=GetX(), y=GetParameter()[0], snp=GetParameter()[2];
888 Double_t xv= vtx->GetXv()*cs + vtx->GetYv()*sn;
889 Double_t yv=-vtx->GetXv()*sn + vtx->GetYv()*cs;
892 //Estimate the impact parameter neglecting the track curvature
893 Double_t d=TMath::Abs(x*snp - y*TMath::Sqrt(1.- snp*snp));
894 if (d > maxd) return kFALSE;
896 //Propagate to the DCA
897 Double_t crv=0.299792458e-3*b*GetParameter()[4];
898 Double_t tgfv=-(crv*x - snp)/(crv*y + TMath::Sqrt(1.-snp*snp));
899 sn=tgfv/TMath::Sqrt(1.+ tgfv*tgfv); cs=TMath::Sqrt(1.- sn*sn);
902 yv=-xv*sn + yv*cs; xv=x;
904 if (!Propagate(alpha+TMath::ASin(sn),xv,b)) return kFALSE;
911 Bool_t Local2GlobalMomentum(Double_t p[3],Double_t alpha) {
912 //----------------------------------------------------------------
913 // This function performs local->global transformation of the
915 // When called, the arguments are:
916 // p[0] = 1/pt of the track;
917 // p[1] = sine of local azim. angle of the track momentum;
918 // p[2] = tangent of the track momentum dip angle;
919 // alpha - rotation angle.
920 // The result is returned as:
924 // Results for (nearly) straight tracks are meaningless !
925 //----------------------------------------------------------------
926 if (TMath::Abs(p[0])<=kAlmost0) return kFALSE;
927 if (TMath::Abs(p[1])> kAlmost1) return kFALSE;
929 Double_t pt=1./TMath::Abs(p[0]);
930 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha);
931 Double_t r=TMath::Sqrt(1 - p[1]*p[1]);
932 p[0]=pt*(r*cs - p[1]*sn); p[1]=pt*(p[1]*cs + r*sn); p[2]=pt*p[2];
937 Bool_t Local2GlobalPosition(Double_t r[3],Double_t alpha) {
938 //----------------------------------------------------------------
939 // This function performs local->global transformation of the
941 // When called, the arguments are:
945 // alpha - rotation angle.
946 // The result is returned as:
950 //----------------------------------------------------------------
951 Double_t cs=TMath::Cos(alpha), sn=TMath::Sin(alpha), x=r[0];
952 r[0]=x*cs - r[1]*sn; r[1]=x*sn + r[1]*cs;
957 void AliExternalTrackParam::GetDirection(Double_t d[3]) const {
958 //----------------------------------------------------------------
959 // This function returns a unit vector along the track direction
960 // in the global coordinate system.
961 //----------------------------------------------------------------
962 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
964 Double_t csp =TMath::Sqrt((1.- snp)*(1.+snp));
965 Double_t norm=TMath::Sqrt(1.+ fP[3]*fP[3]);
966 d[0]=(csp*cs - snp*sn)/norm;
967 d[1]=(snp*cs + csp*sn)/norm;
971 Bool_t AliExternalTrackParam::GetPxPyPz(Double_t *p) const {
972 //---------------------------------------------------------------------
973 // This function returns the global track momentum components
974 // Results for (nearly) straight tracks are meaningless !
975 //---------------------------------------------------------------------
976 p[0]=fP[4]; p[1]=fP[2]; p[2]=fP[3];
977 return Local2GlobalMomentum(p,fAlpha);
980 Double_t AliExternalTrackParam::Px() const {
981 //---------------------------------------------------------------------
982 // Returns x-component of momentum
983 // Result for (nearly) straight tracks is meaningless !
984 //---------------------------------------------------------------------
986 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
992 Double_t AliExternalTrackParam::Py() const {
993 //---------------------------------------------------------------------
994 // Returns y-component of momentum
995 // Result for (nearly) straight tracks is meaningless !
996 //---------------------------------------------------------------------
998 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
1004 Double_t AliExternalTrackParam::Pz() const {
1005 //---------------------------------------------------------------------
1006 // Returns z-component of momentum
1007 // Result for (nearly) straight tracks is meaningless !
1008 //---------------------------------------------------------------------
1010 Double_t p[3]={kVeryBig,kVeryBig,kVeryBig};
1016 Double_t AliExternalTrackParam::Theta() const {
1017 // return theta angle of momentum
1019 return 0.5*TMath::Pi() - TMath::ATan(fP[3]);
1022 Double_t AliExternalTrackParam::Phi() const {
1023 //---------------------------------------------------------------------
1024 // Returns the azimuthal angle of momentum
1026 //---------------------------------------------------------------------
1028 Double_t phi=TMath::ASin(fP[2]) + fAlpha;
1029 if (phi<0.) phi+=2.*TMath::Pi();
1030 else if (phi>=2.*TMath::Pi()) phi-=2.*TMath::Pi();
1035 Double_t AliExternalTrackParam::M() const {
1036 // return particle mass
1038 // No mass information available so far.
1039 // Redifine in derived class!
1044 Double_t AliExternalTrackParam::E() const {
1045 // return particle energy
1047 // No PID information available so far.
1048 // Redifine in derived class!
1053 Double_t AliExternalTrackParam::Eta() const {
1054 // return pseudorapidity
1056 return -TMath::Log(TMath::Tan(0.5 * Theta()));
1059 Double_t AliExternalTrackParam::Y() const {
1062 // No PID information available so far.
1063 // Redifine in derived class!
1068 Bool_t AliExternalTrackParam::GetXYZ(Double_t *r) const {
1069 //---------------------------------------------------------------------
1070 // This function returns the global track position
1071 //---------------------------------------------------------------------
1072 r[0]=fX; r[1]=fP[0]; r[2]=fP[1];
1073 return Local2GlobalPosition(r,fAlpha);
1076 Bool_t AliExternalTrackParam::GetCovarianceXYZPxPyPz(Double_t cv[21]) const {
1077 //---------------------------------------------------------------------
1078 // This function returns the global covariance matrix of the track params
1080 // Cov(x,x) ... : cv[0]
1081 // Cov(y,x) ... : cv[1] cv[2]
1082 // Cov(z,x) ... : cv[3] cv[4] cv[5]
1083 // Cov(px,x)... : cv[6] cv[7] cv[8] cv[9]
1084 // Cov(py,x)... : cv[10] cv[11] cv[12] cv[13] cv[14]
1085 // Cov(pz,x)... : cv[15] cv[16] cv[17] cv[18] cv[19] cv[20]
1087 // Results for (nearly) straight tracks are meaningless !
1088 //---------------------------------------------------------------------
1089 if (TMath::Abs(fP[4])<=kAlmost0) {
1090 for (Int_t i=0; i<21; i++) cv[i]=0.;
1093 if (TMath::Abs(fP[2]) > kAlmost1) {
1094 for (Int_t i=0; i<21; i++) cv[i]=0.;
1097 Double_t pt=1./TMath::Abs(fP[4]);
1098 Double_t cs=TMath::Cos(fAlpha), sn=TMath::Sin(fAlpha);
1099 Double_t r=TMath::Sqrt((1.-fP[2])*(1.+fP[2]));
1101 Double_t m00=-sn, m10=cs;
1102 Double_t m23=-pt*(sn + fP[2]*cs/r), m43=-pt*pt*(r*cs - fP[2]*sn);
1103 Double_t m24= pt*(cs - fP[2]*sn/r), m44=-pt*pt*(r*sn + fP[2]*cs);
1104 Double_t m35=pt, m45=-pt*pt*fP[3];
1110 cv[0 ] = fC[0]*m00*m00;
1111 cv[1 ] = fC[0]*m00*m10;
1112 cv[2 ] = fC[0]*m10*m10;
1116 cv[6 ] = m00*(fC[3]*m23 + fC[10]*m43);
1117 cv[7 ] = m10*(fC[3]*m23 + fC[10]*m43);
1118 cv[8 ] = fC[4]*m23 + fC[11]*m43;
1119 cv[9 ] = m23*(fC[5]*m23 + fC[12]*m43) + m43*(fC[12]*m23 + fC[14]*m43);
1120 cv[10] = m00*(fC[3]*m24 + fC[10]*m44);
1121 cv[11] = m10*(fC[3]*m24 + fC[10]*m44);
1122 cv[12] = fC[4]*m24 + fC[11]*m44;
1123 cv[13] = m23*(fC[5]*m24 + fC[12]*m44) + m43*(fC[12]*m24 + fC[14]*m44);
1124 cv[14] = m24*(fC[5]*m24 + fC[12]*m44) + m44*(fC[12]*m24 + fC[14]*m44);
1125 cv[15] = m00*(fC[6]*m35 + fC[10]*m45);
1126 cv[16] = m10*(fC[6]*m35 + fC[10]*m45);
1127 cv[17] = fC[7]*m35 + fC[11]*m45;
1128 cv[18] = m23*(fC[8]*m35 + fC[12]*m45) + m43*(fC[13]*m35 + fC[14]*m45);
1129 cv[19] = m24*(fC[8]*m35 + fC[12]*m45) + m44*(fC[13]*m35 + fC[14]*m45);
1130 cv[20] = m35*(fC[9]*m35 + fC[13]*m45) + m45*(fC[13]*m35 + fC[14]*m45);
1137 AliExternalTrackParam::GetPxPyPzAt(Double_t x, Double_t b, Double_t *p) const {
1138 //---------------------------------------------------------------------
1139 // This function returns the global track momentum extrapolated to
1140 // the radial position "x" (cm) in the magnetic field "b" (kG)
1141 //---------------------------------------------------------------------
1143 p[1]=fP[2]+(x-fX)*GetC(b);
1145 return Local2GlobalMomentum(p,fAlpha);
1149 AliExternalTrackParam::GetYAt(Double_t x, Double_t b, Double_t &y) const {
1150 //---------------------------------------------------------------------
1151 // This function returns the local Y-coordinate of the intersection
1152 // point between this track and the reference plane "x" (cm).
1153 // Magnetic field "b" (kG)
1154 //---------------------------------------------------------------------
1156 if(TMath::Abs(dx)<=kAlmost0) {y=fP[0]; return kTRUE;}
1158 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
1160 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1161 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1163 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1164 y = fP[0] + dx*(f1+f2)/(r1+r2);
1169 AliExternalTrackParam::GetZAt(Double_t x, Double_t b, Double_t &z) const {
1170 //---------------------------------------------------------------------
1171 // This function returns the local Z-coordinate of the intersection
1172 // point between this track and the reference plane "x" (cm).
1173 // Magnetic field "b" (kG)
1174 //---------------------------------------------------------------------
1176 if(TMath::Abs(dx)<=kAlmost0) {z=fP[1]; return kTRUE;}
1178 Double_t f1=fP[2], f2=f1 + dx*fP[4]*b*kB2C;
1180 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1181 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1183 Double_t r1=sqrt(1.- f1*f1), r2=sqrt(1.- f2*f2);
1184 z = fP[1] + dx*(r2 + f2*(f1+f2)/(r1+r2))*fP[3]; // Many thanks to P.Hristov !
1189 AliExternalTrackParam::GetXYZAt(Double_t x, Double_t b, Double_t *r) const {
1190 //---------------------------------------------------------------------
1191 // This function returns the global track position extrapolated to
1192 // the radial position "x" (cm) in the magnetic field "b" (kG)
1193 //---------------------------------------------------------------------
1195 if(TMath::Abs(dx)<=kAlmost0) return GetXYZ(r);
1197 Double_t f1=fP[2], f2=f1 + dx*GetC(b);
1199 if (TMath::Abs(f1) >= kAlmost1) return kFALSE;
1200 if (TMath::Abs(f2) >= kAlmost1) return kFALSE;
1202 Double_t r1=TMath::Sqrt(1.- f1*f1), r2=TMath::Sqrt(1.- f2*f2);
1204 r[1] = fP[0] + dx*(f1+f2)/(r1+r2);
1205 r[2] = fP[1] + dx*(f1+f2)/(f1*r2 + f2*r1)*fP[3];
1206 return Local2GlobalPosition(r,fAlpha);
1209 //_____________________________________________________________________________
1210 void AliExternalTrackParam::Print(Option_t* /*option*/) const
1212 // print the parameters and the covariance matrix
1214 printf("AliExternalTrackParam: x = %-12g alpha = %-12g\n", fX, fAlpha);
1215 printf(" parameters: %12g %12g %12g %12g %12g\n",
1216 fP[0], fP[1], fP[2], fP[3], fP[4]);
1217 printf(" covariance: %12g\n", fC[0]);
1218 printf(" %12g %12g\n", fC[1], fC[2]);
1219 printf(" %12g %12g %12g\n", fC[3], fC[4], fC[5]);
1220 printf(" %12g %12g %12g %12g\n",
1221 fC[6], fC[7], fC[8], fC[9]);
1222 printf(" %12g %12g %12g %12g %12g\n",
1223 fC[10], fC[11], fC[12], fC[13], fC[14]);
1226 Double_t AliExternalTrackParam::GetSnpAt(Double_t x,Double_t b) const {
1228 // Get sinus at given x
1230 Double_t crv=GetC(b);
1231 if (TMath::Abs(b) < kAlmost0Field) crv=0.;
1233 Double_t res = fP[2]+dx*crv;
1237 Bool_t AliExternalTrackParam::GetDistance(AliExternalTrackParam *param2, Double_t x, Double_t dist[3], Double_t bz){
1238 //------------------------------------------------------------------------
1239 // Get the distance between two tracks at the local position x
1240 // working in the local frame of this track.
1241 // Origin : Marian.Ivanov@cern.ch
1242 //-----------------------------------------------------------------------
1246 if (!GetYAt(x,bz,xyz[1])) return kFALSE;
1247 if (!GetZAt(x,bz,xyz[2])) return kFALSE;
1250 if (TMath::Abs(GetAlpha()-param2->GetAlpha())<kAlmost0){
1252 if (!param2->GetYAt(x,bz,xyz2[1])) return kFALSE;
1253 if (!param2->GetZAt(x,bz,xyz2[2])) return kFALSE;
1257 Double_t dfi = param2->GetAlpha()-GetAlpha();
1258 Double_t ca = TMath::Cos(dfi), sa = TMath::Sin(dfi);
1259 xyz2[0] = xyz[0]*ca+xyz[1]*sa;
1260 xyz2[1] = -xyz[0]*sa+xyz[1]*ca;
1263 if (!param2->GetYAt(xyz2[0],bz,xyz1[1])) return kFALSE;
1264 if (!param2->GetZAt(xyz2[0],bz,xyz1[2])) return kFALSE;
1266 xyz2[0] = xyz1[0]*ca-xyz1[1]*sa;
1267 xyz2[1] = +xyz1[0]*sa+xyz1[1]*ca;
1270 dist[0] = xyz[0]-xyz2[0];
1271 dist[1] = xyz[1]-xyz2[1];
1272 dist[2] = xyz[2]-xyz2[2];