File: | libraries/TRACKING/DReferenceTrajectory.cc |
Location: | line 341, column 2 |
Description: | Value stored to 'Bz_old' is never read |
1 | // $Id$ |
2 | // |
3 | // File: DReferenceTrajectory.cc |
4 | // Created: Wed Jul 19 13:42:58 EDT 2006 |
5 | // Creator: davidl (on Darwin swire-b241.jlab.org 8.7.0 powerpc) |
6 | // |
7 | |
8 | #include <memory> |
9 | |
10 | #include <DVector3.h> |
11 | using namespace std; |
12 | #include <math.h> |
13 | |
14 | #include "DReferenceTrajectory.h" |
15 | #include "DTrackCandidate.h" |
16 | #include "DMagneticFieldStepper.h" |
17 | #include "HDGEOMETRY/DRootGeom.h" |
18 | #define ONE_THIRD0.33333333333333333 0.33333333333333333 |
19 | #define TWO_THIRD0.66666666666666667 0.66666666666666667 |
20 | #define EPS1e-8 1e-8 |
21 | #define NaNstd::numeric_limits<double>::quiet_NaN() std::numeric_limits<double>::quiet_NaN() |
22 | |
23 | struct StepStruct {DReferenceTrajectory::swim_step_t steps[256];}; |
24 | |
25 | //--------------------------------- |
26 | // DReferenceTrajectory (Constructor) |
27 | //--------------------------------- |
28 | DReferenceTrajectory::DReferenceTrajectory(const DMagneticFieldMap *bfield |
29 | , double q |
30 | , swim_step_t *swim_steps |
31 | , int max_swim_steps |
32 | , double step_size) |
33 | { |
34 | // Copy some values into data members |
35 | this->q = q; |
36 | this->step_size = step_size; |
37 | this->bfield = bfield; |
38 | this->Nswim_steps = 0; |
39 | this->dist_to_rt_depth = 0; |
40 | this->mass = 0.13957; // assume pion mass until otherwise specified |
41 | this->hit_cdc_endplate = false; |
42 | this->RootGeom=NULL__null; |
43 | this->geom = NULL__null; |
44 | this->ploss_direction = kForward; |
45 | this->check_material_boundaries = true; |
46 | |
47 | this->last_phi = 0.0; |
48 | this->last_swim_step = NULL__null; |
49 | this->last_dist_along_wire = 0.0; |
50 | this->last_dz_dphi = 0.0; |
51 | |
52 | this->debug_level = 0; |
53 | |
54 | // Initialize some values from configuration parameters |
55 | BOUNDARY_STEP_FRACTION = 0.80; |
56 | MIN_STEP_SIZE = 0.05; // cm |
57 | MAX_STEP_SIZE = 3.0; // cm |
58 | int MAX_SWIM_STEPS = 10000; |
59 | |
60 | gPARMS->SetDefaultParameter("TRK:BOUNDARY_STEP_FRACTION" , BOUNDARY_STEP_FRACTION, "Fraction of estimated distance to boundary to use as step size"); |
61 | gPARMS->SetDefaultParameter("TRK:MIN_STEP_SIZE" , MIN_STEP_SIZE, "Minimum step size in cm to take when swimming a track with adaptive step sizes"); |
62 | gPARMS->SetDefaultParameter("TRK:MAX_STEP_SIZE" , MAX_STEP_SIZE, "Maximum step size in cm to take when swimming a track with adaptive step sizes"); |
63 | gPARMS->SetDefaultParameter("TRK:MAX_SWIM_STEPS" , MAX_SWIM_STEPS, "Number of swim steps for DReferenceTrajectory to allocate memory for (when not using external buffer)"); |
64 | |
65 | // It turns out that the greatest bottleneck in speed here comes from |
66 | // allocating/deallocating the large block of memory required to hold |
67 | // all of the trajectory info. The preferred way of calling this is |
68 | // with a pointer allocated once at program startup. This code block |
69 | // though allows it to be allocated here if necessary. |
70 | if(!swim_steps){ |
71 | own_swim_steps = true; |
72 | this->max_swim_steps = MAX_SWIM_STEPS; |
73 | this->swim_steps = new swim_step_t[this->max_swim_steps]; |
74 | }else{ |
75 | own_swim_steps = false; |
76 | this->max_swim_steps = max_swim_steps; |
77 | this->swim_steps = swim_steps; |
78 | } |
79 | } |
80 | |
81 | //--------------------------------- |
82 | // DReferenceTrajectory (Copy Constructor) |
83 | //--------------------------------- |
84 | DReferenceTrajectory::DReferenceTrajectory(const DReferenceTrajectory& rt) |
85 | { |
86 | /// The copy constructor will always allocate its own memory for the |
87 | /// swim steps and set its internal flag to indicate that is owns them |
88 | /// regardless of the owner of the source trajectory's. |
89 | |
90 | this->Nswim_steps = rt.Nswim_steps; |
91 | this->q = rt.q; |
92 | this->max_swim_steps = rt.max_swim_steps; |
93 | this->own_swim_steps = true; |
94 | this->step_size = rt.step_size; |
95 | this->bfield = rt.bfield; |
96 | this->last_phi = rt.last_phi; |
97 | this->last_dist_along_wire = rt.last_dist_along_wire; |
98 | this->last_dz_dphi = rt.last_dz_dphi; |
99 | this->RootGeom = rt.RootGeom; |
100 | this->geom = rt.geom; |
101 | this->dist_to_rt_depth = 0; |
102 | this->mass = rt.GetMass(); |
103 | this->ploss_direction = rt.ploss_direction; |
104 | this->check_material_boundaries = rt.GetCheckMaterialBoundaries(); |
105 | this->BOUNDARY_STEP_FRACTION = rt.GetBoundaryStepFraction(); |
106 | this->MIN_STEP_SIZE = rt.GetMinStepSize(); |
107 | this->MAX_STEP_SIZE = rt.GetMaxStepSize(); |
108 | this->debug_level=rt.debug_level; |
109 | |
110 | this->swim_steps = new swim_step_t[this->max_swim_steps]; |
111 | this->last_swim_step = NULL__null; |
112 | for(int i=0; i<Nswim_steps; i++) |
113 | { |
114 | swim_steps[i] = rt.swim_steps[i]; |
115 | if(&(rt.swim_steps[i]) == rt.last_swim_step) |
116 | this->last_swim_step = &(swim_steps[i]); |
117 | } |
118 | |
119 | } |
120 | |
121 | //--------------------------------- |
122 | // operator= (Assignment operator) |
123 | //--------------------------------- |
124 | DReferenceTrajectory& DReferenceTrajectory::operator=(const DReferenceTrajectory& rt) |
125 | { |
126 | /// The assignment operator will always make sure the memory allocated |
127 | /// for the swim_steps is owned by the object being copied into. |
128 | /// If it already owns memory of sufficient size, then it will be |
129 | /// reused. If it owns memory that is too small, it will be freed and |
130 | /// a new block allocated. If it does not own its swim_steps coming |
131 | /// in, then it will allocate memory so that it does own it on the |
132 | /// way out. |
133 | |
134 | if(&rt == this)return *this; // protect against self copies |
135 | |
136 | // Free memory if block is too small |
137 | if(own_swim_steps==true && max_swim_steps<rt.Nswim_steps){ |
138 | delete[] swim_steps; |
139 | swim_steps=NULL__null; |
140 | } |
141 | |
142 | // Forget memory block if we don't currently own it |
143 | if(!own_swim_steps){ |
144 | swim_steps=NULL__null; |
145 | } |
146 | |
147 | this->Nswim_steps = rt.Nswim_steps; |
148 | this->q = rt.q; |
149 | this->max_swim_steps = rt.max_swim_steps; |
150 | this->own_swim_steps = true; |
151 | this->step_size = rt.step_size; |
152 | this->bfield = rt.bfield; |
153 | this->last_phi = rt.last_phi; |
154 | this->last_dist_along_wire = rt.last_dist_along_wire; |
155 | this->last_dz_dphi = rt.last_dz_dphi; |
156 | this->RootGeom = rt.RootGeom; |
157 | this->geom = rt.geom; |
158 | this->dist_to_rt_depth = rt.dist_to_rt_depth; |
159 | this->mass = rt.GetMass(); |
160 | this->ploss_direction = rt.ploss_direction; |
161 | this->check_material_boundaries = rt.GetCheckMaterialBoundaries(); |
162 | this->BOUNDARY_STEP_FRACTION = rt.GetBoundaryStepFraction(); |
163 | this->MIN_STEP_SIZE = rt.GetMinStepSize(); |
164 | this->MAX_STEP_SIZE = rt.GetMaxStepSize(); |
165 | |
166 | // Allocate memory if needed |
167 | if(swim_steps==NULL__null)this->swim_steps = new swim_step_t[this->max_swim_steps]; |
168 | |
169 | // Copy swim steps |
170 | this->last_swim_step = NULL__null; |
171 | for(int i=0; i<Nswim_steps; i++) |
172 | { |
173 | swim_steps[i] = rt.swim_steps[i]; |
174 | if(&(rt.swim_steps[i]) == rt.last_swim_step) |
175 | this->last_swim_step = &(swim_steps[i]); |
176 | } |
177 | |
178 | |
179 | return *this; |
180 | } |
181 | |
182 | //--------------------------------- |
183 | // ~DReferenceTrajectory (Destructor) |
184 | //--------------------------------- |
185 | DReferenceTrajectory::~DReferenceTrajectory() |
186 | { |
187 | if(own_swim_steps){ |
188 | delete[] swim_steps; |
189 | } |
190 | } |
191 | |
192 | //--------------------------------- |
193 | // CopyWithShift |
194 | //--------------------------------- |
195 | void DReferenceTrajectory::CopyWithShift(const DReferenceTrajectory *rt, DVector3 shift) |
196 | { |
197 | // First, do a straight copy |
198 | *this = *rt; |
199 | |
200 | // Second, shift all positions |
201 | for(int i=0; i<Nswim_steps; i++)swim_steps[i].origin += shift; |
202 | } |
203 | |
204 | |
205 | //--------------------------------- |
206 | // Reset |
207 | //--------------------------------- |
208 | void DReferenceTrajectory::Reset(void){ |
209 | //reset DReferenceTrajectory for re-use |
210 | this->Nswim_steps = 0; |
211 | this->ploss_direction = kForward; |
212 | this->mass = 0.13957; // assume pion mass until otherwise specified |
213 | this->hit_cdc_endplate = false; |
214 | this->last_phi = 0.0; |
215 | this->last_swim_step = NULL__null; |
216 | this->last_dist_along_wire = 0.0; |
217 | this->last_dz_dphi = 0.0; |
218 | //do not reset "swim_steps" array: "ought" be ok as long as "Nswim_steps" is accurate |
219 | } |
220 | |
221 | //--------------------------------- |
222 | // FastSwim -- light-weight swim to a wire that does not treat multiple |
223 | // scattering but does handle energy loss. |
224 | // No checks for distance to boundaries are done. |
225 | //--------------------------------- |
226 | void DReferenceTrajectory::FastSwim(const DVector3 &pos, const DVector3 &mom, |
227 | DVector3 &last_pos,DVector3 &last_mom, |
228 | double q,double smax, |
229 | const DCoordinateSystem *wire){ |
230 | DVector3 mypos(pos); |
231 | DVector3 mymom(mom); |
232 | |
233 | // Initialize the stepper |
234 | DMagneticFieldStepper stepper(bfield, q, &pos, &mom); |
235 | double s=0,doca=1000.,old_doca=1000.,dP_dx=0.; |
236 | double mass=GetMass(); |
237 | while (s<smax){ |
238 | // Save old value of doca |
239 | old_doca=doca; |
240 | |
241 | // Adjust step size to take smaller steps in regions of high momentum loss |
242 | if(mass>0. && step_size<0.0 && geom){ |
243 | double KrhoZ_overA=0.0; |
244 | double rhoZ_overA=0.0; |
245 | double LogI=0.0; |
246 | double X0=0.0; |
247 | if (geom->FindMatALT1(mypos,mymom,KrhoZ_overA,rhoZ_overA,LogI,X0) |
248 | ==NOERROR){ |
249 | // Calculate momentum loss due to ionization |
250 | dP_dx = dPdx(mymom.Mag(), KrhoZ_overA, rhoZ_overA,LogI); |
251 | double my_step_size = 0.0001/fabs(dP_dx); |
252 | |
253 | if(my_step_size>MAX_STEP_SIZE)my_step_size=MAX_STEP_SIZE; // maximum step size in cm |
254 | if(my_step_size<MIN_STEP_SIZE)my_step_size=MIN_STEP_SIZE; // minimum step size in cm |
255 | |
256 | stepper.SetStepSize(my_step_size); |
257 | } |
258 | } |
259 | // Swim to next |
260 | double ds=stepper.Step(NULL__null); |
261 | s+=ds; |
262 | |
263 | stepper.GetPosMom(mypos,mymom); |
264 | if (mass>0 && dP_dx<0.){ |
265 | double ptot=mymom.Mag(); |
266 | if (ploss_direction==kForward) ptot+=dP_dx*ds; |
267 | else ptot-=dP_dx*ds; |
268 | mymom.SetMag(ptot); |
269 | stepper.SetStartingParams(q, &mypos, &mymom); |
270 | } |
271 | |
272 | // Break if we have passed the wire |
273 | DVector3 wirepos=wire->origin; |
274 | if (fabs(wire->udir.z())>0.){ // for CDC wires |
275 | wirepos+=((mypos.z()-wire->origin.z())/wire->udir.z())*wire->udir; |
276 | } |
277 | doca=(wirepos-mypos).Mag(); |
278 | if (doca>old_doca) break; |
279 | |
280 | // Store the position and momentum for this step |
281 | last_pos=mypos; |
282 | last_mom=mymom; |
283 | } |
284 | } |
285 | |
286 | //--------------------------------- |
287 | // Swim |
288 | //--------------------------------- |
289 | void DReferenceTrajectory::Swim(const DVector3 &pos, const DVector3 &mom, double q, double smax, const DCoordinateSystem *wire) |
290 | { |
291 | /// (Re)Swim the trajectory starting from pos with momentum mom. |
292 | /// This will use the charge and step size (if given) passed to |
293 | /// the constructor when the object was created. It will also |
294 | /// (re)use the sim_step buffer, replacing it's contents. |
295 | |
296 | // If the charged passed to us is greater that 10, it means use the charge |
297 | // already stored in the class. Otherwise, use what was passed to us. |
298 | if(fabs(q)>10) |
299 | q = this->q; |
300 | else |
301 | this->q = q; |
302 | |
303 | DMagneticFieldStepper stepper(bfield, q, &pos, &mom); |
304 | if(step_size>0.0)stepper.SetStepSize(step_size); |
305 | |
306 | // Step until we hit a boundary (don't track more than 20 meters) |
307 | swim_step_t *swim_step = this->swim_steps; |
308 | double t=0.; |
309 | Nswim_steps = 0; |
310 | double itheta02 = 0.0; |
311 | double itheta02s = 0.0; |
312 | double itheta02s2 = 0.0; |
313 | swim_step_t *last_step=NULL__null; |
314 | // Magnetic field |
315 | double Bz_old=0; |
316 | |
317 | // Reset flag indicating whether we hit the CDC endplate |
318 | // and get the parameters of the endplate so we can check |
319 | // if we hit it while swimming. |
320 | hit_cdc_endplate = false; |
321 | #if 0 // The GetCDCEndplate call goes all the way back to the XML and slows down |
322 | // overall tracking by a factor of 20. Therefore, we skip finding it |
323 | // and just hard-code the values instead. 1/28/2011 DL |
324 | double cdc_endplate_z=150+17; // roughly, from memory |
325 | double cdc_endplate_dz=5.0; // roughly, from memory |
326 | double cdc_endplate_rmin=10.0; // roughly, from memory |
327 | double cdc_endplate_rmax=55.0; // roughly, from memory |
328 | if(geom)geom->GetCDCEndplate(cdc_endplate_z, cdc_endplate_dz, cdc_endplate_rmin, cdc_endplate_rmax); |
329 | double cdc_endplate_zmin = cdc_endplate_z - cdc_endplate_dz/2.0; |
330 | double cdc_endplate_zmax = cdc_endplate_zmin + cdc_endplate_dz; |
331 | #else |
332 | double cdc_endplate_rmin=10.0; // roughly, from memory |
333 | double cdc_endplate_rmax=55.0; // roughly, from memory |
334 | double cdc_endplate_zmin = 167.6; |
335 | double cdc_endplate_zmax = 168.2; |
336 | #endif |
337 | |
338 | // Get Bfield from stepper to initialize Bz_old |
339 | DVector3 B; |
340 | stepper.GetBField(B); |
341 | Bz_old = B.z(); |
Value stored to 'Bz_old' is never read | |
342 | |
343 | for(double s=0; fabs(s)<smax; Nswim_steps++, swim_step++){ |
344 | |
345 | |
346 | if(Nswim_steps>=this->max_swim_steps){ |
347 | jerr<<__FILE__"DReferenceTrajectory.cc"<<":"<<__LINE__347<<" Too many steps in trajectory. Truncating..."<<endl; |
348 | break; |
349 | } |
350 | |
351 | stepper.GetDirs(swim_step->sdir, swim_step->tdir, swim_step->udir); |
352 | stepper.GetPosMom(swim_step->origin, swim_step->mom); |
353 | swim_step->Ro = stepper.GetRo(); |
354 | swim_step->s = s; |
355 | swim_step->t = t; |
356 | |
357 | //magnitude of momentum and beta |
358 | double p_sq=swim_step->mom.Mag2(); |
359 | double one_over_beta=sqrt(1.+mass*mass/p_sq); |
360 | |
361 | // Add material if geom or RootGeom is not NULL |
362 | // If both are non-NULL, then use RootGeom |
363 | double dP = 0.0; |
364 | double dP_dx=0.0; |
365 | double s_to_boundary=1.0E6; // initialize to "infinity" in case we don't set this below |
366 | if(RootGeom || geom){ |
367 | double KrhoZ_overA=0.0; |
368 | double rhoZ_overA=0.0; |
369 | double LogI=0.0; |
370 | double X0=0.0; |
371 | jerror_t err; |
372 | if(RootGeom){ |
373 | double rhoZ_overA,rhoZ_overA_logI; |
374 | err = RootGeom->FindMatLL(swim_step->origin, |
375 | rhoZ_overA, |
376 | rhoZ_overA_logI, |
377 | X0); |
378 | KrhoZ_overA=0.1535e-3*rhoZ_overA; |
379 | LogI=rhoZ_overA_logI/rhoZ_overA; |
380 | }else{ |
381 | if(check_material_boundaries){ |
382 | err = geom->FindMatALT1(swim_step->origin, swim_step->mom, KrhoZ_overA, rhoZ_overA,LogI, X0, &s_to_boundary); |
383 | }else{ |
384 | err = geom->FindMatALT1(swim_step->origin, swim_step->mom, KrhoZ_overA, rhoZ_overA,LogI, X0); |
385 | } |
386 | |
387 | // Check if we hit the CDC endplate |
388 | double z = swim_step->origin.Z(); |
389 | if(z>=cdc_endplate_zmin && z<=cdc_endplate_zmax){ |
390 | double r = swim_step->origin.Perp(); |
391 | if(r>=cdc_endplate_rmin && r<=cdc_endplate_rmax){ |
392 | hit_cdc_endplate = true; |
393 | } |
394 | } |
395 | } |
396 | |
397 | if(err == NOERROR){ |
398 | if(X0>0.0){ |
399 | double p=sqrt(p_sq); |
400 | double delta_s = s; |
401 | if(last_step)delta_s -= last_step->s; |
402 | double radlen = delta_s/X0; |
403 | |
404 | if(radlen>1.0E-5){ // PDG 2008 pg 271, second to last paragraph |
405 | |
406 | double theta0 = 0.0136*one_over_beta/p*sqrt(radlen)*(1.0+0.038*log(radlen)); // From PDG 2008 eq 27.12 |
407 | double theta02 = theta0*theta0; |
408 | itheta02 += theta02; |
409 | itheta02s += s*theta02; |
410 | itheta02s2 += s*s*theta02; |
411 | } |
412 | |
413 | // Calculate momentum loss due to ionization |
414 | dP_dx = dPdx(p, KrhoZ_overA, rhoZ_overA,LogI); |
415 | } |
416 | } |
417 | last_step = swim_step; |
418 | } |
419 | swim_step->itheta02 = itheta02; |
420 | swim_step->itheta02s = itheta02s; |
421 | swim_step->itheta02s2 = itheta02s2; |
422 | |
423 | // Adjust step size to take smaller steps in regions of high momentum loss or field gradient |
424 | if(step_size<0.0){ // step_size<0 indicates auto-calculated step size |
425 | // Take step so as to change momentum by 100keV |
426 | //double my_step_size=p/fabs(dP_dx)*0.01; |
427 | double my_step_size = 0.0001/fabs(dP_dx); |
428 | |
429 | // Now check the field gradient |
430 | #if 0 |
431 | stepper.GetBField(B); |
432 | double Bz = B.z(); |
433 | if (fabs(Bz-Bz_old)>EPS1e-8){ |
434 | double my_step_size_B=0.01*my_step_size |
435 | *fabs(Bz/(Bz_old-Bz)); |
436 | if (my_step_size_B<my_step_size) |
437 | my_step_size=my_step_size_B; |
438 | } |
439 | Bz_old=Bz; // Save old z-component of B-field |
440 | #endif |
441 | // Use the estimated distance to the boundary to make sure we don't overstep |
442 | // into a high density region and miss some material. Use half the estimated |
443 | // distance since it's only an estimate. Note that even though this would lead |
444 | // to infinitely small steps, there is a minimum step size imposed below to |
445 | // ensure the step size is reasonable. |
446 | double step_size_to_boundary = BOUNDARY_STEP_FRACTION*s_to_boundary; |
447 | if(step_size_to_boundary < my_step_size)my_step_size = step_size_to_boundary; |
448 | |
449 | if(my_step_size>MAX_STEP_SIZE)my_step_size=MAX_STEP_SIZE; // maximum step size in cm |
450 | if(my_step_size<MIN_STEP_SIZE)my_step_size=MIN_STEP_SIZE; // minimum step size in cm |
451 | |
452 | stepper.SetStepSize(my_step_size); |
453 | } |
454 | |
455 | // Swim to next |
456 | double ds=stepper.Step(NULL__null); |
457 | |
458 | // Calculate momentum loss due to the step we're about to take |
459 | dP = ds*dP_dx; |
460 | swim_step->dP = dP; // n.b. stepper has been updated for next round but we're still on present step |
461 | |
462 | // Adjust momentum due to ionization losses |
463 | if(dP!=0.0){ |
464 | DVector3 pos, mom; |
465 | stepper.GetPosMom(pos, mom); |
466 | double ptot = mom.Mag() - dP; // correct for energy loss |
467 | bool ranged_out = false; |
468 | if(ptot<0.0)ranged_out=true; |
469 | if(dP<0.0 && ploss_direction==kForward)ranged_out=true; |
470 | if(dP>0.0 && ploss_direction==kBackward)ranged_out=true; |
471 | if(mom.Mag()==0.0)ranged_out=true; |
472 | if(ranged_out){ |
473 | Nswim_steps++; // This will at least allow for very low momentum particles to have 1 swim step |
474 | break; |
475 | } |
476 | mom.SetMag(ptot); |
477 | stepper.SetStartingParams(q, &pos, &mom); |
478 | } |
479 | |
480 | // update flight time |
481 | t+=ds*one_over_beta/SPEED_OF_LIGHT29.9792; |
482 | s += ds; |
483 | |
484 | |
485 | // Exit loop if we leave the tracking volume |
486 | if(swim_step->origin.Perp()>88.0 |
487 | && swim_step->origin.Z()<407.0){Nswim_steps++; break;} // ran into BCAL |
488 | if (swim_step->origin.X()>129. || swim_step->origin.Y()>129.) |
489 | {Nswim_steps++; break;} // left extent of TOF |
490 | if(swim_step->origin.Z()>670.0){Nswim_steps++; break;} // ran into FCAL |
491 | if(swim_step->origin.Z()<-100.0){Nswim_steps++; break;} // exit upstream |
492 | if(wire && Nswim_steps>0){ // optionally check if we passed a wire we're supposed to be swimming to |
493 | swim_step_t *closest_step = FindClosestSwimStep(wire); |
494 | if(++closest_step!=swim_step){Nswim_steps++; break;} |
495 | } |
496 | } |
497 | |
498 | // OK. At this point the positions of the trajectory in the lab |
499 | // frame have been recorded along with the momentum of the |
500 | // particle and the directions of reference trajectory |
501 | // coordinate system at each point. |
502 | } |
503 | |
504 | |
505 | // Routine to find position on the trajectory where the track crosses a radial |
506 | // position R. Also returns the path length to this position. |
507 | jerror_t DReferenceTrajectory::GetIntersectionWithRadius(double R, |
508 | DVector3 &mypos, |
509 | double *s, |
510 | double *t) const{ |
511 | if(Nswim_steps<1){ |
512 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 512<<" "<<"No swim steps! You must \"Swim\" the track before calling GetIntersectionWithRadius(...)"<<endl; |
513 | } |
514 | // Loop over swim steps and find the one that crosses the radius |
515 | swim_step_t *swim_step = swim_steps; |
516 | swim_step_t *step=NULL__null; |
517 | swim_step_t *last_step=NULL__null; |
518 | for(int i=0; i<Nswim_steps; i++, swim_step++){ |
519 | if (swim_step->origin.Perp()>R){ |
520 | step=swim_step; |
521 | break; |
522 | } |
523 | if (swim_step->origin.Z()>407.0) return VALUE_OUT_OF_RANGE; |
524 | last_step=swim_step; |
525 | } |
526 | if (step==NULL__null||last_step==NULL__null) return VALUE_OUT_OF_RANGE; |
527 | |
528 | // At this point, the location where the track intersects the cyclinder |
529 | // is somewhere between last_step and step. For simplicity, we're going |
530 | // to just find the intersection of the cylinder with the line that joins |
531 | // the 2 positions. We do this by working in the X/Y plane only and |
532 | // finding the value of "alpha" which is the fractional distance the |
533 | // intersection point is between last_pos and mypos. We'll then apply |
534 | // the alpha found in the 2D X/Y space to the 3D x/y/Z space to find |
535 | // the actual intersection point. |
536 | DVector2 x1(last_step->origin.X(), last_step->origin.Y()); |
537 | DVector2 x2(step->origin.X(), step->origin.Y()); |
538 | DVector2 dx = x2-x1; |
539 | double A = dx.Mod2(); |
540 | double B = 2.0*(x1.X()*dx.X() + x1.Y()*dx.Y()); |
541 | double C = x1.Mod2() - R*R; |
542 | |
543 | double sqrt_D=sqrt(B*B-4.0*A*C); |
544 | double one_over_denom=0.5/A; |
545 | double alpha1 = (-B + sqrt_D)*one_over_denom; |
546 | double alpha2 = (-B - sqrt_D)*one_over_denom; |
547 | double alpha = alpha1; |
548 | if(alpha1<0.0 || alpha1>1.0)alpha=alpha2; |
549 | if(!finite(alpha))return VALUE_OUT_OF_RANGE; |
550 | |
551 | DVector3 delta = step->origin - last_step->origin; |
552 | mypos = last_step->origin + alpha*delta; |
553 | |
554 | // The value of s actually represents the pathlength |
555 | // to the outside point. Adjust it back to the |
556 | // intersection point (approximately). |
557 | if (s) *s = step->s-(1.0-alpha)*delta.Mag(); |
558 | |
559 | // flight time |
560 | if (t){ |
561 | double p_sq=step->mom.Mag2(); |
562 | double one_over_beta=sqrt(1.+mass*mass/p_sq); |
563 | *t = step->t-(1.0-alpha)*delta.Mag()*one_over_beta/SPEED_OF_LIGHT29.9792; |
564 | } |
565 | |
566 | return NOERROR; |
567 | } |
568 | |
569 | //--------------------------------- |
570 | // GetIntersectionWithPlane |
571 | //--------------------------------- |
572 | void DReferenceTrajectory::GetIntersectionWithPlane(const DVector3 &origin, const DVector3 &norm, DVector3 &pos, double *s,double *t) const{ |
573 | DVector3 dir; |
574 | GetIntersectionWithPlane(origin,norm,pos,dir,s,t); |
575 | } |
576 | void DReferenceTrajectory::GetIntersectionWithPlane(const DVector3 &origin, const DVector3 &norm, DVector3 &pos, DVector3 &dir, double *s,double *t) const |
577 | { |
578 | /// Get the intersection point of this trajectory with a plane. |
579 | /// The plane is specified by <i>origin</i> and <i>norm</i>. The |
580 | /// <i>origin</i> vector should give the coordinates of any point |
581 | /// on the plane and <i>norm</i> should give a vector normal to |
582 | /// the plane. The <i>norm</i> vector will be copied and normalized |
583 | /// so it can be of any magnitude upon entry. |
584 | /// |
585 | /// The coordinates of the intersection point will copied into |
586 | /// the supplied <i>pos</i> vector. If a non-NULL pointer for <i>s</i> |
587 | /// is passed in, the pathlength of the trajectory from its begining |
588 | /// to the intersection point is copied into location pointed to. |
589 | |
590 | // Set reasonable defaults |
591 | pos.SetXYZ(0,0,0); |
592 | if(s)*s=0.0; |
593 | |
594 | // Find the closest swim step to the position where the track crosses |
595 | // the plane |
596 | swim_step_t *step = FindPlaneCrossing(origin,norm); |
597 | // Kludge for tracking to forward detectors assuming that the planes |
598 | // are perpendicular to the beam line |
599 | if (step && step->origin.Z()>600. |
600 | ){ |
601 | double p_sq=step->mom.Mag2(); |
602 | //double ds=(origin.z()-step->origin.z())*p/step->mom.z(); |
603 | double dz_over_pz=(origin.z()-step->origin.z())/step->mom.z(); |
604 | double ds=sqrt(p_sq)*dz_over_pz; |
605 | pos.SetXYZ(step->origin.x()+dz_over_pz*step->mom.x(), |
606 | step->origin.y()+dz_over_pz*step->mom.y(), |
607 | origin.z()); |
608 | dir=step->mom; |
609 | dir.SetMag(1.0); |
610 | if (s){ |
611 | *s=step->s+ds; |
612 | } |
613 | // flight time |
614 | if (t){ |
615 | double one_over_beta=sqrt(1.+mass*mass/p_sq); |
616 | *t = step->t+ds*one_over_beta/SPEED_OF_LIGHT29.9792; |
617 | } |
618 | |
619 | return; |
620 | } |
621 | |
622 | if(!step){ |
623 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 623<<" "<<"Could not find closest swim step!"<<endl; |
624 | return; |
625 | } |
626 | |
627 | // Here we follow a scheme described in more detail in the |
628 | // DistToRT(DVector3 hit) method below. The basic idea is to |
629 | // express a point on the helix in terms of a single variable |
630 | // and then solve for that variable by setting the distance |
631 | // to zero. |
632 | // |
633 | // x = Ro*(cos(phi) - 1) |
634 | // y = Ro*sin(phi) |
635 | // z = phi*(dz/dphi) |
636 | // |
637 | // As is done below, we work in the RT coordinate system. Well, |
638 | // sort of. The distance to the plane is given by: |
639 | // |
640 | // d = ( x - c ).n |
641 | // |
642 | // where x is a point on the helix, c is the "origin" point |
643 | // which lies somewhere in the plane and n is the "norm" |
644 | // vector. Since we want a point in the plane, we set d=0 |
645 | // and solve for phi (with the components of x expressed in |
646 | // terms of phi as given in the DistToRT method below). |
647 | // |
648 | // Thus, the equation we need to solve is: |
649 | // |
650 | // x.n - c.n = 0 |
651 | // |
652 | // notice that "c" only gets dotted into "n" so that |
653 | // dot product can occur in any coordinate system. Therefore, |
654 | // we do that in the lab coordinate system to avoid the |
655 | // overhead of transforming "c" to the RT system. The "n" |
656 | // vector, however, still must be transformed. |
657 | // |
658 | // Expanding the trig functions to 2nd order in phi, performing |
659 | // the x.n dot product, and gathering equal powers of phi |
660 | // leads us to he following: |
661 | // |
662 | // (-Ro*nx/2)*phi^2 + (Ro*ny+dz_dphi*nz)*phi - c.n = 0 |
663 | // |
664 | // which is quadratic in phi. We solve for both roots, but use |
665 | // the one with the smller absolute value (if both are finite). |
666 | |
667 | double &Ro = step->Ro; |
668 | |
669 | // OK, having said all of that, it turns out that the above |
670 | // mechanism will tend to fail in regions of low or no |
671 | // field because the value of Ro is very large. Thus, we need to |
672 | // use a straight line projection in such cases. We also |
673 | // want to use a straight line projection if the helical intersection |
674 | // fails for some other reason. |
675 | // |
676 | // The algorthim is then to only try the helical calculation |
677 | // for small (<10m) values of Ro and then do the straight line |
678 | // if R is larger than that OR the helical calculation fails. |
679 | |
680 | // Try helical calculation |
681 | if(Ro<1000.0){ |
682 | double nx = norm.Dot(step->sdir); |
683 | double ny = norm.Dot(step->tdir); |
684 | double nz = norm.Dot(step->udir); |
685 | |
686 | double delta_z = step->mom.Dot(step->udir); |
687 | double delta_phi = step->mom.Dot(step->tdir)/Ro; |
688 | double dz_dphi = delta_z/delta_phi; |
689 | |
690 | double A = -Ro*nx/2.0; |
691 | double B = Ro*ny + dz_dphi*nz; |
692 | double C = norm.Dot(step->origin-origin); |
693 | double sqroot=sqrt(B*B-4.0*A*C); |
694 | double twoA=2.0*A; |
695 | |
696 | double phi_1 = (-B + sqroot)/(twoA); |
697 | double phi_2 = (-B - sqroot)/(twoA); |
698 | |
699 | double phi = fabs(phi_1)<fabs(phi_2) ? phi_1:phi_2; |
700 | if(!finite(phi_1))phi = phi_2; |
701 | if(!finite(phi_2))phi = phi_1; |
702 | if(finite(phi)){ |
703 | |
704 | double my_s = -Ro/2.0 * phi*phi; |
705 | double my_t = Ro * phi; |
706 | double my_u = dz_dphi * phi; |
707 | |
708 | pos = step->origin + my_s*step->sdir + my_t*step->tdir + my_u*step->udir; |
709 | dir = step->mom; |
710 | dir.SetMag(1.0); |
711 | if(s){ |
712 | double delta_s = sqrt(my_t*my_t + my_u*my_u); |
713 | *s = step->s + (phi>0 ? +delta_s:-delta_s); |
714 | } |
715 | // flight time |
716 | if (t){ |
717 | double delta_s = sqrt(my_t*my_t + my_u*my_u); |
718 | double ds=(phi>0 ? +delta_s:-delta_s); |
719 | double p_sq=step->mom.Mag2(); |
720 | double one_over_beta=sqrt(1.+mass*mass/p_sq); |
721 | *t = step->t+ds*one_over_beta/SPEED_OF_LIGHT29.9792; |
722 | } |
723 | |
724 | // Success. Go ahead and return |
725 | return; |
726 | } |
727 | } |
728 | |
729 | // If we got here then we need to try a straight line calculation |
730 | double alpha = norm.Dot(origin)/norm.Dot(step->mom); |
731 | pos = alpha*step->mom; |
732 | dir = step->mom; |
733 | dir.SetMag(1.0); |
734 | if(s){ |
735 | double delta_s = alpha*step->mom.Mag(); |
736 | *s = step->s + delta_s; |
737 | } |
738 | // flight time |
739 | if (t){ |
740 | double p_sq=step->mom.Mag2(); |
741 | double one_over_beta=sqrt(1.+mass*mass/p_sq); |
742 | *t = step->t+alpha*sqrt(p_sq)*one_over_beta/SPEED_OF_LIGHT29.9792; |
743 | } |
744 | } |
745 | |
746 | //--------------------------------- |
747 | // InsertSteps |
748 | //--------------------------------- |
749 | int DReferenceTrajectory::InsertSteps(const swim_step_t *start_step, double delta_s, double step_size) |
750 | { |
751 | /// Insert additional steps into the reference trajectory starting |
752 | /// at start_step and swimming for at least delta_s by step_size |
753 | /// sized steps. Both delta_s and step_size are in centimeters. |
754 | /// If the value of delta_s is negative then the particle's momentum |
755 | /// and charge are reversed before swimming. This could be a problem |
756 | /// if energy loss is implemented. |
757 | |
758 | if(!start_step)return -1; |
759 | |
760 | // We do this by creating another, temporary DReferenceTrajectory object |
761 | // on the stack and swimming it. |
762 | DVector3 pos = start_step->origin; |
763 | DVector3 mom = start_step->mom; |
764 | double my_q = q; |
765 | int direction = +1; |
766 | if(delta_s<0.0){ |
767 | mom *= -1.0; |
768 | my_q = -q; |
769 | direction = -1; |
770 | } |
771 | |
772 | // Here I allocate the steps using an auto_ptr so I don't have to mess with |
773 | // deleting them at all of the possible exits. The problem with auto_ptr |
774 | // is it can't handle arrays so it has to be wrapped in a struct. |
775 | auto_ptr<StepStruct> steps_aptr(new StepStruct); |
776 | DReferenceTrajectory::swim_step_t *steps = steps_aptr->steps; |
777 | DReferenceTrajectory rt(bfield , my_q , steps , 256); |
778 | rt.SetStepSize(step_size); |
779 | rt.Swim(pos, mom, my_q, fabs(delta_s)); |
780 | if(rt.Nswim_steps==0)return 1; |
781 | |
782 | // Check that there is enough space to add these points |
783 | if((Nswim_steps+rt.Nswim_steps)>max_swim_steps){ |
784 | //_DBG_<<"Not enough swim steps available to add new ones! Max="<<max_swim_steps<<" had="<<Nswim_steps<<" new="<<rt.Nswim_steps<<endl; |
785 | return 2; |
786 | } |
787 | |
788 | // At this point, we may have swum forward or backwards so the points |
789 | // will need to be added either before start_step or after it. We also |
790 | // may want to replace an old step that overlaps our high density steps |
791 | // since they are presumably more accurate. Find the indexes of the |
792 | // existing steps that the new steps will be inserted between. |
793 | double sdiff = rt.swim_steps[rt.Nswim_steps-1].s; |
794 | double s1 = start_step->s; |
795 | double s2 = start_step->s + (double)direction*sdiff; |
796 | double smin = s1<s2 ? s1:s2; |
797 | double smax = s1<s2 ? s2:s1; |
798 | int istep_start = 0; |
799 | int istep_end = 0; |
800 | for(int i=0; i<Nswim_steps; i++){ |
801 | if(swim_steps[i].s < smin)istep_start = i; |
802 | if(swim_steps[i].s <= smax)istep_end = i+1; |
803 | } |
804 | |
805 | // istep_start and istep_end now point to the steps we want to keep. |
806 | // All steps between them (exclusive) will be overwritten. Note that |
807 | // the original start_step should be in the "overwrite" range since |
808 | // it is included already in the new trajectory. |
809 | int steps_to_overwrite = istep_end - istep_start - 1; |
810 | int steps_to_shift = rt.Nswim_steps - steps_to_overwrite; |
811 | |
812 | // Shift the steps down (or is it up?) starting with istep_end. |
813 | for(int i=Nswim_steps-1; i>=istep_end; i--)swim_steps[i+steps_to_shift] = swim_steps[i]; |
814 | |
815 | // Copy the new steps into this object |
816 | double s_0 = start_step->s; |
817 | double itheta02_0 = start_step->itheta02; |
818 | double itheta02s_0 = start_step->itheta02s; |
819 | double itheta02s2_0 = start_step->itheta02s2; |
820 | for(int i=0; i<rt.Nswim_steps; i++){ |
821 | int index = direction>0 ? (istep_start+1+i):(istep_start+1+rt.Nswim_steps-1-i); |
822 | swim_steps[index] = rt.swim_steps[i]; |
823 | swim_steps[index].s = s_0 + (double)direction*swim_steps[index].s; |
824 | swim_steps[index].itheta02 = itheta02_0 + (double)direction*swim_steps[index].itheta02; |
825 | swim_steps[index].itheta02s = itheta02s_0 + (double)direction*swim_steps[index].itheta02s; |
826 | swim_steps[index].itheta02s2 = itheta02s2_0 + (double)direction*swim_steps[index].itheta02s2; |
827 | if(direction<0.0){ |
828 | swim_steps[index].sdir *= -1.0; |
829 | swim_steps[index].tdir *= -1.0; |
830 | } |
831 | } |
832 | Nswim_steps += rt.Nswim_steps-steps_to_overwrite; |
833 | |
834 | // Note that the above procedure may leave us with "kinks" in the itheta0 |
835 | // variables. It may be that we need to recalculate those for all of the |
836 | // new points and the ones after them by making one more pass. I'm hoping |
837 | // it is a realitively small correction though so we can skip it here. |
838 | return 0; |
839 | } |
840 | |
841 | //--------------------------------- |
842 | // DistToRTwithTime |
843 | //--------------------------------- |
844 | double DReferenceTrajectory::DistToRTwithTime(DVector3 hit, double *s,double *t) const{ |
845 | double dist=DistToRT(hit,s); |
846 | if (s!=NULL__null && t!=NULL__null && last_swim_step!=NULL__null){ |
847 | double p_sq=last_swim_step->mom.Mag2(); |
848 | double one_over_beta=sqrt(1.+mass*mass/p_sq); |
849 | *t=last_swim_step->t+(*s-last_swim_step->s)*one_over_beta/SPEED_OF_LIGHT29.9792; |
850 | } |
851 | return dist; |
852 | } |
853 | |
854 | //--------------------------------- |
855 | // DistToRT |
856 | //--------------------------------- |
857 | double DReferenceTrajectory::DistToRT(DVector3 hit, double *s) const |
858 | { |
859 | last_swim_step=NULL__null; |
860 | if(Nswim_steps<1)_DBG__std::cerr<<"DReferenceTrajectory.cc"<<":"<< 860<<std::endl; |
861 | |
862 | // First, find closest step to point |
863 | swim_step_t *swim_step = swim_steps; |
864 | swim_step_t *step=NULL__null; |
865 | //double min_delta2 = 1.0E6; |
866 | double old_delta2=10.e6,delta2=1.0e6; |
867 | for(int i=0; i<Nswim_steps; i++, swim_step++){ |
868 | |
869 | DVector3 pos_diff = swim_step->origin - hit; |
870 | delta2 = pos_diff.Mag2(); |
871 | if (delta2>old_delta2) break; |
872 | |
873 | //if(delta2 < min_delta2){ |
874 | //min_delta2 = delta2; |
875 | |
876 | step = swim_step; |
877 | old_delta2=delta2; |
878 | //} |
879 | } |
880 | if(step==NULL__null){ |
881 | // It seems to occasionally occur that we have 1 swim step |
882 | // and it's values are invalid. Supress warning messages |
883 | // for these as they are "known" (even if not fully understood!) |
884 | if(Nswim_steps>1){ |
885 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 885<<" "<<"\"hit\" passed to DistToRT(DVector3) out of range!"<<endl; |
886 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 886<<" "<<"hit x,y,z = "<<hit.x()<<", "<<hit.y()<<", "<<hit.z()<<" Nswim_steps="<<Nswim_steps<<" min_delta2="<<delta2<<endl; |
887 | } |
888 | return 1.0E6; |
889 | } |
890 | |
891 | // store last step |
892 | last_swim_step=step; |
893 | |
894 | |
895 | // Next, define a point on the helical segment defined by the |
896 | // swim step it the RT coordinate system. The directions of |
897 | // the RT coordinate system are defined by step->xdir, step->ydir, |
898 | // and step->zdir. The coordinates of a point on the helix |
899 | // in this coordinate system are: |
900 | // |
901 | // x = Ro*(cos(phi) - 1) |
902 | // y = Ro*sin(phi) |
903 | // z = phi*(dz/dphi) |
904 | // |
905 | // where phi is the phi angle of the point in this coordinate system. |
906 | // phi=0 corresponds to the swim step point itself |
907 | // |
908 | // Transform the given coordinates to the RT coordinate system |
909 | // and call these x0,y0,z0. Then, the distance of point to a |
910 | // point on the helical segment is given by: |
911 | // |
912 | // d^2 = (x0-x)^2 + (y0-y)^2 + (z0-z)^2 |
913 | // |
914 | // where x,y,z are all functions of phi as given above. |
915 | // |
916 | // writing out d^2 in terms of phi, but using the small angle |
917 | // approximation for the trig functions, an equation for the |
918 | // distance in only phi is obtained. Taking the derivative |
919 | // and setting it equal to zero leaves a 3rd order polynomial |
920 | // in phi whose root corresponds to the minimum distance. |
921 | // Skipping some math, this equation has the form: |
922 | // |
923 | // d(d^2)/dphi = 0 = Ro^2*phi^3 + 2*alpha*phi + beta |
924 | // |
925 | // where: |
926 | // alpha = x0*Ro + Ro^2 + (dz/dphi)^2 |
927 | // |
928 | // beta = -2*y0*Ro - 2*z0*(dz/dphi) |
929 | // |
930 | // The above 3rd order poly is convenient in that it does not |
931 | // contain a phi^2 term. This means we can skip the step |
932 | // done in the general case where a change of variables is |
933 | // made such that the 2nd order term disappears. |
934 | // |
935 | // In general, an equation of the form |
936 | // |
937 | // w^3 + 3.0*b*w + 2*c = 0 |
938 | // |
939 | // has one real root: |
940 | // |
941 | // w0 = q - p |
942 | // |
943 | // where: |
944 | // q^3 = d - c |
945 | // p^3 = d + c |
946 | // d^2 = b^3 + c^2 (don't confuse with d^2 above!) |
947 | // |
948 | // So for us ... |
949 | // |
950 | // 3b = 2*alpha/(Ro^2) |
951 | // 2c = beta/(Ro^2) |
952 | |
953 | hit -= step->origin; |
954 | double x0 = hit.Dot(step->sdir); |
955 | double y0 = hit.Dot(step->tdir); |
956 | double z0 = hit.Dot(step->udir); |
957 | double &Ro = step->Ro; |
958 | double Ro2 = Ro*Ro; |
959 | double delta_z = step->mom.Dot(step->udir); |
960 | double delta_phi = step->mom.Dot(step->tdir)/Ro; |
961 | double dz_dphi = delta_z/delta_phi; |
962 | |
963 | // double alpha = x0*Ro + Ro2 + pow(dz_dphi,2.0); |
964 | double alpha=x0*Ro + Ro2 +dz_dphi*dz_dphi; |
965 | // double beta = -2.0*y0*Ro - 2.0*z0*dz_dphi; |
966 | double beta = -2.0*(y0*Ro + z0*dz_dphi); |
967 | // double b = (2.0*alpha/Ro2)/3.0; |
968 | double b= TWO_THIRD0.66666666666666667*alpha/Ro2; |
969 | // double c = (beta/Ro2)/2.0; |
970 | double c = 0.5*(beta/Ro2); |
971 | // double d = sqrt(pow(b,3.0) + pow(c,2.0)); |
972 | double d2=b*b*b+c*c; |
973 | double phi=0.,dist2=1e8; |
974 | if (d2>=0){ |
975 | double d=sqrt(d2); |
976 | //double q = pow(d-c, ONE_THIRD); |
977 | //double p = pow(d+c, ONE_THIRD); |
978 | double p=cbrt(d+c); |
979 | double q=cbrt(d-c); |
980 | phi = q - p; |
981 | double phisq=phi*phi; |
982 | |
983 | dist2 = 0.25*Ro2*phisq*phisq + alpha*phisq + beta*phi |
984 | + x0*x0 + y0*y0 + z0*z0; |
985 | } |
986 | else{ |
987 | // Use DeMoivre's theorem to find the cube root of a complex |
988 | // number. In this case there are three real solutions. |
989 | double d=sqrt(-d2); |
990 | c*=-1.; |
991 | double temp=sqrt(cbrt(c*c+d*d)); |
992 | double theta1=ONE_THIRD0.33333333333333333*atan2(d,c); |
993 | double sum_over_2=temp*cos(theta1); |
994 | double diff_over_2=-temp*sin(theta1); |
995 | |
996 | double phi0=2.*sum_over_2; |
997 | double phi0sq=phi0*phi0; |
998 | double phi1=-sum_over_2+sqrt(3)*diff_over_2; |
999 | double phi1sq=phi1*phi1; |
1000 | double phi2=-sum_over_2-sqrt(3)*diff_over_2; |
1001 | double phi2sq=phi2*phi2; |
1002 | double d2_2 = 0.25*Ro2*phi2sq*phi2sq + alpha*phi2sq + beta*phi2 + x0*x0 + y0*y0 + z0*z0; |
1003 | double d2_1 = 0.25*Ro2*phi1sq*phi1sq + alpha*phi1sq + beta*phi1 + x0*x0 + y0*y0 + z0*z0; |
1004 | double d2_0 = 0.25*Ro2*phi0sq*phi0sq + alpha*phi0sq + beta*phi0 + x0*x0 + y0*y0 + z0*z0; |
1005 | |
1006 | if (d2_0<d2_1 && d2_0<d2_2){ |
1007 | phi=phi0; |
1008 | dist2=d2_0; |
1009 | } |
1010 | else if (d2_1<d2_0 && d2_1<d2_2){ |
1011 | phi=phi1; |
1012 | dist2=d2_1; |
1013 | } |
1014 | else{ |
1015 | phi=phi2; |
1016 | dist2=d2_2; |
1017 | } |
1018 | |
1019 | if (isnan(Ro)) |
1020 | { |
1021 | } |
1022 | } |
1023 | |
1024 | |
1025 | |
1026 | // Calculate distance along track ("s") |
1027 | if(s!=NULL__null){ |
1028 | double dz = dz_dphi*phi; |
1029 | double Rodphi = Ro*phi; |
1030 | double ds = sqrt(dz*dz + Rodphi*Rodphi); |
1031 | *s = step->s + (phi>0.0 ? ds:-ds); |
1032 | } |
1033 | |
1034 | this->last_phi = phi; |
1035 | this->last_swim_step = step; |
1036 | this->last_dz_dphi = dz_dphi; |
1037 | |
1038 | return sqrt(dist2); |
1039 | } |
1040 | |
1041 | //--------------------------------- |
1042 | // FindClosestSwimStep |
1043 | //--------------------------------- |
1044 | DReferenceTrajectory::swim_step_t* DReferenceTrajectory::FindClosestSwimStep(const DCoordinateSystem *wire, int *istep_ptr) const |
1045 | { |
1046 | /// Find the closest swim step to the given wire. The value of |
1047 | /// "L" should be the active wire length. The coordinate system |
1048 | /// defined by "wire" should have its origin at the center of |
1049 | /// the wire with the wire running in the direction of udir. |
1050 | |
1051 | if(istep_ptr)*istep_ptr=-1; |
1052 | |
1053 | if(Nswim_steps<1){ |
1054 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1054<<" "<<"No swim steps! You must \"Swim\" the track before calling FindClosestSwimStep(...)"<<endl; |
1055 | } |
1056 | |
1057 | // Make sure we have a wire first! |
1058 | if(!wire)return NULL__null; |
1059 | |
1060 | // Loop over swim steps and find the one closest to the wire |
1061 | swim_step_t *swim_step = swim_steps; |
1062 | swim_step_t *step=NULL__null; |
1063 | //double min_delta2 = 1.0E6; |
1064 | double old_delta2=1.0e6; |
1065 | double L_over_2 = wire->L/2.0; // half-length of wire in cm |
1066 | int istep=-1; |
1067 | |
1068 | double dx, dy, dz; |
1069 | |
1070 | // w is a vector to the origin of the wire |
1071 | // u is a unit vector along the wire |
1072 | |
1073 | double wx, wy, wz; |
1074 | double ux, uy, uz; |
1075 | |
1076 | wx = wire->origin.X(); |
1077 | wy = wire->origin.Y(); |
1078 | wz = wire->origin.Z(); |
1079 | |
1080 | ux = wire->udir.X(); |
1081 | uy = wire->udir.Y(); |
1082 | uz = wire->udir.Z(); |
1083 | |
1084 | int i; |
1085 | for(i=0; i<Nswim_steps; i++, swim_step++){ |
1086 | // Find the point's position along the wire. If the point |
1087 | // is past the end of the wire, calculate the distance |
1088 | // from the end of the wire. |
1089 | // DVector3 pos_diff = swim_step->origin - wire->origin; |
1090 | |
1091 | dx = swim_step->origin.X() - wx; |
1092 | dy = swim_step->origin.Y() - wy; |
1093 | dz = swim_step->origin.Z() - wz; |
1094 | |
1095 | // double u = wire->udir.Dot(pos_diff); |
1096 | double u = ux * dx + uy * dy + uz * dz; |
1097 | |
1098 | // Find distance perpendicular to wire |
1099 | // double delta2 = pos_diff.Mag2() - u*u; |
1100 | double delta2 = dx*dx + dy*dy + dz*dz - u*u; |
1101 | |
1102 | // If point is past end of wire, calculate distance |
1103 | // from wire's end by adding on distance along wire direction. |
1104 | if( fabs(u)>L_over_2){ |
1105 | // delta2 += pow(fabs(u)-L_over_2, 2.0); |
1106 | double u_minus_L_over_2=fabs(u)-L_over_2; |
1107 | delta2 += ( u_minus_L_over_2*u_minus_L_over_2 ); |
1108 | // printf("step %d\n",i); |
1109 | } |
1110 | |
1111 | if(debug_level>3)_DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1111<<" "<<"delta2="<<delta2<<" old_delta2="<<old_delta2<<endl; |
1112 | if (delta2>old_delta2) break; |
1113 | |
1114 | //if(delta2 < min_delta2){ |
1115 | // min_delta2 = delta2; |
1116 | step = swim_step; |
1117 | istep=i; |
1118 | |
1119 | //} |
1120 | //printf("%d delta %f min %f\n",i,delta2,min_delta2); |
1121 | old_delta2=delta2; |
1122 | } |
1123 | |
1124 | if(istep_ptr)*istep_ptr=istep; |
1125 | |
1126 | if(debug_level>3)_DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1126<<" "<<"found closest step at i="<<i<<" istep_ptr="<<istep_ptr<<endl; |
1127 | |
1128 | return step; |
1129 | } |
1130 | |
1131 | //--------------------------------- |
1132 | // FindClosestSwimStep |
1133 | //--------------------------------- |
1134 | DReferenceTrajectory::swim_step_t* DReferenceTrajectory::FindClosestSwimStep(const DVector3 &origin, DVector3 norm, int *istep_ptr) const |
1135 | { |
1136 | /// Find the closest swim step to the plane specified by origin |
1137 | /// and norm. origin should indicate any point in the plane and |
1138 | /// norm a vector normal to the plane. |
1139 | if(istep_ptr)*istep_ptr=-1; |
1140 | |
1141 | if(Nswim_steps<1){ |
1142 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1142<<" "<<"No swim steps! You must \"Swim\" the track before calling FindClosestSwimStep(...)"<<endl; |
1143 | } |
1144 | |
1145 | // Make sure normal vector is unit lenght |
1146 | norm.SetMag(1.0); |
1147 | |
1148 | // Loop over swim steps and find the one closest to the plane |
1149 | swim_step_t *swim_step = swim_steps; |
1150 | swim_step_t *step=NULL__null; |
1151 | //double min_dist = 1.0E6; |
1152 | double old_dist=1.0e6; |
1153 | int istep=-1; |
1154 | |
1155 | for(int i=0; i<Nswim_steps; i++, swim_step++){ |
1156 | |
1157 | // Distance to plane is dot product of normal vector with any |
1158 | // vector pointing from the current step to a point in the plane |
1159 | double dist = fabs(norm.Dot(swim_step->origin-origin)); |
1160 | |
1161 | if (dist>old_dist) break; |
1162 | |
1163 | // Check if we're the closest step |
1164 | //if(dist < min_dist){ |
1165 | //min_dist = dist; |
1166 | |
1167 | step = swim_step; |
1168 | istep=i; |
1169 | //} |
1170 | old_dist=dist; |
1171 | |
1172 | // We should probably have a break condition here so we don't |
1173 | // waste time looking all the way to the end of the track after |
1174 | // we've passed the plane. |
1175 | } |
1176 | |
1177 | if(istep_ptr)*istep_ptr=istep; |
1178 | |
1179 | return step; |
1180 | } |
1181 | |
1182 | |
1183 | //--------------------------------- |
1184 | // FindPlaneCrossing |
1185 | //--------------------------------- |
1186 | DReferenceTrajectory::swim_step_t* DReferenceTrajectory::FindPlaneCrossing(const DVector3 &origin, DVector3 norm, int *istep_ptr) const |
1187 | { |
1188 | /// Find the closest swim step to the position where the track crosses |
1189 | /// the plane specified by origin |
1190 | /// and norm. origin should indicate any point in the plane and |
1191 | /// norm a vector normal to the plane. |
1192 | if(istep_ptr)*istep_ptr=-1; |
1193 | |
1194 | if(Nswim_steps<1){ |
1195 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1195<<" "<<"No swim steps! You must \"Swim\" the track before calling FindPlaneCrossing(...)"<<endl; |
1196 | *((int*)NULL__null) = 1; // force seg. fault |
1197 | } |
1198 | |
1199 | // Make sure normal vector is unit lenght |
1200 | norm.SetMag(1.0); |
1201 | |
1202 | // Loop over swim steps and find the one closest to the plane |
1203 | swim_step_t *swim_step = swim_steps; |
1204 | swim_step_t *step=NULL__null; |
1205 | //double min_dist = 1.0E6; |
1206 | int istep=-1; |
1207 | double old_dist=1.0e6; |
1208 | |
1209 | for(int i=0; i<Nswim_steps; i++, swim_step++){ |
1210 | |
1211 | // Distance to plane is dot product of normal vector with any |
1212 | // vector pointing from the current step to a point in the plane |
1213 | //double dist = fabs(norm.Dot(swim_step->origin-origin)); |
1214 | double dist = norm.Dot(swim_step->origin-origin); |
1215 | |
1216 | // We've crossed the plane when the sign of dist changes |
1217 | if (dist*old_dist<0 && i>0) { |
1218 | if (fabs(dist)<fabs(old_dist)){ |
1219 | step=swim_step; |
1220 | istep=i; |
1221 | } |
1222 | break; |
1223 | } |
1224 | step = swim_step; |
1225 | istep=i; |
1226 | old_dist=dist; |
1227 | } |
1228 | |
1229 | if(istep_ptr)*istep_ptr=istep; |
1230 | |
1231 | return step; |
1232 | } |
1233 | |
1234 | |
1235 | |
1236 | |
1237 | //--------------------------------- |
1238 | // DistToRT |
1239 | //--------------------------------- |
1240 | double DReferenceTrajectory::DistToRT(const DCoordinateSystem *wire, double *s) const |
1241 | { |
1242 | /// Find the closest distance to the given wire in cm. The value of |
1243 | /// "L" should be the active wire length (in cm). The coordinate system |
1244 | /// defined by "wire" should have its origin at the center of |
1245 | /// the wire with the wire running in the direction of udir. |
1246 | swim_step_t *step=FindClosestSwimStep(wire); |
1247 | |
1248 | return (step && step->s>0) ? DistToRT(wire, step, s):std::numeric_limits<double>::quiet_NaN(); |
1249 | } |
1250 | |
1251 | //--------------------------------- |
1252 | // DistToRTBruteForce |
1253 | //--------------------------------- |
1254 | double DReferenceTrajectory::DistToRTBruteForce(const DCoordinateSystem *wire, double *s) const |
1255 | { |
1256 | /// Find the closest distance to the given wire in cm. The value of |
1257 | /// "L" should be the active wire length (in cm). The coordinate system |
1258 | /// defined by "wire" should have its origin at the center of |
1259 | /// the wire with the wire running in the direction of udir. |
1260 | swim_step_t *step=FindClosestSwimStep(wire); |
1261 | |
1262 | return step ? DistToRTBruteForce(wire, step, s):std::numeric_limits<double>::quiet_NaN(); |
1263 | } |
1264 | |
1265 | //------------------ |
1266 | // DistToRT |
1267 | //------------------ |
1268 | double DReferenceTrajectory::DistToRT(const DCoordinateSystem *wire, const swim_step_t *step, double *s) const |
1269 | { |
1270 | /// Calculate the distance of the given wire(in the lab |
1271 | /// reference frame) to the Reference Trajectory which the |
1272 | /// given swim step belongs to. This uses the momentum directions |
1273 | /// and positions of the swim step |
1274 | /// to define a curve and calculate the distance of the hit |
1275 | /// from it. The swim step should be the closest one to the wire. |
1276 | /// IMPORTANT: This approximates the helix locally by a parabola. |
1277 | /// This means the swim step should be fairly close |
1278 | /// to the wire so that this approximation is valid. If the |
1279 | /// reference trajectory from which the swim step came is too |
1280 | /// sparse, the results will not be nearly as good. |
1281 | |
1282 | // Interestingly enough, this is one of the harder things to figure |
1283 | // out in the tracking code which is why the explanations may be |
1284 | // a bit long. |
1285 | |
1286 | // The general idea is to define the helix in a coordinate system |
1287 | // in which the wire runs along the z-axis. The distance to the |
1288 | // wire is then defined just in the X/Y plane of this coord. system. |
1289 | // The distance is expressed as a function of the phi angle in the |
1290 | // natural coordinate system of the helix. This way, phi=0 corresponds |
1291 | // to the swim step point itself and the DOCA point should be |
1292 | // at a small phi angle. |
1293 | // |
1294 | // The minimum distance between the helical segment and the wire |
1295 | // will be a function of sin(phi), cos(phi) and phi. Approximating |
1296 | // sin(phi) by phi and cos(phi) by (1-phi^2) leaves a 4th order |
1297 | // polynomial in phi. Taking the derivative leaves a 3rd order |
1298 | // polynomial whose root is the phi corresponding to the |
1299 | // Distance Of Closest Approach(DOCA) point on the helix. Plugging |
1300 | // that value of phi back into the distance formula gives |
1301 | // us the minimum distance between the track and the wire. |
1302 | |
1303 | // First, we need to define the coordinate system in which the |
1304 | // wire runs along the z-axis. This is actually done already |
1305 | // in the CDC package for each wire once, at program start. |
1306 | // The directions of the axes are defined in wire->sdir, |
1307 | // wire->tdir, and wire->udir. |
1308 | |
1309 | // Next, define a point on the helical segment defined by the |
1310 | // swim step it the RT coordinate system. The directions of |
1311 | // the RT coordinate system are defined by step->xdir, step->ydir, |
1312 | // and step->zdir. The coordinates of a point on the helix |
1313 | // in this coordinate system are: |
1314 | // |
1315 | // x = Ro*(cos(phi) - 1) |
1316 | // y = Ro*sin(phi) |
1317 | // z = phi*(dz/dphi) |
1318 | // |
1319 | // where phi is the phi angle of the point in this coordinate system. |
1320 | |
1321 | // Now, a vector describing the helical point in the LAB coordinate |
1322 | // system is: |
1323 | // |
1324 | // h = x*xdir + y*ydir + z*zdir + pos |
1325 | // |
1326 | // where h,xdir,ydir,zdir and pos are all 3-vectors. |
1327 | // xdir,ydir,zdir are unit vectors defining the directions |
1328 | // of the RT coord. system axes in the lab coord. system. |
1329 | // pos is a vector defining the position of the swim step |
1330 | // in the lab coord.system |
1331 | |
1332 | // Now we just need to find the extent of "h" in the wire's |
1333 | // coordinate system (period . means dot product): |
1334 | // |
1335 | // s = (h-wpos).sdir |
1336 | // t = (h-wpos).tdir |
1337 | // u = (h-wpos).udir |
1338 | // |
1339 | // where wpos is the position of the center of the wire in |
1340 | // the lab coord. system and is given by wire->wpos. |
1341 | |
1342 | // At this point, the values of s,t, and u repesent a point |
1343 | // on the helix in the coord. system of the wire with the |
1344 | // wire in the "u" direction and positioned at the origin. |
1345 | // The distance(squared) from the wire to the point on the helix |
1346 | // is given by: |
1347 | // |
1348 | // d^2 = s^2 + t^2 |
1349 | // |
1350 | // where s and t are both functions of phi. |
1351 | |
1352 | // So, we'll define the values of "s" and "t" above as: |
1353 | // |
1354 | // s = A*x + B*y + C*z + D |
1355 | // t = E*x + F*y + G*z + H |
1356 | // |
1357 | // where A,B,C,D,E,F,G, and H are constants defined below |
1358 | // and x,y,z are all functions of phi defined above. |
1359 | // (period . means dot product) |
1360 | // |
1361 | // A = sdir.xdir |
1362 | // B = sdir.ydir |
1363 | // C = sdir.zdir |
1364 | // D = sdir.(pos-wpos) |
1365 | // |
1366 | // E = tdir.xdir |
1367 | // F = tdir.ydir |
1368 | // G = tdir.zdir |
1369 | // H = tdir.(pos-wpos) |
1370 | const DVector3 &xdir = step->sdir; |
1371 | const DVector3 &ydir = step->tdir; |
1372 | const DVector3 &zdir = step->udir; |
1373 | const DVector3 &sdir = wire->sdir; |
1374 | const DVector3 &tdir = wire->tdir; |
1375 | const DVector3 &udir = wire->udir; |
1376 | DVector3 pos_diff = step->origin - wire->origin; |
1377 | |
1378 | double A = sdir.Dot(xdir); |
1379 | double B = sdir.Dot(ydir); |
1380 | double C = sdir.Dot(zdir); |
1381 | double D = sdir.Dot(pos_diff); |
1382 | |
1383 | double E = tdir.Dot(xdir); |
1384 | double F = tdir.Dot(ydir); |
1385 | double G = tdir.Dot(zdir); |
1386 | double H = tdir.Dot(pos_diff); |
1387 | |
1388 | // OK, here is the dirty part. Using the approximations given above |
1389 | // to write the x and y functions in terms of phi^2 and phi (instead |
1390 | // of cos and sin) we put them into the equations for s and t above. |
1391 | // Then, inserting those into the equation for d^2 above that, we |
1392 | // get a very long equation in terms of the constants A,...H and |
1393 | // phi up to 4th order. Combining coefficients for similar powers |
1394 | // of phi yields an equation of the form: |
1395 | // |
1396 | // d^2 = Q*phi^4 + R*phi^3 + S*phi^2 + T*phi + U |
1397 | // |
1398 | // The dirty part is that it takes the better part of a sheet of |
1399 | // paper to work out the relations for Q,...U in terms of |
1400 | // A,...H, and Ro, dz/dphi. You can work it out yourself on |
1401 | // paper to verify that the equations below are correct. |
1402 | double Ro = step->Ro; |
1403 | double Ro2 = Ro*Ro; |
1404 | double delta_z = step->mom.Dot(step->udir); |
1405 | double delta_phi = step->mom.Dot(step->tdir)/Ro; |
1406 | double dz_dphi = delta_z/delta_phi; |
1407 | double dz_dphi2=dz_dphi*dz_dphi; |
1408 | double Ro_dz_dphi=Ro*dz_dphi; |
1409 | |
1410 | // double Q = pow(A*Ro/2.0, 2.0) + pow(E*Ro/2.0, 2.0); |
1411 | double Q=0.25*Ro2*(A*A+E*E); |
1412 | // double R = -(2.0*A*B*Ro2 + 2.0*A*C*Ro_dz_dphi + 2.0*E*F*Ro2 + 2.0*E*G*Ro_dz_dphi)/2.0; |
1413 | double R = -((A*B+E*F)*Ro2 + (A*C+E*G)*Ro_dz_dphi); |
1414 | // double S = pow(B*Ro, 2.0) + pow(C*dz_dphi,2.0) + 2.0*B*C*Ro_dz_dphi - 2.0*A*D*Ro/2.0 |
1415 | //+ pow(F*Ro, 2.0) + pow(G*dz_dphi,2.0) + 2.0*F*G*Ro_dz_dphi - 2.0*E*H*Ro/2.0; |
1416 | double S= (B*B+F*F)*Ro2+(C*C+G*G)*dz_dphi2+2.0*(B*C+F*G)*Ro_dz_dphi |
1417 | -(A*D+E*H)*Ro; |
1418 | // double T = 2.0*B*D*Ro + 2.0*C*D*dz_dphi + 2.0*F*H*Ro + 2.0*G*H*dz_dphi; |
1419 | double T = 2.0*((B*D+F*H)*Ro + (C*D+G*H)*dz_dphi); |
1420 | double U = D*D + H*H; |
1421 | |
1422 | // Aaarghh! my fingers hurt just from typing all of that! |
1423 | // |
1424 | // OK, now we differentiate the above equation for d^2 to get: |
1425 | // |
1426 | // d(d^2)/dphi = 4*Q*phi^3 + 3*R*phi^2 + 2*S*phi + T |
1427 | // |
1428 | // NOTE: don't confuse "R" with "Ro" in the above equations! |
1429 | // |
1430 | // Now we have to solve the 3rd order polynomial for the phi value of |
1431 | // the point of closest approach on the RT. This is a well documented |
1432 | // procedure. Essentially, when you have an equation of the form: |
1433 | // |
1434 | // x^3 + a2*x^2 + a1*x + a0 = 0; |
1435 | // |
1436 | // a change of variables is made such that w = x + a2/3 which leads |
1437 | // to a third order poly with no w^2 term: |
1438 | // |
1439 | // w^3 + 3.0*b*w + 2*c = 0 |
1440 | // |
1441 | // where: |
1442 | // b = a1/3 - (a2^2)/9 |
1443 | // c = a0/2 - a1*a2/6 + (a2^3)/27 |
1444 | // |
1445 | // The one real root of this is: |
1446 | // |
1447 | // w0 = q - p |
1448 | // |
1449 | // where: |
1450 | // q^3 = d - c |
1451 | // p^3 = d + c |
1452 | // d^2 = b^3 + c^2 (don't confuse with d^2 above!) |
1453 | // |
1454 | // For us this means that: |
1455 | // a2 = 3*R/(4*Q) |
1456 | // a1 = 2*S/(4*Q) |
1457 | // a0 = T/(4*Q) |
1458 | // |
1459 | // A potential problem could occur if Q is at or very close to zero. |
1460 | // This situation occurs when both A and E are zero. This would mean |
1461 | // that both sdir and tdir are perpendicular to xdir which means |
1462 | // xdir is in the same direction as udir (got that?). Physically, |
1463 | // this corresponds to the situation when both the momentum and |
1464 | // the magnetic field are perpendicular to the wire (though not |
1465 | // necessarily perpendicular to each other). This situation can't |
1466 | // really occur in the CDC detector where the chambers are well |
1467 | // contained in a region where the field is essentially along z as |
1468 | // are the wires. |
1469 | // |
1470 | // Just to be safe, we check that Q is greater than |
1471 | // some minimum before solving for phi. If it is too small, we fall |
1472 | // back to solving the quadratic equation for phi. |
1473 | double phi =0.0; |
1474 | if(fabs(Q)>1.0E-6){ |
1475 | /* |
1476 | double fourQ = 4.0*Q; |
1477 | double a2 = 3.0*R/fourQ; |
1478 | double a1 = 2.0*S/fourQ; |
1479 | double a0 = T/fourQ; |
1480 | */ |
1481 | double one_over_fourQ=0.25/Q; |
1482 | double a2=3.0*R*one_over_fourQ; |
1483 | double a1=2.0*S*one_over_fourQ; |
1484 | double a0=T*one_over_fourQ; |
1485 | double a2sq=a2*a2; |
1486 | /* |
1487 | double b = a1/3.0 - a2*a2/9.0; |
1488 | double c = a0/2.0 - a1*a2/6.0 + a2*a2*a2/27.0; |
1489 | */ |
1490 | double b=ONE_THIRD0.33333333333333333*(a1-ONE_THIRD0.33333333333333333*a2sq); |
1491 | double c=0.5*(a0-ONE_THIRD0.33333333333333333*a1*a2)+a2*a2sq/27.0; |
1492 | double my_d2=b*b*b+c*c; |
1493 | if (my_d2>0){ |
1494 | //double d = sqrt(pow(b, 3.0) + pow(c, 2.0)); // occasionally, this is zero. See below |
1495 | double d=sqrt(my_d2); |
1496 | //double q = pow(d - c, ONE_THIRD); |
1497 | //double p = pow(d + c, ONE_THIRD); |
1498 | double q=cbrt(d-c); |
1499 | double p=cbrt(d+c); |
1500 | |
1501 | double w0 = q - p; |
1502 | //phi = w0 - a2/3.0; |
1503 | phi = w0 - ONE_THIRD0.33333333333333333*a2; |
1504 | } |
1505 | else{ |
1506 | // Use DeMoivre's theorem to find the cube root of a complex |
1507 | // number. In this case there are three real solutions. |
1508 | double d=sqrt(-my_d2); |
1509 | c*=-1.; |
1510 | double temp=sqrt(cbrt(c*c+d*d)); |
1511 | double theta1=ONE_THIRD0.33333333333333333*atan2(d,c); |
1512 | double sum_over_2=temp*cos(theta1); |
1513 | double diff_over_2=-temp*sin(theta1); |
1514 | |
1515 | double phi0=-a2/3+2.*sum_over_2; |
1516 | double phi1=-a2/3-sum_over_2+sqrt(3)*diff_over_2; |
1517 | double phi2=-a2/3-sum_over_2-sqrt(3)*diff_over_2; |
1518 | |
1519 | double d2_0 = U + phi0*(T + phi0*(S + phi0*(R + phi0*Q))); |
1520 | double d2_1 = U + phi1*(T + phi1*(S + phi1*(R + phi1*Q))); |
1521 | double d2_2 = U + phi2*(T + phi2*(S + phi2*(R + phi2*Q))); |
1522 | |
1523 | if (d2_0<d2_1 && d2_0<d2_2){ |
1524 | phi=phi0; |
1525 | } |
1526 | else if (d2_1<d2_0 && d2_1<d2_2){ |
1527 | phi=phi1; |
1528 | } |
1529 | else{ |
1530 | phi=phi2; |
1531 | } |
1532 | } |
1533 | } |
1534 | |
1535 | if(fabs(Q)<=1.0E-6 || !finite(phi)){ |
1536 | double a = 3.0*R; |
1537 | double b = 2.0*S; |
1538 | double c = 1.0*T; |
1539 | phi = (-b + sqrt(b*b - 4.0*a*c))/(2.0*a); |
1540 | } |
1541 | |
1542 | // The accuracy of this method is limited by how close the step is to the |
1543 | // actual minimum. If the value of phi is large then the step size is |
1544 | // not too close and we should add another couple of steps in the right |
1545 | // place in order to get a more accurate value. Note that while this will |
1546 | // increase the time it takes this round, presumably the fitter will be |
1547 | // calling this often for each wire and having a high density of points |
1548 | // near the wires will just make subsequent calls go quicker. This also |
1549 | // allows larger initial step sizes with the high density regions getting |
1550 | // filled in as needed leading to overall faster tracking. |
1551 | #if 0 |
1552 | if(finite(phi) && fabs(phi)>2.0E-4){ |
1553 | if(dist_to_rt_depth>=3){ |
1554 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1554<<" "<<"3 or more recursive calls to DistToRT(). Something is wrong! bailing ..."<<endl; |
1555 | //for(int k=0; k<Nswim_steps; k++){ |
1556 | // DVector3 &v = swim_steps[k].origin; |
1557 | // _DBG_<<" "<<k<<": "<<v.X()<<", "<<v.Y()<<", "<<v.Z()<<endl; |
1558 | //} |
1559 | //exit(-1); |
1560 | return std::numeric_limits<double>::quiet_NaN(); |
1561 | } |
1562 | double scale_step = 1.0; |
1563 | double s_range = 1.0*scale_step; |
1564 | double step_size = 0.02*scale_step; |
1565 | int err = InsertSteps(step, phi>0.0 ? +s_range:-s_range, step_size); // Add new steps near this step by swimming in the direction of phi |
1566 | if(!err){ |
1567 | step=FindClosestSwimStep(wire); // Find the new closest step |
1568 | if(!step)return std::numeric_limits<double>::quiet_NaN(); |
1569 | dist_to_rt_depth++; |
1570 | double doca = DistToRT(wire, step, s); // re-call ourself with the new step |
1571 | dist_to_rt_depth--; |
1572 | return doca; |
1573 | }else{ |
1574 | if(err<0)return std::numeric_limits<double>::quiet_NaN(); |
1575 | |
1576 | // If InsertSteps() returns an error > 0 then it indicates that it |
1577 | // was unable to add additional steps (perhaps because there |
1578 | // aren't enough spaces available). In that case, we just go ahead |
1579 | // and use the phi we have and make the best estimate possible. |
1580 | } |
1581 | } |
1582 | #endif |
1583 | |
1584 | // It is possible at this point that the value of phi corresponds to |
1585 | // a point past the end of the wire. We should check for this here and |
1586 | // recalculate, if necessary, the DOCA at the end of the wire. First, |
1587 | // calculate h (the vector defined way up above) and dot it into the |
1588 | // wire's u-direction to get the position of the DOCA point along the |
1589 | // wire. |
1590 | double x = -0.5*Ro*phi*phi; |
1591 | double y = Ro*phi; |
1592 | double z = dz_dphi*phi; |
1593 | DVector3 h = pos_diff + x*xdir + y*ydir + z*zdir; |
1594 | double u = h.Dot(udir); |
1595 | if(fabs(u) > wire->L/2.0){ |
1596 | // Looks like our DOCA point is past the end of the wire. |
1597 | // Find phi corresponding to the end of the wire. |
1598 | double L_over_2 = u>0.0 ? wire->L/2.0:-wire->L/2.0; |
1599 | double a = -0.5*Ro*udir.Dot(xdir); |
1600 | double b = Ro*udir.Dot(ydir) + dz_dphi*udir.Dot(zdir); |
1601 | double c = udir.Dot(pos_diff) - L_over_2; |
1602 | double twoa=2.0*a; |
1603 | double sqroot=sqrt(b*b-4.0*a*c); |
1604 | double phi1 = (-b + sqroot)/(twoa); |
1605 | double phi2 = (-b - sqroot)/(twoa); |
1606 | phi = fabs(phi1)<fabs(phi2) ? phi1:phi2; |
1607 | u=L_over_2; |
1608 | } |
1609 | this->last_dist_along_wire = u; |
1610 | |
1611 | // Use phi to calculate DOCA |
1612 | double d2 = U + phi*(T + phi*(S + phi*(R + phi*Q))); |
1613 | double d = sqrt(d2); |
1614 | |
1615 | // Calculate distance along track ("s") |
1616 | double dz = dz_dphi*phi; |
1617 | double Rodphi = Ro*phi; |
1618 | double ds = sqrt(dz*dz + Rodphi*Rodphi); |
1619 | if(s)*s=step->s + (phi>0.0 ? ds:-ds); |
1620 | if(debug_level>3){ |
1621 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1621<<" "<<"distance to rt: "<<*s<<" from step at "<<step->s<<" with ds="<<ds<<" d="<<d<<" dz="<<dz<<" Rodphi="<<Rodphi<<endl; |
1622 | _DBG_std::cerr<<"DReferenceTrajectory.cc"<<":"<< 1622<<" "<<"phi="<<phi<<" U="<<U<<" u="<<u<<endl; |
1623 | } |
1624 | |
1625 | // Remember phi and step so additional info on the point can be obtained |
1626 | this->last_phi = phi; |
1627 | this->last_swim_step = step; |
1628 | this->last_dz_dphi = dz_dphi; |
1629 | |
1630 | return d; // WARNING: This could return nan! |
1631 | } |
1632 | |
1633 | //------------------ |
1634 | // DistToRTBruteForce |
1635 | //------------------ |
1636 | double DReferenceTrajectory::DistToRTBruteForce(const DCoordinateSystem *wire, const swim_step_t *step, double *s) const |
1637 | { |
1638 | /// Calculate the distance of the given wire(in the lab |
1639 | /// reference frame) to the Reference Trajectory which the |
1640 | /// given swim step belongs to. This uses the momentum directions |
1641 | /// and positions of the swim step |
1642 | /// to define a curve and calculate the distance of the hit |
1643 | /// from it. The swim step should be the closest one to the wire. |
1644 | /// IMPORTANT: This calculates the distance using a "brute force" |
1645 | /// method of taking tiny swim steps to find the minimum distance. |
1646 | /// It is vey SLOW and you should be using DistToRT(...) instead. |
1647 | /// This is only here to provide an independent check of DistToRT(...). |
1648 | |
1649 | const DVector3 &xdir = step->sdir; |
1650 | const DVector3 &ydir = step->tdir; |
1651 | const DVector3 &zdir = step->udir; |
1652 | const DVector3 &sdir = wire->sdir; |
1653 | const DVector3 &tdir = wire->tdir; |
1654 | DVector3 pos_diff = step->origin - wire->origin; |
1655 | |
1656 | double Ro = step->Ro; |
1657 | double delta_z = step->mom.Dot(step->udir); |
1658 | double delta_phi = step->mom.Dot(step->tdir)/Ro; |
1659 | double dz_dphi = delta_z/delta_phi; |
1660 | |
1661 | // Brute force |
1662 | double min_d2 = 1.0E6; |
1663 | double phi=M_PI3.14159265358979323846; |
1664 | for(int i=-2000; i<2000; i++){ |
1665 | double myphi=(double)i*0.000005; |
1666 | DVector3 d = Ro*(cos(myphi)-1.0)*xdir |
1667 | + Ro*sin(myphi)*ydir |
1668 | + dz_dphi*myphi*zdir |
1669 | + pos_diff; |
1670 | |
1671 | double d2 = pow(d.Dot(sdir),2.0) + pow(d.Dot(tdir),2.0); |
1672 | if(d2<min_d2){ |
1673 | min_d2 = d2; |
1674 | phi = myphi; |
1675 | this->last_phi = myphi; |
1676 | } |
1677 | } |
1678 | double d2 = min_d2; |
1679 | double d = sqrt(d2); |
1680 | this->last_phi = phi; |
1681 | this->last_swim_step = step; |
1682 | this->last_dz_dphi = dz_dphi; |
1683 | |
1684 | // Calculate distance along track ("s") |
1685 | double dz = dz_dphi*phi; |
1686 | double Rodphi = Ro*phi; |
1687 | double ds = sqrt(dz*dz + Rodphi*Rodphi); |
1688 | if(s)*s=step->s + (phi>0.0 ? ds:-ds); |
1689 | |
1690 | return d; |
1691 | } |
1692 | |
1693 | //------------------ |
1694 | // Straw_dx |
1695 | //------------------ |
1696 | double DReferenceTrajectory::Straw_dx(const DCoordinateSystem *wire, double radius) |
1697 | { |
1698 | /// Find the distance traveled within the specified radius of the |
1699 | /// specified wire. This will give the "dx" component of a dE/dx |
1700 | /// measurement for cylindrical geometry as we have with straw tubes. |
1701 | /// |
1702 | /// At this point, the estimate is done using a simple linear |
1703 | /// extrapolation from the DOCA point in the direction of the momentum |
1704 | /// to the 2 points at which it itersects the given radius. Segments |
1705 | /// which extend past the end of the wire will be clipped to the end |
1706 | /// of the wire before calculating the total dx. |
1707 | |
1708 | // First, find the DOCA point for this wire |
1709 | double s; |
1710 | double doca = DistToRT(wire, &s); |
1711 | if(!finite(doca)) |
1712 | return 0.0; |
1713 | |
1714 | // If doca is outside of the given radius, then we're done |
1715 | if(doca>=radius)return 0.0; |
1716 | |
1717 | // Get the location and momentum direction of the DOCA point |
1718 | DVector3 pos, momdir; |
1719 | GetLastDOCAPoint(pos, momdir); |
1720 | if(momdir.Mag()!=0.0)momdir.SetMag(1.0); |
1721 | |
1722 | // Get wire direction |
1723 | const DVector3 &udir = wire->udir; |
1724 | |
1725 | // Calculate vectors used to form quadratic equation for "alpha" |
1726 | // the distance along the mometum direction from the DOCA point |
1727 | // to the intersection with a cylinder of the given radius. |
1728 | DVector3 A = udir.Cross(pos-wire->origin); |
1729 | DVector3 B = udir.Cross(momdir); |
1730 | |
1731 | // If the magnitude of B is zero at this point, it means the momentum |
1732 | // direction is parallel to the wire. In this case, this method will |
1733 | // not work. Return NaN. |
1734 | if(B.Mag()<1.0E-10)return std::numeric_limits<double>::quiet_NaN(); |
1735 | |
1736 | double a = B.Mag(); |
1737 | double b = A.Dot(B); |
1738 | double c = A.Mag() - radius; |
1739 | double d = sqrt(b*b - 4.0*a*c); |
1740 | |
1741 | // The 2 roots should correspond to the 2 intersection points. |
1742 | double alpha1 = (-b + d)/(2.0*a); |
1743 | double alpha2 = (-b - d)/(2.0*a); |
1744 | |
1745 | DVector3 int1 = pos + alpha1*momdir; |
1746 | DVector3 int2 = pos + alpha2*momdir; |
1747 | |
1748 | // Check if point1 is past the end of the wire |
1749 | double q = udir.Dot(int1 - wire->origin); |
1750 | if(fabs(q) > wire->L/2.0){ |
1751 | double gamma = udir.Dot(wire->origin - pos) + (q>0.0 ? +1.0:-1.0)*wire->L/2.0; |
1752 | gamma /= momdir.Dot(udir); |
1753 | int1 = pos + gamma*momdir; |
1754 | } |
1755 | |
1756 | // Check if point2 is past the end of the wire |
1757 | q = udir.Dot(int2 - wire->origin); |
1758 | if(fabs(q) > wire->L/2.0){ |
1759 | double gamma = udir.Dot(wire->origin - pos) + (q>0.0 ? +1.0:-1.0)*wire->L/2.0; |
1760 | gamma /= momdir.Dot(udir); |
1761 | int2 = pos + gamma*momdir; |
1762 | } |
1763 | |
1764 | // Calculate distance |
1765 | DVector3 delta = int1 - int2; |
1766 | |
1767 | return delta.Mag(); |
1768 | } |
1769 | |
1770 | //------------------ |
1771 | // GetLastDOCAPoint |
1772 | //------------------ |
1773 | void DReferenceTrajectory::GetLastDOCAPoint(DVector3 &pos, DVector3 &mom) const |
1774 | { |
1775 | /// Use values saved by the last call to one of the DistToRT functions |
1776 | /// to calculate the 3-D DOCA position in lab coordinates and momentum |
1777 | /// in GeV/c. |
1778 | |
1779 | if(last_swim_step==NULL__null){ |
1780 | if(Nswim_steps>0){ |
1781 | last_swim_step = &swim_steps[0]; |
1782 | last_phi = 0.0; |
1783 | }else{ |
1784 | pos.SetXYZ(NaNstd::numeric_limits<double>::quiet_NaN(),NaNstd::numeric_limits<double>::quiet_NaN(),NaNstd::numeric_limits<double>::quiet_NaN()); |
1785 | mom.SetXYZ(NaNstd::numeric_limits<double>::quiet_NaN(),NaNstd::numeric_limits<double>::quiet_NaN(),NaNstd::numeric_limits<double>::quiet_NaN()); |
1786 | return; |
1787 | } |
1788 | } |
1789 | |
1790 | // If last_phi is not finite, set it to 0 as a last resort |
1791 | if(!finite(last_phi))last_phi = 0.0; |
1792 | |
1793 | const DVector3 &xdir = last_swim_step->sdir; |
1794 | const DVector3 &ydir = last_swim_step->tdir; |
1795 | const DVector3 &zdir = last_swim_step->udir; |
1796 | |
1797 | double x = -(last_swim_step->Ro/2.0)*last_phi*last_phi; |
1798 | double y = last_swim_step->Ro*last_phi; |
1799 | double z = last_dz_dphi*last_phi; |
1800 | |
1801 | pos = last_swim_step->origin + x*xdir + y*ydir + z*zdir; |
1802 | mom = last_swim_step->mom; |
1803 | |
1804 | mom.Rotate(-last_phi, zdir); |
1805 | } |
1806 | |
1807 | //------------------ |
1808 | // GetLastDOCAPoint |
1809 | //------------------ |
1810 | DVector3 DReferenceTrajectory::GetLastDOCAPoint(void) const |
1811 | { |
1812 | /// Use values saved by the last call to one of the DistToRT functions |
1813 | /// to calculate the 3-D DOCA position in lab coordinates. This is |
1814 | /// mainly intended for debugging. |
1815 | if(last_swim_step==NULL__null){ |
1816 | if(Nswim_steps>0){ |
1817 | last_swim_step = &swim_steps[0]; |
1818 | last_phi = 0.0; |
1819 | }else{ |
1820 | return DVector3(NaNstd::numeric_limits<double>::quiet_NaN(),NaNstd::numeric_limits<double>::quiet_NaN(),NaNstd::numeric_limits<double>::quiet_NaN()); |
1821 | } |
1822 | } |
1823 | const DVector3 &xdir = last_swim_step->sdir; |
1824 | const DVector3 &ydir = last_swim_step->tdir; |
1825 | const DVector3 &zdir = last_swim_step->udir; |
1826 | double Ro = last_swim_step->Ro; |
1827 | double delta_z = last_swim_step->mom.Dot(zdir); |
1828 | double delta_phi = last_swim_step->mom.Dot(ydir)/Ro; |
1829 | double dz_dphi = delta_z/delta_phi; |
1830 | |
1831 | double x = -(Ro/2.0)*last_phi*last_phi; |
1832 | double y = Ro*last_phi; |
1833 | double z = dz_dphi*last_phi; |
1834 | |
1835 | return last_swim_step->origin + x*xdir + y*ydir + z*zdir; |
1836 | } |
1837 | |
1838 | //------------------ |
1839 | // dPdx |
1840 | //------------------ |
1841 | double DReferenceTrajectory::dPdx_from_A_Z_rho(double ptot, double A, double Z, double density) const |
1842 | { |
1843 | double I = (Z*12.0 + 7.0)*1.0E-9; // From Leo 2nd ed. pg 25. |
1844 | if (Z>=13) I=(9.76*Z+58.8*pow(Z,-0.19))*1.0e-9; |
1845 | double rhoZ_overA=density*Z/A; |
1846 | double KrhoZ_overA = 0.1535e-3*rhoZ_overA; |
1847 | |
1848 | return dPdx(ptot, KrhoZ_overA,rhoZ_overA,log(I)); |
1849 | } |
1850 | |
1851 | //------------------ |
1852 | // dPdx |
1853 | //------------------ |
1854 | double DReferenceTrajectory::dPdx(double ptot, double KrhoZ_overA, |
1855 | double rhoZ_overA,double LogI) const |
1856 | { |
1857 | /// Calculate the momentum loss per unit distance traversed of the material with |
1858 | /// the given A, Z, and density. Value returned is in GeV/c per cm |
1859 | /// This follows the July 2008 PDG section 27.2 ppg 268-270. |
1860 | if(mass==0.0)return 0.0; // no ionization losses for neutrals |
1861 | |
1862 | double gammabeta = ptot/mass; |
1863 | double gammabeta2=gammabeta*gammabeta; |
1864 | double gamma = sqrt(gammabeta2+1); |
1865 | double beta = gammabeta/gamma; |
1866 | double beta2=beta*beta; |
1867 | double me = 0.511E-3; |
1868 | double m_ratio=me/mass; |
1869 | double two_me_gammabeta2=2.*me*gammabeta2; |
1870 | |
1871 | double Tmax = two_me_gammabeta2/(1.0+2.0*gamma*m_ratio+m_ratio*m_ratio); |
1872 | //double K = 0.307075E-3; // GeV gm^-1 cm^2 |
1873 | // Density effect |
1874 | double delta=0.; |
1875 | double X=log10(gammabeta); |
1876 | double X0,X1; |
1877 | double Cbar=2.*(LogI-log(28.816e-9*sqrt(rhoZ_overA)))+1.; |
1878 | if (rhoZ_overA>0.01){ // not a gas |
1879 | if (LogI<-1.6118){ // I<100 |
1880 | if (Cbar<=3.681) X0=0.2; |
1881 | else X0=0.326*Cbar-1.; |
1882 | X1=2.; |
1883 | } |
1884 | else{ |
1885 | if (Cbar<=5.215) X0=0.2; |
1886 | else X0=0.326*Cbar-1.5; |
1887 | X1=3.; |
1888 | } |
1889 | } |
1890 | else { // gases |
1891 | X1=4.; |
1892 | if (Cbar<=9.5) X0=1.6; |
1893 | else if (Cbar>9.5 && Cbar<=10.) X0=1.7; |
1894 | else if (Cbar>10 && Cbar<=10.5) X0=1.8; |
1895 | else if (Cbar>10.5 && Cbar<=11.) X0=1.9; |
1896 | else if (Cbar>11.0 && Cbar<=12.25) X0=2.; |
1897 | else if (Cbar>12.25 && Cbar<=13.804){ |
1898 | X0=2.; |
1899 | X1=5.; |
1900 | } |
1901 | else { |
1902 | X0=0.326*Cbar-2.5; |
1903 | X1=5.; |
1904 | } |
1905 | } |
1906 | if (X>=X0 && X<X1) |
1907 | delta=4.606*X-Cbar+(Cbar-4.606*X0)*pow((X1-X)/(X1-X0),3.); |
1908 | else if (X>=X1) |
1909 | delta= 4.606*X-Cbar; |
1910 | |
1911 | double dEdx = KrhoZ_overA/beta2*(log(two_me_gammabeta2*Tmax) |
1912 | -2.*LogI - 2.0*beta2 -delta); |
1913 | |
1914 | double dP_dx = dEdx/beta; |
1915 | |
1916 | double g = 0.350/sqrt(-log(0.06)); |
1917 | dP_dx *= 1.0 + exp(-pow(ptot/g,2.0)); // empirical for really low momentum particles |
1918 | |
1919 | if(ploss_direction==kBackward)dP_dx = -dP_dx; |
1920 | |
1921 | return dP_dx; |
1922 | } |
1923 | |
1924 | //------------------ |
1925 | // Dump |
1926 | //------------------ |
1927 | void DReferenceTrajectory::Dump(double zmin, double zmax) |
1928 | { |
1929 | swim_step_t *step = swim_steps; |
1930 | for(int i=0; i<Nswim_steps; i++, step++){ |
1931 | vector<pair<string,string> > item; |
1932 | double x = step->origin.X(); |
1933 | double y = step->origin.Y(); |
1934 | double z = step->origin.Z(); |
1935 | if(z<zmin || z>zmax)continue; |
1936 | |
1937 | double px = step->mom.X(); |
1938 | double py = step->mom.Y(); |
1939 | double pz = step->mom.Z(); |
1940 | |
1941 | cout<<i<<": "; |
1942 | cout<<"(x,y,z)=("<<x<<","<<y<<","<<z<<") "; |
1943 | cout<<"(px,py,pz)=("<<px<<","<<py<<","<<pz<<") "; |
1944 | cout<<"(Ro,s,t)=("<<step->Ro<<","<<step->s<<","<<step->t<<") "; |
1945 | cout<<endl; |
1946 | } |
1947 | |
1948 | } |
1949 | |
1950 | // Propagate the covariance matrix for {px,py,pz,x,y,z,t} along the step ds |
1951 | jerror_t DReferenceTrajectory::PropagateCovariance(double ds,double q, |
1952 | double mass, |
1953 | const DVector3 &mom, |
1954 | const DVector3 &pos, |
1955 | DMatrixDSym &C) const{ |
1956 | DMatrix J(7,7); |
1957 | |
1958 | double one_over_p_sq=1./mom.Mag2(); |
1959 | double one_over_p=sqrt(one_over_p_sq); |
1960 | double px=mom.X(); |
1961 | double py=mom.Y(); |
1962 | double pz=mom.Z(); |
1963 | double Bx,By,Bz; |
1964 | this->bfield->GetField(pos.x(),pos.y(),pos.z(),Bx,By,Bz); |
1965 | |
1966 | double ds_over_p=ds*one_over_p; |
1967 | double factor=0.003*q*ds_over_p; |
1968 | double temp=(Bz*py-Bx*pz)*one_over_p_sq; |
1969 | J(0,0)=1-factor*px*temp; |
1970 | J(0,1)=factor*(Bz-py*temp); |
1971 | J(0,2)=-factor*(By+pz*temp); |
1972 | |
1973 | temp=(Bx*pz-Bz*px)*one_over_p_sq; |
1974 | J(1,0)=-factor*(Bz+px*temp); |
1975 | J(1,1)=1-factor*py*temp; |
1976 | J(1,2)=factor*(Bx-pz*temp); |
1977 | |
1978 | temp=(By*px-Bx*py)*one_over_p_sq; |
1979 | J(2,0)=factor*(By-px*temp); |
1980 | J(2,1)=-factor*(Bx+py*temp); |
1981 | J(2,2)=1-factor*pz*temp; |
1982 | |
1983 | J(3,3)=1.; |
1984 | double ds_over_p3=one_over_p_sq*ds_over_p; |
1985 | J(3,0)=ds_over_p*(1-px*px*one_over_p_sq); |
1986 | J(3,1)=-px*py*ds_over_p3; |
1987 | J(3,2)=-px*pz*ds_over_p3; |
1988 | |
1989 | J(4,4)=1.; |
1990 | J(4,0)=J(3,1); |
1991 | J(4,1)=ds_over_p*(1-py*py*one_over_p_sq); |
1992 | J(4,2)=-py*pz*ds_over_p3; |
1993 | |
1994 | J(5,5)=1.; |
1995 | J(5,0)=J(3,2); |
1996 | J(5,1)=J(4,2); |
1997 | J(5,2)=ds_over_p*(1-pz*pz*one_over_p_sq); |
1998 | |
1999 | J(6,6)=1.; |
2000 | double m_sq=mass*mass; |
2001 | double fac2=(-ds/SPEED_OF_LIGHT29.9792)*m_sq*one_over_p_sq*one_over_p_sq |
2002 | /sqrt(1.+m_sq*one_over_p_sq); |
2003 | J(6,0)=fac2*px; |
2004 | J(6,1)=fac2*py; |
2005 | J(6,2)=fac2*pz; |
2006 | |
2007 | C=C.Similarity(J); |
2008 | |
2009 | return NOERROR; |
2010 | } |
2011 | |
2012 | |
2013 | // Find the mid-point of the line connecting the points of closest approach of the |
2014 | // trajectories of two tracks. Return the positions, momenta, and error matrices |
2015 | // at these points for the two tracks. |
2016 | jerror_t |
2017 | DReferenceTrajectory::IntersectTracks( const DReferenceTrajectory *rt2, |
2018 | DKinematicData *track1_kd, |
2019 | DKinematicData *track2_kd, |
2020 | DVector3 &pos, double &doca, double &var_doca) const{ |
2021 | const swim_step_t *swim_step1=this->swim_steps; |
2022 | const swim_step_t *swim_step2=rt2->swim_steps; |
2023 | |
2024 | DMatrixDSym cov1=track1_kd->errorMatrix(); |
2025 | DMatrixDSym cov2=track2_kd->errorMatrix(); |
2026 | double q1=this->q; |
2027 | double q2=rt2->q; |
2028 | double mass1=this->mass; |
2029 | double mass2=rt2->mass; |
2030 | |
2031 | // Initialize the doca and traverse both particles' trajectories |
2032 | doca=1000.; |
2033 | DVector3 oldpos1,oldpos2,oldmom1,oldmom2; |
2034 | double tflight1=0.,tflight2=0.; |
2035 | for (int i=0;i<this->Nswim_steps-1&&i<rt2->Nswim_steps-1; |
2036 | i++, swim_step1++, swim_step2++){ |
2037 | DVector3 pos1=swim_step1->origin; |
2038 | DVector3 pos2=swim_step2->origin; |
2039 | DVector3 diff=pos1-pos2; |
2040 | double new_doca=diff.Mag(); |
2041 | |
2042 | if (new_doca>doca){ |
2043 | if (i==1){ // backtrack to find the true doca |
2044 | tflight1=tflight2=0.; |
2045 | |
2046 | swim_step1=this->swim_steps; |
2047 | swim_step2=rt2->swim_steps; |
2048 | |
2049 | cov1=track1_kd->errorMatrix(); |
2050 | cov2=track2_kd->errorMatrix(); |
2051 | |
2052 | pos1=swim_step1->origin; |
2053 | DVector3 mom1=swim_step1->mom; |
2054 | DMagneticFieldStepper stepper1(this->bfield, this->q, &pos1, &mom1); |
2055 | |
2056 | pos2=swim_step2->origin; |
2057 | DVector3 mom2=swim_step2->mom; |
2058 | DMagneticFieldStepper stepper2(this->bfield, rt2->q, &pos2, &mom2); |
2059 | |
2060 | int inew=0; |
2061 | while (inew<100){ |
2062 | double ds1=stepper1.Step(&pos1,-0.5); |
2063 | double ds2=stepper2.Step(&pos2,-0.5); |
2064 | |
2065 | // Compute the revised estimate for the doca |
2066 | diff=pos1-pos2; |
2067 | new_doca=diff.Mag(); |
2068 | |
2069 | if (new_doca>doca){ |
2070 | break; |
2071 | } |
2072 | |
2073 | // Propagate the covariance matrices along the trajectories |
2074 | this->PropagateCovariance(ds1,q1,mass1,mom1,oldpos1,cov1); |
2075 | rt2->PropagateCovariance(ds2,q2,mass2,mom2,oldpos2,cov2); |
2076 | |
2077 | // Store the current positions, doca and adjust flight times |
2078 | oldpos1=pos1; |
2079 | oldpos2=pos2; |
2080 | doca=new_doca; |
2081 | |
2082 | double one_over_p1_sq=1./mom1.Mag2(); |
2083 | tflight1+=ds1*sqrt(1.+mass1*mass1*one_over_p1_sq)/SPEED_OF_LIGHT29.9792; |
2084 | |
2085 | double one_over_p2_sq=1./mom2.Mag2(); |
2086 | tflight2+=ds2*sqrt(1.+mass2*mass2*one_over_p2_sq)/SPEED_OF_LIGHT29.9792; |
2087 | |
2088 | // New momenta |
2089 | stepper1.GetMomentum(mom1); |
2090 | stepper2.GetMomentum(mom2); |
2091 | |
2092 | oldmom1=/*(-1.)*/mom1; |
2093 | oldmom2=/*(-1.)*/mom2; |
2094 | |
2095 | inew++; |
2096 | } |
2097 | } |
2098 | |
2099 | // "Vertex" is mid-point of line connecting the positions of closest |
2100 | // approach of the two tracks |
2101 | pos=0.5*(oldpos1+oldpos2); |
2102 | |
2103 | track1_kd->setErrorMatrix(cov1); |
2104 | track1_kd->setMomentum(oldmom1); |
2105 | track1_kd->setPosition(oldpos1); |
2106 | double err_t0=track1_kd->t0_err(); |
2107 | track1_kd->setT0(track1_kd->t0()+tflight1,sqrt(err_t0*err_t0+cov1(6,6)),track1_kd->t0_detector()); |
2108 | |
2109 | track2_kd->setErrorMatrix(cov2); |
2110 | track2_kd->setMomentum(oldmom2); |
2111 | track2_kd->setPosition(oldpos2); |
2112 | err_t0=track2_kd->t0_err(); |
2113 | track2_kd->setT0(track2_kd->t0()+tflight2,sqrt(err_t0*err_t0+cov2(6,6)),track2_kd->t0_detector()); |
2114 | |
2115 | // Compute the variance on the doca |
2116 | diff=oldpos1-oldpos2; |
2117 | double dx=diff.x(); |
2118 | double dy=diff.y(); |
2119 | double dz=diff.z(); |
2120 | var_doca=(dx*dx*(cov1(3,3)+cov2(3,3))+dy*dy*(cov1(4,4)+cov2(4,4)) |
2121 | +dz*dz*(cov1(5,5)+cov2(5,5))+2.*dx*dy*(cov1(3,4)+cov2(3,4)) |
2122 | +2.*dx*dz*(cov1(3,5)+cov2(3,5))+2.*dy*dz*(cov1(4,5)+cov2(4,5))) |
2123 | /(doca*doca); |
2124 | |
2125 | break; |
2126 | } |
2127 | |
2128 | // Propagate the covariance matrices along the trajectories |
2129 | this->PropagateCovariance(this->swim_steps[i+1].s-swim_step1->s,q1,mass1, |
2130 | swim_step1->mom,swim_step1->origin,cov1); |
2131 | rt2->PropagateCovariance(rt2->swim_steps[i+1].s-swim_step2->s,q2,mass2, |
2132 | swim_step2->mom,swim_step2->origin,cov2); |
2133 | |
2134 | // Store the current positions and doca |
2135 | oldpos1=pos1; |
2136 | oldpos2=pos2; |
2137 | oldmom1=swim_step1->mom; |
2138 | oldmom2=swim_step2->mom; |
2139 | tflight1=swim_step1->t; |
2140 | tflight2=swim_step2->t; |
2141 | doca=new_doca; |
2142 | } |
2143 | |
2144 | return NOERROR; |
2145 | } |
2146 | |
2147 | |
2148 |