File: | libraries/TRACKING/DReferenceTrajectory.cc |
Location: | line 1196, column 1 |
Description: | Dereference of null pointer |
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(); | |||
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 |