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G4Sphere.cc
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27 // $Id: G4Sphere.cc 104316 2017-05-24 13:04:23Z gcosmo $
28 //
29 // class G4Sphere
30 //
31 // Implementation for G4Sphere class
32 //
33 // History:
34 //
35 // 26.10.16 E.Tcherniaev: re-implemented CalculateExtent() using
36 // G4BoundingEnvelope, removed CreateRotatedVertices()
37 // 05.04.12 M.Kelsey: GetPointOnSurface() throw flat in cos(theta), sqrt(r)
38 // 14.09.09 T.Nikitina: fix for phi section in DistanceToOut(p,v,..),as for
39 // G4Tubs,G4Cons
40 // 26.03.09 G.Cosmo : optimisations and uniform use of local radial tolerance
41 // 12.06.08 V.Grichine: fix for theta intersections in DistanceToOut(p,v,...)
42 // 22.07.05 O.Link : Added check for intersection with double cone
43 // 03.05.05 V.Grichine: SurfaceNormal(p) according to J. Apostolakis proposal
44 // 16.09.04 V.Grichine: bug fixed in SurfaceNormal(p), theta normals
45 // 16.07.04 V.Grichine: bug fixed in DistanceToOut(p,v), Rmin go outside
46 // 02.06.04 V.Grichine: bug fixed in DistanceToIn(p,v), on Rmax,Rmin go inside
47 // 30.10.03 J.Apostolakis: new algorithm in Inside for SPhi-sections
48 // 29.10.03 J.Apostolakis: fix in Inside for SPhi-0.5*kAngTol < phi<SPhi, SPhi<0
49 // 19.06.02 V.Grichine: bug fixed in Inside(p), && -> && fDTheta - kAngTolerance
50 // 30.01.02 V.Grichine: bug fixed in Inside(p), && -> || at l.451
51 // 06.03.00 V.Grichine: modifications in Distance ToOut(p,v,...)
52 // 18.11.99 V.Grichine: side = kNull in Distance ToOut(p,v,...)
53 // 25.11.98 V.Grichine: bug fixed in DistanceToIn(p,v), phi intersections
54 // 12.11.98 V.Grichine: bug fixed in DistanceToIn(p,v), theta intersections
55 // 09.10.98 V.Grichine: modifications in DistanceToOut(p,v,...)
56 // 17.09.96 V.Grichine: final modifications to commit
57 // 28.03.94 P.Kent: old C++ code converted to tolerant geometry
58 // --------------------------------------------------------------------
59 
60 #include "G4Sphere.hh"
61 
62 #if !defined(G4GEOM_USE_USPHERE)
63 
64 #include "G4GeomTools.hh"
65 #include "G4VoxelLimits.hh"
66 #include "G4AffineTransform.hh"
67 #include "G4GeometryTolerance.hh"
68 #include "G4BoundingEnvelope.hh"
69 
70 #include "G4VPVParameterisation.hh"
71 
72 #include "Randomize.hh"
73 
74 #include "meshdefs.hh"
75 
76 #include "G4VGraphicsScene.hh"
77 #include "G4VisExtent.hh"
78 
79 using namespace CLHEP;
80 
81 // Private enum: Not for external use - used by distanceToOut
82 
83 enum ESide {kNull,kRMin,kRMax,kSPhi,kEPhi,kSTheta,kETheta};
84 
85 // used by normal
86 
87 enum ENorm {kNRMin,kNRMax,kNSPhi,kNEPhi,kNSTheta,kNETheta};
88 
90 //
91 // constructor - check parameters, convert angles so 0<sphi+dpshi<=2_PI
92 // - note if pDPhi>2PI then reset to 2PI
93 
94 G4Sphere::G4Sphere( const G4String& pName,
95  G4double pRmin, G4double pRmax,
96  G4double pSPhi, G4double pDPhi,
97  G4double pSTheta, G4double pDTheta )
98  : G4CSGSolid(pName), fEpsilon(2.e-11), fSPhi(0.0),
99  fFullPhiSphere(true), fFullThetaSphere(true)
100 {
101  kAngTolerance = G4GeometryTolerance::GetInstance()->GetAngularTolerance();
102  kRadTolerance = G4GeometryTolerance::GetInstance()->GetRadialTolerance();
103 
104  halfCarTolerance = 0.5*kCarTolerance;
105  halfAngTolerance = 0.5*kAngTolerance;
106 
107  // Check radii and set radial tolerances
108 
109  if ( (pRmin >= pRmax) || (pRmax < 1.1*kRadTolerance) || (pRmin < 0) )
110  {
111  std::ostringstream message;
112  message << "Invalid radii for Solid: " << GetName() << G4endl
113  << " pRmin = " << pRmin << ", pRmax = " << pRmax;
114  G4Exception("G4Sphere::G4Sphere()", "GeomSolids0002",
115  FatalException, message);
116  }
117  fRmin=pRmin; fRmax=pRmax;
118  fRminTolerance = (fRmin) ? std::max( kRadTolerance, fEpsilon*fRmin ) : 0;
119  fRmaxTolerance = std::max( kRadTolerance, fEpsilon*fRmax );
120 
121  // Check angles
122 
123  CheckPhiAngles(pSPhi, pDPhi);
124  CheckThetaAngles(pSTheta, pDTheta);
125 }
126 
128 //
129 // Fake default constructor - sets only member data and allocates memory
130 // for usage restricted to object persistency.
131 //
132 G4Sphere::G4Sphere( __void__& a )
133  : G4CSGSolid(a), fRminTolerance(0.), fRmaxTolerance(0.),
134  kAngTolerance(0.), kRadTolerance(0.), fEpsilon(0.),
135  fRmin(0.), fRmax(0.), fSPhi(0.), fDPhi(0.), fSTheta(0.),
136  fDTheta(0.), sinCPhi(0.), cosCPhi(0.), cosHDPhiOT(0.), cosHDPhiIT(0.),
137  sinSPhi(0.), cosSPhi(0.), sinEPhi(0.), cosEPhi(0.), hDPhi(0.), cPhi(0.),
138  ePhi(0.), sinSTheta(0.), cosSTheta(0.), sinETheta(0.), cosETheta(0.),
139  tanSTheta(0.), tanSTheta2(0.), tanETheta(0.), tanETheta2(0.), eTheta(0.),
140  fFullPhiSphere(false), fFullThetaSphere(false), fFullSphere(true),
141  halfCarTolerance(0.), halfAngTolerance(0.)
142 {
143 }
144 
146 //
147 // Destructor
148 
149 G4Sphere::~G4Sphere()
150 {
151 }
152 
154 //
155 // Copy constructor
156 
157 G4Sphere::G4Sphere(const G4Sphere& rhs)
158  : G4CSGSolid(rhs), fRminTolerance(rhs.fRminTolerance),
159  fRmaxTolerance(rhs.fRmaxTolerance), kAngTolerance(rhs.kAngTolerance),
160  kRadTolerance(rhs.kRadTolerance), fEpsilon(rhs.fEpsilon),
161  fRmin(rhs.fRmin), fRmax(rhs.fRmax), fSPhi(rhs.fSPhi), fDPhi(rhs.fDPhi),
162  fSTheta(rhs.fSTheta), fDTheta(rhs.fDTheta),
163  sinCPhi(rhs.sinCPhi), cosCPhi(rhs.cosCPhi),
164  cosHDPhiOT(rhs.cosHDPhiOT), cosHDPhiIT(rhs.cosHDPhiIT),
165  sinSPhi(rhs.sinSPhi), cosSPhi(rhs.cosSPhi),
166  sinEPhi(rhs.sinEPhi), cosEPhi(rhs.cosEPhi),
167  hDPhi(rhs.hDPhi), cPhi(rhs.cPhi), ePhi(rhs.ePhi),
168  sinSTheta(rhs.sinSTheta), cosSTheta(rhs.cosSTheta),
169  sinETheta(rhs.sinETheta), cosETheta(rhs.cosETheta),
170  tanSTheta(rhs.tanSTheta), tanSTheta2(rhs.tanSTheta2),
171  tanETheta(rhs.tanETheta), tanETheta2(rhs.tanETheta2), eTheta(rhs.eTheta),
172  fFullPhiSphere(rhs.fFullPhiSphere), fFullThetaSphere(rhs.fFullThetaSphere),
173  fFullSphere(rhs.fFullSphere),
174  halfCarTolerance(rhs.halfCarTolerance),
175  halfAngTolerance(rhs.halfAngTolerance)
176 {
177 }
178 
180 //
181 // Assignment operator
182 
183 G4Sphere& G4Sphere::operator = (const G4Sphere& rhs)
184 {
185  // Check assignment to self
186  //
187  if (this == &rhs) { return *this; }
188 
189  // Copy base class data
190  //
191  G4CSGSolid::operator=(rhs);
192 
193  // Copy data
194  //
195  fRminTolerance = rhs.fRminTolerance; fRmaxTolerance = rhs.fRmaxTolerance;
196  kAngTolerance = rhs.kAngTolerance; kRadTolerance = rhs.kRadTolerance;
197  fEpsilon = rhs.fEpsilon; fRmin = rhs.fRmin; fRmax = rhs.fRmax;
198  fSPhi = rhs.fSPhi; fDPhi = rhs.fDPhi; fSTheta = rhs.fSTheta;
199  fDTheta = rhs.fDTheta; sinCPhi = rhs.sinCPhi; cosCPhi = rhs.cosCPhi;
200  cosHDPhiOT = rhs.cosHDPhiOT; cosHDPhiIT = rhs.cosHDPhiIT;
201  sinSPhi = rhs.sinSPhi; cosSPhi = rhs.cosSPhi;
202  sinEPhi = rhs.sinEPhi; cosEPhi = rhs.cosEPhi;
203  hDPhi = rhs.hDPhi; cPhi = rhs.cPhi; ePhi = rhs.ePhi;
204  sinSTheta = rhs.sinSTheta; cosSTheta = rhs.cosSTheta;
205  sinETheta = rhs.sinETheta; cosETheta = rhs.cosETheta;
206  tanSTheta = rhs.tanSTheta; tanSTheta2 = rhs.tanSTheta2;
207  tanETheta = rhs.tanETheta; tanETheta2 = rhs.tanETheta2;
208  eTheta = rhs.eTheta; fFullPhiSphere = rhs.fFullPhiSphere;
209  fFullThetaSphere = rhs.fFullThetaSphere; fFullSphere = rhs.fFullSphere;
210  halfCarTolerance = rhs.halfCarTolerance;
211  halfAngTolerance = rhs.halfAngTolerance;
212 
213  return *this;
214 }
215 
217 //
218 // Dispatch to parameterisation for replication mechanism dimension
219 // computation & modification.
220 
221 void G4Sphere::ComputeDimensions( G4VPVParameterisation* p,
222  const G4int n,
223  const G4VPhysicalVolume* pRep)
224 {
225  p->ComputeDimensions(*this,n,pRep);
226 }
227 
229 //
230 // Get bounding box
231 
232 void G4Sphere::BoundingLimits(G4ThreeVector& pMin, G4ThreeVector& pMax) const
233 {
234  G4double rmin = GetInnerRadius();
235  G4double rmax = GetOuterRadius();
236 
237  // Find bounding box
238  //
239  if (GetDeltaThetaAngle() >= pi && GetDeltaPhiAngle() >= twopi)
240  {
241  pMin.set(-rmax,-rmax,-rmax);
242  pMax.set( rmax, rmax, rmax);
243  }
244  else
245  {
246  G4double sinStart = GetSinStartTheta();
247  G4double cosStart = GetCosStartTheta();
248  G4double sinEnd = GetSinEndTheta();
249  G4double cosEnd = GetCosEndTheta();
250 
251  G4double stheta = GetStartThetaAngle();
252  G4double etheta = stheta + GetDeltaThetaAngle();
253  G4double rhomin = rmin*std::min(sinStart,sinEnd);
254  G4double rhomax = rmax;
255  if (stheta > halfpi) rhomax = rmax*sinStart;
256  if (etheta < halfpi) rhomax = rmax*sinEnd;
257 
258  G4TwoVector xymin,xymax;
259  G4GeomTools::DiskExtent(rhomin,rhomax,
260  GetSinStartPhi(),GetCosStartPhi(),
261  GetSinEndPhi(),GetCosEndPhi(),
262  xymin,xymax);
263 
264  G4double zmin = std::min(rmin*cosEnd,rmax*cosEnd);
265  G4double zmax = std::max(rmin*cosStart,rmax*cosStart);
266  pMin.set(xymin.x(),xymin.y(),zmin);
267  pMax.set(xymax.x(),xymax.y(),zmax);
268  }
269 
270  // Check correctness of the bounding box
271  //
272  if (pMin.x() >= pMax.x() || pMin.y() >= pMax.y() || pMin.z() >= pMax.z())
273  {
274  std::ostringstream message;
275  message << "Bad bounding box (min >= max) for solid: "
276  << GetName() << " !"
277  << "\npMin = " << pMin
278  << "\npMax = " << pMax;
279  G4Exception("G4Sphere::BoundingLimits()", "GeomMgt0001",
280  JustWarning, message);
281  DumpInfo();
282  }
283 }
284 
286 //
287 // Calculate extent under transform and specified limit
288 
289 G4bool G4Sphere::CalculateExtent( const EAxis pAxis,
290  const G4VoxelLimits& pVoxelLimit,
291  const G4AffineTransform& pTransform,
292  G4double& pMin, G4double& pMax ) const
293 {
294  G4ThreeVector bmin, bmax;
295 
296  // Get bounding box
297  BoundingLimits(bmin,bmax);
298 
299  // Find extent
300  G4BoundingEnvelope bbox(bmin,bmax);
301  return bbox.CalculateExtent(pAxis,pVoxelLimit,pTransform,pMin,pMax);
302 }
303 
305 //
306 // Return whether point inside/outside/on surface
307 // Split into radius, phi, theta checks
308 // Each check modifies 'in', or returns as approprate
309 
310 EInside G4Sphere::Inside( const G4ThreeVector& p ) const
311 {
312  G4double rho,rho2,rad2,tolRMin,tolRMax;
313  G4double pPhi,pTheta;
314  EInside in = kOutside;
315 
316  const G4double halfRmaxTolerance = fRmaxTolerance*0.5;
317  const G4double halfRminTolerance = fRminTolerance*0.5;
318  const G4double Rmax_minus = fRmax - halfRmaxTolerance;
319  const G4double Rmin_plus = (fRmin > 0) ? fRmin+halfRminTolerance : 0;
320 
321  rho2 = p.x()*p.x() + p.y()*p.y() ;
322  rad2 = rho2 + p.z()*p.z() ;
323 
324  // Check radial surfaces. Sets 'in'
325 
326  tolRMin = Rmin_plus;
327  tolRMax = Rmax_minus;
328 
329  if(rad2 == 0.0)
330  {
331  if (fRmin > 0.0)
332  {
333  return in = kOutside;
334  }
335  if ( (!fFullPhiSphere) || (!fFullThetaSphere) )
336  {
337  return in = kSurface;
338  }
339  else
340  {
341  return in = kInside;
342  }
343  }
344 
345  if ( (rad2 <= Rmax_minus*Rmax_minus) && (rad2 >= Rmin_plus*Rmin_plus) )
346  {
347  in = kInside;
348  }
349  else
350  {
351  tolRMax = fRmax + halfRmaxTolerance; // outside case
352  tolRMin = std::max(fRmin-halfRminTolerance, 0.); // outside case
353  if ( (rad2 <= tolRMax*tolRMax) && (rad2 >= tolRMin*tolRMin) )
354  {
355  in = kSurface;
356  }
357  else
358  {
359  return in = kOutside;
360  }
361  }
362 
363  // Phi boundaries : Do not check if it has no phi boundary!
364 
365  if ( !fFullPhiSphere && rho2 ) // [fDPhi < twopi] and [p.x or p.y]
366  {
367  pPhi = std::atan2(p.y(),p.x()) ;
368 
369  if ( pPhi < fSPhi - halfAngTolerance ) { pPhi += twopi; }
370  else if ( pPhi > ePhi + halfAngTolerance ) { pPhi -= twopi; }
371 
372  if ( (pPhi < fSPhi - halfAngTolerance)
373  || (pPhi > ePhi + halfAngTolerance) ) { return in = kOutside; }
374 
375  else if (in == kInside) // else it's kSurface anyway already
376  {
377  if ( (pPhi < fSPhi + halfAngTolerance)
378  || (pPhi > ePhi - halfAngTolerance) ) { in = kSurface; }
379  }
380  }
381 
382  // Theta bondaries
383 
384  if ( (rho2 || p.z()) && (!fFullThetaSphere) )
385  {
386  rho = std::sqrt(rho2);
387  pTheta = std::atan2(rho,p.z());
388 
389  if ( in == kInside )
390  {
391  if ( ((fSTheta > 0.0) && (pTheta < fSTheta + halfAngTolerance))
392  || ((eTheta < pi) && (pTheta > eTheta - halfAngTolerance)) )
393  {
394  if ( (( (fSTheta>0.0)&&(pTheta>=fSTheta-halfAngTolerance) )
395  || (fSTheta == 0.0) )
396  && ((eTheta==pi)||(pTheta <= eTheta + halfAngTolerance) ) )
397  {
398  in = kSurface;
399  }
400  else
401  {
402  in = kOutside;
403  }
404  }
405  }
406  else
407  {
408  if ( ((fSTheta > 0.0)&&(pTheta < fSTheta - halfAngTolerance))
409  ||((eTheta < pi )&&(pTheta > eTheta + halfAngTolerance)) )
410  {
411  in = kOutside;
412  }
413  }
414  }
415  return in;
416 }
417 
419 //
420 // Return unit normal of surface closest to p
421 // - note if point on z axis, ignore phi divided sides
422 // - unsafe if point close to z axis a rmin=0 - no explicit checks
423 
424 G4ThreeVector G4Sphere::SurfaceNormal( const G4ThreeVector& p ) const
425 {
426  G4int noSurfaces = 0;
427  G4double rho, rho2, radius, pTheta, pPhi=0.;
428  G4double distRMin = kInfinity;
429  G4double distSPhi = kInfinity, distEPhi = kInfinity;
430  G4double distSTheta = kInfinity, distETheta = kInfinity;
431  G4ThreeVector nR, nPs, nPe, nTs, nTe, nZ(0.,0.,1.);
432  G4ThreeVector norm, sumnorm(0.,0.,0.);
433 
434  rho2 = p.x()*p.x()+p.y()*p.y();
435  radius = std::sqrt(rho2+p.z()*p.z());
436  rho = std::sqrt(rho2);
437 
438  G4double distRMax = std::fabs(radius-fRmax);
439  if (fRmin) distRMin = std::fabs(radius-fRmin);
440 
441  if ( rho && !fFullSphere )
442  {
443  pPhi = std::atan2(p.y(),p.x());
444 
445  if (pPhi < fSPhi-halfAngTolerance) { pPhi += twopi; }
446  else if (pPhi > ePhi+halfAngTolerance) { pPhi -= twopi; }
447  }
448  if ( !fFullPhiSphere )
449  {
450  if ( rho )
451  {
452  distSPhi = std::fabs( pPhi-fSPhi );
453  distEPhi = std::fabs( pPhi-ePhi );
454  }
455  else if( !fRmin )
456  {
457  distSPhi = 0.;
458  distEPhi = 0.;
459  }
460  nPs = G4ThreeVector(sinSPhi,-cosSPhi,0);
461  nPe = G4ThreeVector(-sinEPhi,cosEPhi,0);
462  }
463  if ( !fFullThetaSphere )
464  {
465  if ( rho )
466  {
467  pTheta = std::atan2(rho,p.z());
468  distSTheta = std::fabs(pTheta-fSTheta);
469  distETheta = std::fabs(pTheta-eTheta);
470 
471  nTs = G4ThreeVector(-cosSTheta*p.x()/rho,
472  -cosSTheta*p.y()/rho,
473  sinSTheta );
474 
475  nTe = G4ThreeVector( cosETheta*p.x()/rho,
476  cosETheta*p.y()/rho,
477  -sinETheta );
478  }
479  else if( !fRmin )
480  {
481  if ( fSTheta )
482  {
483  distSTheta = 0.;
484  nTs = G4ThreeVector(0.,0.,-1.);
485  }
486  if ( eTheta < pi )
487  {
488  distETheta = 0.;
489  nTe = G4ThreeVector(0.,0.,1.);
490  }
491  }
492  }
493  if( radius ) { nR = G4ThreeVector(p.x()/radius,p.y()/radius,p.z()/radius); }
494 
495  if( distRMax <= halfCarTolerance )
496  {
497  noSurfaces ++;
498  sumnorm += nR;
499  }
500  if( fRmin && (distRMin <= halfCarTolerance) )
501  {
502  noSurfaces ++;
503  sumnorm -= nR;
504  }
505  if( !fFullPhiSphere )
506  {
507  if (distSPhi <= halfAngTolerance)
508  {
509  noSurfaces ++;
510  sumnorm += nPs;
511  }
512  if (distEPhi <= halfAngTolerance)
513  {
514  noSurfaces ++;
515  sumnorm += nPe;
516  }
517  }
518  if ( !fFullThetaSphere )
519  {
520  if ((distSTheta <= halfAngTolerance) && (fSTheta > 0.))
521  {
522  noSurfaces ++;
523  if ((radius <= halfCarTolerance) && fFullPhiSphere) { sumnorm += nZ; }
524  else { sumnorm += nTs; }
525  }
526  if ((distETheta <= halfAngTolerance) && (eTheta < pi))
527  {
528  noSurfaces ++;
529  if ((radius <= halfCarTolerance) && fFullPhiSphere) { sumnorm -= nZ; }
530  else { sumnorm += nTe; }
531  if(sumnorm.z() == 0.) { sumnorm += nZ; }
532  }
533  }
534  if ( noSurfaces == 0 )
535  {
536 #ifdef G4CSGDEBUG
537  G4Exception("G4Sphere::SurfaceNormal(p)", "GeomSolids1002",
538  JustWarning, "Point p is not on surface !?" );
539 #endif
540  norm = ApproxSurfaceNormal(p);
541  }
542  else if ( noSurfaces == 1 ) { norm = sumnorm; }
543  else { norm = sumnorm.unit(); }
544  return norm;
545 }
546 
547 
549 //
550 // Algorithm for SurfaceNormal() following the original specification
551 // for points not on the surface
552 
553 G4ThreeVector G4Sphere::ApproxSurfaceNormal( const G4ThreeVector& p ) const
554 {
555  ENorm side;
556  G4ThreeVector norm;
557  G4double rho,rho2,radius,pPhi,pTheta;
558  G4double distRMin,distRMax,distSPhi,distEPhi,
559  distSTheta,distETheta,distMin;
560 
561  rho2=p.x()*p.x()+p.y()*p.y();
562  radius=std::sqrt(rho2+p.z()*p.z());
563  rho=std::sqrt(rho2);
564 
565  //
566  // Distance to r shells
567  //
568 
569  distRMax=std::fabs(radius-fRmax);
570  if (fRmin)
571  {
572  distRMin=std::fabs(radius-fRmin);
573 
574  if (distRMin<distRMax)
575  {
576  distMin=distRMin;
577  side=kNRMin;
578  }
579  else
580  {
581  distMin=distRMax;
582  side=kNRMax;
583  }
584  }
585  else
586  {
587  distMin=distRMax;
588  side=kNRMax;
589  }
590 
591  //
592  // Distance to phi planes
593  //
594  // Protected against (0,0,z)
595 
596  pPhi = std::atan2(p.y(),p.x());
597  if (pPhi<0) { pPhi += twopi; }
598 
599  if (!fFullPhiSphere && rho)
600  {
601  if (fSPhi<0)
602  {
603  distSPhi=std::fabs(pPhi-(fSPhi+twopi))*rho;
604  }
605  else
606  {
607  distSPhi=std::fabs(pPhi-fSPhi)*rho;
608  }
609 
610  distEPhi=std::fabs(pPhi-fSPhi-fDPhi)*rho;
611 
612  // Find new minimum
613  //
614  if (distSPhi<distEPhi)
615  {
616  if (distSPhi<distMin)
617  {
618  distMin=distSPhi;
619  side=kNSPhi;
620  }
621  }
622  else
623  {
624  if (distEPhi<distMin)
625  {
626  distMin=distEPhi;
627  side=kNEPhi;
628  }
629  }
630  }
631 
632  //
633  // Distance to theta planes
634  //
635 
636  if (!fFullThetaSphere && radius)
637  {
638  pTheta=std::atan2(rho,p.z());
639  distSTheta=std::fabs(pTheta-fSTheta)*radius;
640  distETheta=std::fabs(pTheta-fSTheta-fDTheta)*radius;
641 
642  // Find new minimum
643  //
644  if (distSTheta<distETheta)
645  {
646  if (distSTheta<distMin)
647  {
648  distMin = distSTheta ;
649  side = kNSTheta ;
650  }
651  }
652  else
653  {
654  if (distETheta<distMin)
655  {
656  distMin = distETheta ;
657  side = kNETheta ;
658  }
659  }
660  }
661 
662  switch (side)
663  {
664  case kNRMin: // Inner radius
665  norm=G4ThreeVector(-p.x()/radius,-p.y()/radius,-p.z()/radius);
666  break;
667  case kNRMax: // Outer radius
668  norm=G4ThreeVector(p.x()/radius,p.y()/radius,p.z()/radius);
669  break;
670  case kNSPhi:
671  norm=G4ThreeVector(sinSPhi,-cosSPhi,0);
672  break;
673  case kNEPhi:
674  norm=G4ThreeVector(-sinEPhi,cosEPhi,0);
675  break;
676  case kNSTheta:
677  norm=G4ThreeVector(-cosSTheta*std::cos(pPhi),
678  -cosSTheta*std::sin(pPhi),
679  sinSTheta );
680  break;
681  case kNETheta:
682  norm=G4ThreeVector( cosETheta*std::cos(pPhi),
683  cosETheta*std::sin(pPhi),
684  -sinETheta );
685  break;
686  default: // Should never reach this case ...
687  DumpInfo();
688  G4Exception("G4Sphere::ApproxSurfaceNormal()",
689  "GeomSolids1002", JustWarning,
690  "Undefined side for valid surface normal to solid.");
691  break;
692  }
693 
694  return norm;
695 }
696 
698 //
699 // Calculate distance to shape from outside, along normalised vector
700 // - return kInfinity if no intersection, or intersection distance <= tolerance
701 //
702 // -> If point is outside outer radius, compute intersection with rmax
703 // - if no intersection return
704 // - if valid phi,theta return intersection Dist
705 //
706 // -> If shell, compute intersection with inner radius, taking largest +ve root
707 // - if valid phi,theta, save intersection
708 //
709 // -> If phi segmented, compute intersection with phi half planes
710 // - if valid intersection(r,theta), return smallest intersection of
711 // inner shell & phi intersection
712 //
713 // -> If theta segmented, compute intersection with theta cones
714 // - if valid intersection(r,phi), return smallest intersection of
715 // inner shell & theta intersection
716 //
717 //
718 // NOTE:
719 // - `if valid' (above) implies tolerant checking of intersection points
720 //
721 // OPT:
722 // Move tolIO/ORmin/RMax2 precalcs to where they are needed -
723 // not required for most cases.
724 // Avoid atan2 for non theta cut G4Sphere.
725 
726 G4double G4Sphere::DistanceToIn( const G4ThreeVector& p,
727  const G4ThreeVector& v ) const
728 {
729  G4double snxt = kInfinity ; // snxt = default return value
730  G4double rho2, rad2, pDotV2d, pDotV3d, pTheta ;
731  G4double tolSTheta=0., tolETheta=0. ;
732  const G4double dRmax = 100.*fRmax;
733 
734  const G4double halfRmaxTolerance = fRmaxTolerance*0.5;
735  const G4double halfRminTolerance = fRminTolerance*0.5;
736  const G4double tolORMin2 = (fRmin>halfRminTolerance)
737  ? (fRmin-halfRminTolerance)*(fRmin-halfRminTolerance) : 0;
738  const G4double tolIRMin2 =
739  (fRmin+halfRminTolerance)*(fRmin+halfRminTolerance);
740  const G4double tolORMax2 =
741  (fRmax+halfRmaxTolerance)*(fRmax+halfRmaxTolerance);
742  const G4double tolIRMax2 =
743  (fRmax-halfRmaxTolerance)*(fRmax-halfRmaxTolerance);
744 
745  // Intersection point
746  //
747  G4double xi, yi, zi, rhoi, rhoi2, radi2, iTheta ;
748 
749  // Phi intersection
750  //
751  G4double Comp ;
752 
753  // Phi precalcs
754  //
755  G4double Dist, cosPsi ;
756 
757  // Theta precalcs
758  //
759  G4double dist2STheta, dist2ETheta ;
760  G4double t1, t2, b, c, d2, d, sd = kInfinity ;
761 
762  // General Precalcs
763  //
764  rho2 = p.x()*p.x() + p.y()*p.y() ;
765  rad2 = rho2 + p.z()*p.z() ;
766  pTheta = std::atan2(std::sqrt(rho2),p.z()) ;
767 
768  pDotV2d = p.x()*v.x() + p.y()*v.y() ;
769  pDotV3d = pDotV2d + p.z()*v.z() ;
770 
771  // Theta precalcs
772  //
773  if (!fFullThetaSphere)
774  {
775  tolSTheta = fSTheta - halfAngTolerance ;
776  tolETheta = eTheta + halfAngTolerance ;
777 
778  // Special case rad2 = 0 comparing with direction
779  //
780  if ((rad2!=0.0) || (fRmin!=0.0))
781  {
782  // Keep going for computation of distance...
783  }
784  else // Positioned on the sphere's origin
785  {
786  G4double vTheta = std::atan2(std::sqrt(v.x()*v.x()+v.y()*v.y()),v.z()) ;
787  if ( (vTheta < tolSTheta) || (vTheta > tolETheta) )
788  {
789  return snxt ; // kInfinity
790  }
791  return snxt = 0.0 ;
792  }
793  }
794 
795  // Outer spherical shell intersection
796  // - Only if outside tolerant fRmax
797  // - Check for if inside and outer G4Sphere heading through solid (-> 0)
798  // - No intersect -> no intersection with G4Sphere
799  //
800  // Shell eqn: x^2+y^2+z^2=RSPH^2
801  //
802  // => (px+svx)^2+(py+svy)^2+(pz+svz)^2=R^2
803  //
804  // => (px^2+py^2+pz^2) +2sd(pxvx+pyvy+pzvz)+sd^2(vx^2+vy^2+vz^2)=R^2
805  // => rad2 +2sd(pDotV3d) +sd^2 =R^2
806  //
807  // => sd=-pDotV3d+-std::sqrt(pDotV3d^2-(rad2-R^2))
808 
809  c = rad2 - fRmax*fRmax ;
810 
811  if (c > fRmaxTolerance*fRmax)
812  {
813  // If outside tolerant boundary of outer G4Sphere
814  // [should be std::sqrt(rad2)-fRmax > halfRmaxTolerance]
815 
816  d2 = pDotV3d*pDotV3d - c ;
817 
818  if ( d2 >= 0 )
819  {
820  sd = -pDotV3d - std::sqrt(d2) ;
821 
822  if (sd >= 0 )
823  {
824  if ( sd>dRmax ) // Avoid rounding errors due to precision issues seen on
825  { // 64 bits systems. Split long distances and recompute
826  G4double fTerm = sd-std::fmod(sd,dRmax);
827  sd = fTerm + DistanceToIn(p+fTerm*v,v);
828  }
829  xi = p.x() + sd*v.x() ;
830  yi = p.y() + sd*v.y() ;
831  rhoi = std::sqrt(xi*xi + yi*yi) ;
832 
833  if (!fFullPhiSphere && rhoi) // Check phi intersection
834  {
835  cosPsi = (xi*cosCPhi + yi*sinCPhi)/rhoi ;
836 
837  if (cosPsi >= cosHDPhiOT)
838  {
839  if (!fFullThetaSphere) // Check theta intersection
840  {
841  zi = p.z() + sd*v.z() ;
842 
843  // rhoi & zi can never both be 0
844  // (=>intersect at origin =>fRmax=0)
845  //
846  iTheta = std::atan2(rhoi,zi) ;
847  if ( (iTheta >= tolSTheta) && (iTheta <= tolETheta) )
848  {
849  return snxt = sd ;
850  }
851  }
852  else
853  {
854  return snxt=sd;
855  }
856  }
857  }
858  else
859  {
860  if (!fFullThetaSphere) // Check theta intersection
861  {
862  zi = p.z() + sd*v.z() ;
863 
864  // rhoi & zi can never both be 0
865  // (=>intersect at origin => fRmax=0 !)
866  //
867  iTheta = std::atan2(rhoi,zi) ;
868  if ( (iTheta >= tolSTheta) && (iTheta <= tolETheta) )
869  {
870  return snxt=sd;
871  }
872  }
873  else
874  {
875  return snxt = sd;
876  }
877  }
878  }
879  }
880  else // No intersection with G4Sphere
881  {
882  return snxt=kInfinity;
883  }
884  }
885  else
886  {
887  // Inside outer radius
888  // check not inside, and heading through G4Sphere (-> 0 to in)
889 
890  d2 = pDotV3d*pDotV3d - c ;
891 
892  if ( (rad2 > tolIRMax2)
893  && ( (d2 >= fRmaxTolerance*fRmax) && (pDotV3d < 0) ) )
894  {
895  if (!fFullPhiSphere)
896  {
897  // Use inner phi tolerant boundary -> if on tolerant
898  // phi boundaries, phi intersect code handles leaving/entering checks
899 
900  cosPsi = (p.x()*cosCPhi + p.y()*sinCPhi)/std::sqrt(rho2) ;
901 
902  if (cosPsi>=cosHDPhiIT)
903  {
904  // inside radii, delta r -ve, inside phi
905 
906  if ( !fFullThetaSphere )
907  {
908  if ( (pTheta >= tolSTheta + kAngTolerance)
909  && (pTheta <= tolETheta - kAngTolerance) )
910  {
911  return snxt=0;
912  }
913  }
914  else // strictly inside Theta in both cases
915  {
916  return snxt=0;
917  }
918  }
919  }
920  else
921  {
922  if ( !fFullThetaSphere )
923  {
924  if ( (pTheta >= tolSTheta + kAngTolerance)
925  && (pTheta <= tolETheta - kAngTolerance) )
926  {
927  return snxt=0;
928  }
929  }
930  else // strictly inside Theta in both cases
931  {
932  return snxt=0;
933  }
934  }
935  }
936  }
937 
938  // Inner spherical shell intersection
939  // - Always farthest root, because would have passed through outer
940  // surface first.
941  // - Tolerant check if travelling through solid
942 
943  if (fRmin)
944  {
945  c = rad2 - fRmin*fRmin ;
946  d2 = pDotV3d*pDotV3d - c ;
947 
948  // Within tolerance inner radius of inner G4Sphere
949  // Check for immediate entry/already inside and travelling outwards
950 
951  if ( (c > -halfRminTolerance) && (rad2 < tolIRMin2)
952  && ( (d2 < fRmin*kCarTolerance) || (pDotV3d >= 0) ) )
953  {
954  if ( !fFullPhiSphere )
955  {
956  // Use inner phi tolerant boundary -> if on tolerant
957  // phi boundaries, phi intersect code handles leaving/entering checks
958 
959  cosPsi = (p.x()*cosCPhi+p.y()*sinCPhi)/std::sqrt(rho2) ;
960  if (cosPsi >= cosHDPhiIT)
961  {
962  // inside radii, delta r -ve, inside phi
963  //
964  if ( !fFullThetaSphere )
965  {
966  if ( (pTheta >= tolSTheta + kAngTolerance)
967  && (pTheta <= tolETheta - kAngTolerance) )
968  {
969  return snxt=0;
970  }
971  }
972  else
973  {
974  return snxt = 0 ;
975  }
976  }
977  }
978  else
979  {
980  if ( !fFullThetaSphere )
981  {
982  if ( (pTheta >= tolSTheta + kAngTolerance)
983  && (pTheta <= tolETheta - kAngTolerance) )
984  {
985  return snxt = 0 ;
986  }
987  }
988  else
989  {
990  return snxt=0;
991  }
992  }
993  }
994  else // Not special tolerant case
995  {
996  if (d2 >= 0)
997  {
998  sd = -pDotV3d + std::sqrt(d2) ;
999  if ( sd >= halfRminTolerance ) // It was >= 0 ??
1000  {
1001  xi = p.x() + sd*v.x() ;
1002  yi = p.y() + sd*v.y() ;
1003  rhoi = std::sqrt(xi*xi+yi*yi) ;
1004 
1005  if ( !fFullPhiSphere && rhoi ) // Check phi intersection
1006  {
1007  cosPsi = (xi*cosCPhi + yi*sinCPhi)/rhoi ;
1008 
1009  if (cosPsi >= cosHDPhiOT)
1010  {
1011  if ( !fFullThetaSphere ) // Check theta intersection
1012  {
1013  zi = p.z() + sd*v.z() ;
1014 
1015  // rhoi & zi can never both be 0
1016  // (=>intersect at origin =>fRmax=0)
1017  //
1018  iTheta = std::atan2(rhoi,zi) ;
1019  if ( (iTheta >= tolSTheta) && (iTheta<=tolETheta) )
1020  {
1021  snxt = sd;
1022  }
1023  }
1024  else
1025  {
1026  snxt=sd;
1027  }
1028  }
1029  }
1030  else
1031  {
1032  if ( !fFullThetaSphere ) // Check theta intersection
1033  {
1034  zi = p.z() + sd*v.z() ;
1035 
1036  // rhoi & zi can never both be 0
1037  // (=>intersect at origin => fRmax=0 !)
1038  //
1039  iTheta = std::atan2(rhoi,zi) ;
1040  if ( (iTheta >= tolSTheta) && (iTheta <= tolETheta) )
1041  {
1042  snxt = sd;
1043  }
1044  }
1045  else
1046  {
1047  snxt = sd;
1048  }
1049  }
1050  }
1051  }
1052  }
1053  }
1054 
1055  // Phi segment intersection
1056  //
1057  // o Tolerant of points inside phi planes by up to kCarTolerance*0.5
1058  //
1059  // o NOTE: Large duplication of code between sphi & ephi checks
1060  // -> only diffs: sphi -> ephi, Comp -> -Comp and half-plane
1061  // intersection check <=0 -> >=0
1062  // -> Should use some form of loop Construct
1063  //
1064  if ( !fFullPhiSphere )
1065  {
1066  // First phi surface ('S'tarting phi)
1067  // Comp = Component in outwards normal dirn
1068  //
1069  Comp = v.x()*sinSPhi - v.y()*cosSPhi ;
1070 
1071  if ( Comp < 0 )
1072  {
1073  Dist = p.y()*cosSPhi - p.x()*sinSPhi ;
1074 
1075  if (Dist < halfCarTolerance)
1076  {
1077  sd = Dist/Comp ;
1078 
1079  if (sd < snxt)
1080  {
1081  if ( sd > 0 )
1082  {
1083  xi = p.x() + sd*v.x() ;
1084  yi = p.y() + sd*v.y() ;
1085  zi = p.z() + sd*v.z() ;
1086  rhoi2 = xi*xi + yi*yi ;
1087  radi2 = rhoi2 + zi*zi ;
1088  }
1089  else
1090  {
1091  sd = 0 ;
1092  xi = p.x() ;
1093  yi = p.y() ;
1094  zi = p.z() ;
1095  rhoi2 = rho2 ;
1096  radi2 = rad2 ;
1097  }
1098  if ( (radi2 <= tolORMax2)
1099  && (radi2 >= tolORMin2)
1100  && ((yi*cosCPhi-xi*sinCPhi) <= 0) )
1101  {
1102  // Check theta intersection
1103  // rhoi & zi can never both be 0
1104  // (=>intersect at origin =>fRmax=0)
1105  //
1106  if ( !fFullThetaSphere )
1107  {
1108  iTheta = std::atan2(std::sqrt(rhoi2),zi) ;
1109  if ( (iTheta >= tolSTheta) && (iTheta <= tolETheta) )
1110  {
1111  // r and theta intersections good
1112  // - check intersecting with correct half-plane
1113 
1114  if ((yi*cosCPhi-xi*sinCPhi) <= 0)
1115  {
1116  snxt = sd;
1117  }
1118  }
1119  }
1120  else
1121  {
1122  snxt = sd;
1123  }
1124  }
1125  }
1126  }
1127  }
1128 
1129  // Second phi surface ('E'nding phi)
1130  // Component in outwards normal dirn
1131 
1132  Comp = -( v.x()*sinEPhi-v.y()*cosEPhi ) ;
1133 
1134  if (Comp < 0)
1135  {
1136  Dist = -(p.y()*cosEPhi-p.x()*sinEPhi) ;
1137  if ( Dist < halfCarTolerance )
1138  {
1139  sd = Dist/Comp ;
1140 
1141  if ( sd < snxt )
1142  {
1143  if (sd > 0)
1144  {
1145  xi = p.x() + sd*v.x() ;
1146  yi = p.y() + sd*v.y() ;
1147  zi = p.z() + sd*v.z() ;
1148  rhoi2 = xi*xi + yi*yi ;
1149  radi2 = rhoi2 + zi*zi ;
1150  }
1151  else
1152  {
1153  sd = 0 ;
1154  xi = p.x() ;
1155  yi = p.y() ;
1156  zi = p.z() ;
1157  rhoi2 = rho2 ;
1158  radi2 = rad2 ;
1159  }
1160  if ( (radi2 <= tolORMax2)
1161  && (radi2 >= tolORMin2)
1162  && ((yi*cosCPhi-xi*sinCPhi) >= 0) )
1163  {
1164  // Check theta intersection
1165  // rhoi & zi can never both be 0
1166  // (=>intersect at origin =>fRmax=0)
1167  //
1168  if ( !fFullThetaSphere )
1169  {
1170  iTheta = std::atan2(std::sqrt(rhoi2),zi) ;
1171  if ( (iTheta >= tolSTheta) && (iTheta <= tolETheta) )
1172  {
1173  // r and theta intersections good
1174  // - check intersecting with correct half-plane
1175 
1176  if ((yi*cosCPhi-xi*sinCPhi) >= 0)
1177  {
1178  snxt = sd;
1179  }
1180  }
1181  }
1182  else
1183  {
1184  snxt = sd;
1185  }
1186  }
1187  }
1188  }
1189  }
1190  }
1191 
1192  // Theta segment intersection
1193 
1194  if ( !fFullThetaSphere )
1195  {
1196 
1197  // Intersection with theta surfaces
1198  // Known failure cases:
1199  // o Inside tolerance of stheta surface, skim
1200  // ~parallel to cone and Hit & enter etheta surface [& visa versa]
1201  //
1202  // To solve: Check 2nd root of etheta surface in addition to stheta
1203  //
1204  // o start/end theta is exactly pi/2
1205  // Intersections with cones
1206  //
1207  // Cone equation: x^2+y^2=z^2tan^2(t)
1208  //
1209  // => (px+svx)^2+(py+svy)^2=(pz+svz)^2tan^2(t)
1210  //
1211  // => (px^2+py^2-pz^2tan^2(t))+2sd(pxvx+pyvy-pzvztan^2(t))
1212  // + sd^2(vx^2+vy^2-vz^2tan^2(t)) = 0
1213  //
1214  // => sd^2(1-vz^2(1+tan^2(t))+2sd(pdotv2d-pzvztan^2(t))
1215  // + (rho2-pz^2tan^2(t)) = 0
1216 
1217  if (fSTheta)
1218  {
1219  dist2STheta = rho2 - p.z()*p.z()*tanSTheta2 ;
1220  }
1221  else
1222  {
1223  dist2STheta = kInfinity ;
1224  }
1225  if ( eTheta < pi )
1226  {
1227  dist2ETheta=rho2-p.z()*p.z()*tanETheta2;
1228  }
1229  else
1230  {
1231  dist2ETheta=kInfinity;
1232  }
1233  if ( pTheta < tolSTheta )
1234  {
1235  // Inside (theta<stheta-tol) stheta cone
1236  // First root of stheta cone, second if first root -ve
1237 
1238  t1 = 1 - v.z()*v.z()*(1 + tanSTheta2) ;
1239  t2 = pDotV2d - p.z()*v.z()*tanSTheta2 ;
1240  if (t1)
1241  {
1242  b = t2/t1 ;
1243  c = dist2STheta/t1 ;
1244  d2 = b*b - c ;
1245 
1246  if ( d2 >= 0 )
1247  {
1248  d = std::sqrt(d2) ;
1249  sd = -b - d ; // First root
1250  zi = p.z() + sd*v.z();
1251 
1252  if ( (sd < 0) || (zi*(fSTheta - halfpi) > 0) )
1253  {
1254  sd = -b+d; // Second root
1255  }
1256  if ((sd >= 0) && (sd < snxt))
1257  {
1258  xi = p.x() + sd*v.x();
1259  yi = p.y() + sd*v.y();
1260  zi = p.z() + sd*v.z();
1261  rhoi2 = xi*xi + yi*yi;
1262  radi2 = rhoi2 + zi*zi;
1263  if ( (radi2 <= tolORMax2)
1264  && (radi2 >= tolORMin2)
1265  && (zi*(fSTheta - halfpi) <= 0) )
1266  {
1267  if ( !fFullPhiSphere && rhoi2 ) // Check phi intersection
1268  {
1269  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1270  if (cosPsi >= cosHDPhiOT)
1271  {
1272  snxt = sd;
1273  }
1274  }
1275  else
1276  {
1277  snxt = sd;
1278  }
1279  }
1280  }
1281  }
1282  }
1283 
1284  // Possible intersection with ETheta cone.
1285  // Second >= 0 root should be considered
1286 
1287  if ( eTheta < pi )
1288  {
1289  t1 = 1 - v.z()*v.z()*(1 + tanETheta2) ;
1290  t2 = pDotV2d - p.z()*v.z()*tanETheta2 ;
1291  if (t1)
1292  {
1293  b = t2/t1 ;
1294  c = dist2ETheta/t1 ;
1295  d2 = b*b - c ;
1296 
1297  if (d2 >= 0)
1298  {
1299  d = std::sqrt(d2) ;
1300  sd = -b + d ; // Second root
1301 
1302  if ( (sd >= 0) && (sd < snxt) )
1303  {
1304  xi = p.x() + sd*v.x() ;
1305  yi = p.y() + sd*v.y() ;
1306  zi = p.z() + sd*v.z() ;
1307  rhoi2 = xi*xi + yi*yi ;
1308  radi2 = rhoi2 + zi*zi ;
1309 
1310  if ( (radi2 <= tolORMax2)
1311  && (radi2 >= tolORMin2)
1312  && (zi*(eTheta - halfpi) <= 0) )
1313  {
1314  if (!fFullPhiSphere && rhoi2) // Check phi intersection
1315  {
1316  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1317  if (cosPsi >= cosHDPhiOT)
1318  {
1319  snxt = sd;
1320  }
1321  }
1322  else
1323  {
1324  snxt = sd;
1325  }
1326  }
1327  }
1328  }
1329  }
1330  }
1331  }
1332  else if ( pTheta > tolETheta )
1333  {
1334  // dist2ETheta<-kRadTolerance*0.5 && dist2STheta>0)
1335  // Inside (theta > etheta+tol) e-theta cone
1336  // First root of etheta cone, second if first root 'imaginary'
1337 
1338  t1 = 1 - v.z()*v.z()*(1 + tanETheta2) ;
1339  t2 = pDotV2d - p.z()*v.z()*tanETheta2 ;
1340  if (t1)
1341  {
1342  b = t2/t1 ;
1343  c = dist2ETheta/t1 ;
1344  d2 = b*b - c ;
1345 
1346  if (d2 >= 0)
1347  {
1348  d = std::sqrt(d2) ;
1349  sd = -b - d ; // First root
1350  zi = p.z() + sd*v.z();
1351 
1352  if ( (sd < 0) || (zi*(eTheta - halfpi) > 0) )
1353  {
1354  sd = -b + d ; // second root
1355  }
1356  if ( (sd >= 0) && (sd < snxt) )
1357  {
1358  xi = p.x() + sd*v.x() ;
1359  yi = p.y() + sd*v.y() ;
1360  zi = p.z() + sd*v.z() ;
1361  rhoi2 = xi*xi + yi*yi ;
1362  radi2 = rhoi2 + zi*zi ;
1363 
1364  if ( (radi2 <= tolORMax2)
1365  && (radi2 >= tolORMin2)
1366  && (zi*(eTheta - halfpi) <= 0) )
1367  {
1368  if (!fFullPhiSphere && rhoi2) // Check phi intersection
1369  {
1370  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1371  if (cosPsi >= cosHDPhiOT)
1372  {
1373  snxt = sd;
1374  }
1375  }
1376  else
1377  {
1378  snxt = sd;
1379  }
1380  }
1381  }
1382  }
1383  }
1384 
1385  // Possible intersection with STheta cone.
1386  // Second >= 0 root should be considered
1387 
1388  if ( fSTheta )
1389  {
1390  t1 = 1 - v.z()*v.z()*(1 + tanSTheta2) ;
1391  t2 = pDotV2d - p.z()*v.z()*tanSTheta2 ;
1392  if (t1)
1393  {
1394  b = t2/t1 ;
1395  c = dist2STheta/t1 ;
1396  d2 = b*b - c ;
1397 
1398  if (d2 >= 0)
1399  {
1400  d = std::sqrt(d2) ;
1401  sd = -b + d ; // Second root
1402 
1403  if ( (sd >= 0) && (sd < snxt) )
1404  {
1405  xi = p.x() + sd*v.x() ;
1406  yi = p.y() + sd*v.y() ;
1407  zi = p.z() + sd*v.z() ;
1408  rhoi2 = xi*xi + yi*yi ;
1409  radi2 = rhoi2 + zi*zi ;
1410 
1411  if ( (radi2 <= tolORMax2)
1412  && (radi2 >= tolORMin2)
1413  && (zi*(fSTheta - halfpi) <= 0) )
1414  {
1415  if (!fFullPhiSphere && rhoi2) // Check phi intersection
1416  {
1417  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1418  if (cosPsi >= cosHDPhiOT)
1419  {
1420  snxt = sd;
1421  }
1422  }
1423  else
1424  {
1425  snxt = sd;
1426  }
1427  }
1428  }
1429  }
1430  }
1431  }
1432  }
1433  else if ( (pTheta < tolSTheta + kAngTolerance)
1434  && (fSTheta > halfAngTolerance) )
1435  {
1436  // In tolerance of stheta
1437  // If entering through solid [r,phi] => 0 to in
1438  // else try 2nd root
1439 
1440  t2 = pDotV2d - p.z()*v.z()*tanSTheta2 ;
1441  if ( (t2>=0 && tolIRMin2<rad2 && rad2<tolIRMax2 && fSTheta<halfpi)
1442  || (t2<0 && tolIRMin2<rad2 && rad2<tolIRMax2 && fSTheta>halfpi)
1443  || (v.z()<0 && tolIRMin2<rad2 && rad2<tolIRMax2 && fSTheta==halfpi) )
1444  {
1445  if (!fFullPhiSphere && rho2) // Check phi intersection
1446  {
1447  cosPsi = (p.x()*cosCPhi + p.y()*sinCPhi)/std::sqrt(rho2) ;
1448  if (cosPsi >= cosHDPhiIT)
1449  {
1450  return 0 ;
1451  }
1452  }
1453  else
1454  {
1455  return 0 ;
1456  }
1457  }
1458 
1459  // Not entering immediately/travelling through
1460 
1461  t1 = 1 - v.z()*v.z()*(1 + tanSTheta2) ;
1462  if (t1)
1463  {
1464  b = t2/t1 ;
1465  c = dist2STheta/t1 ;
1466  d2 = b*b - c ;
1467 
1468  if (d2 >= 0)
1469  {
1470  d = std::sqrt(d2) ;
1471  sd = -b + d ;
1472  if ( (sd >= halfCarTolerance) && (sd < snxt) && (fSTheta < halfpi) )
1473  { // ^^^^^^^^^^^^^^^^^^^^^ shouldn't it be >=0 instead ?
1474  xi = p.x() + sd*v.x() ;
1475  yi = p.y() + sd*v.y() ;
1476  zi = p.z() + sd*v.z() ;
1477  rhoi2 = xi*xi + yi*yi ;
1478  radi2 = rhoi2 + zi*zi ;
1479 
1480  if ( (radi2 <= tolORMax2)
1481  && (radi2 >= tolORMin2)
1482  && (zi*(fSTheta - halfpi) <= 0) )
1483  {
1484  if ( !fFullPhiSphere && rhoi2 ) // Check phi intersection
1485  {
1486  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1487  if ( cosPsi >= cosHDPhiOT )
1488  {
1489  snxt = sd;
1490  }
1491  }
1492  else
1493  {
1494  snxt = sd;
1495  }
1496  }
1497  }
1498  }
1499  }
1500  }
1501  else if ((pTheta > tolETheta-kAngTolerance) && (eTheta < pi-kAngTolerance))
1502  {
1503 
1504  // In tolerance of etheta
1505  // If entering through solid [r,phi] => 0 to in
1506  // else try 2nd root
1507 
1508  t2 = pDotV2d - p.z()*v.z()*tanETheta2 ;
1509 
1510  if ( ((t2<0) && (eTheta < halfpi)
1511  && (tolIRMin2 < rad2) && (rad2 < tolIRMax2))
1512  || ((t2>=0) && (eTheta > halfpi)
1513  && (tolIRMin2 < rad2) && (rad2 < tolIRMax2))
1514  || ((v.z()>0) && (eTheta == halfpi)
1515  && (tolIRMin2 < rad2) && (rad2 < tolIRMax2)) )
1516  {
1517  if (!fFullPhiSphere && rho2) // Check phi intersection
1518  {
1519  cosPsi = (p.x()*cosCPhi + p.y()*sinCPhi)/std::sqrt(rho2) ;
1520  if (cosPsi >= cosHDPhiIT)
1521  {
1522  return 0 ;
1523  }
1524  }
1525  else
1526  {
1527  return 0 ;
1528  }
1529  }
1530 
1531  // Not entering immediately/travelling through
1532 
1533  t1 = 1 - v.z()*v.z()*(1 + tanETheta2) ;
1534  if (t1)
1535  {
1536  b = t2/t1 ;
1537  c = dist2ETheta/t1 ;
1538  d2 = b*b - c ;
1539 
1540  if (d2 >= 0)
1541  {
1542  d = std::sqrt(d2) ;
1543  sd = -b + d ;
1544 
1545  if ( (sd >= halfCarTolerance)
1546  && (sd < snxt) && (eTheta > halfpi) )
1547  {
1548  xi = p.x() + sd*v.x() ;
1549  yi = p.y() + sd*v.y() ;
1550  zi = p.z() + sd*v.z() ;
1551  rhoi2 = xi*xi + yi*yi ;
1552  radi2 = rhoi2 + zi*zi ;
1553 
1554  if ( (radi2 <= tolORMax2)
1555  && (radi2 >= tolORMin2)
1556  && (zi*(eTheta - halfpi) <= 0) )
1557  {
1558  if (!fFullPhiSphere && rhoi2) // Check phi intersection
1559  {
1560  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1561  if (cosPsi >= cosHDPhiOT)
1562  {
1563  snxt = sd;
1564  }
1565  }
1566  else
1567  {
1568  snxt = sd;
1569  }
1570  }
1571  }
1572  }
1573  }
1574  }
1575  else
1576  {
1577  // stheta+tol<theta<etheta-tol
1578  // For BOTH stheta & etheta check 2nd root for validity [r,phi]
1579 
1580  t1 = 1 - v.z()*v.z()*(1 + tanSTheta2) ;
1581  t2 = pDotV2d - p.z()*v.z()*tanSTheta2 ;
1582  if (t1)
1583  {
1584  b = t2/t1;
1585  c = dist2STheta/t1 ;
1586  d2 = b*b - c ;
1587 
1588  if (d2 >= 0)
1589  {
1590  d = std::sqrt(d2) ;
1591  sd = -b + d ; // second root
1592 
1593  if ((sd >= 0) && (sd < snxt))
1594  {
1595  xi = p.x() + sd*v.x() ;
1596  yi = p.y() + sd*v.y() ;
1597  zi = p.z() + sd*v.z() ;
1598  rhoi2 = xi*xi + yi*yi ;
1599  radi2 = rhoi2 + zi*zi ;
1600 
1601  if ( (radi2 <= tolORMax2)
1602  && (radi2 >= tolORMin2)
1603  && (zi*(fSTheta - halfpi) <= 0) )
1604  {
1605  if (!fFullPhiSphere && rhoi2) // Check phi intersection
1606  {
1607  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1608  if (cosPsi >= cosHDPhiOT)
1609  {
1610  snxt = sd;
1611  }
1612  }
1613  else
1614  {
1615  snxt = sd;
1616  }
1617  }
1618  }
1619  }
1620  }
1621  t1 = 1 - v.z()*v.z()*(1 + tanETheta2) ;
1622  t2 = pDotV2d - p.z()*v.z()*tanETheta2 ;
1623  if (t1)
1624  {
1625  b = t2/t1 ;
1626  c = dist2ETheta/t1 ;
1627  d2 = b*b - c ;
1628 
1629  if (d2 >= 0)
1630  {
1631  d = std::sqrt(d2) ;
1632  sd = -b + d; // second root
1633 
1634  if ((sd >= 0) && (sd < snxt))
1635  {
1636  xi = p.x() + sd*v.x() ;
1637  yi = p.y() + sd*v.y() ;
1638  zi = p.z() + sd*v.z() ;
1639  rhoi2 = xi*xi + yi*yi ;
1640  radi2 = rhoi2 + zi*zi ;
1641 
1642  if ( (radi2 <= tolORMax2)
1643  && (radi2 >= tolORMin2)
1644  && (zi*(eTheta - halfpi) <= 0) )
1645  {
1646  if (!fFullPhiSphere && rhoi2) // Check phi intersection
1647  {
1648  cosPsi = (xi*cosCPhi + yi*sinCPhi)/std::sqrt(rhoi2) ;
1649  if ( cosPsi >= cosHDPhiOT )
1650  {
1651  snxt = sd;
1652  }
1653  }
1654  else
1655  {
1656  snxt = sd;
1657  }
1658  }
1659  }
1660  }
1661  }
1662  }
1663  }
1664  return snxt;
1665 }
1666 
1668 //
1669 // Calculate distance (<= actual) to closest surface of shape from outside
1670 // - Calculate distance to radial planes
1671 // - Only to phi planes if outside phi extent
1672 // - Only to theta planes if outside theta extent
1673 // - Return 0 if point inside
1674 
1675 G4double G4Sphere::DistanceToIn( const G4ThreeVector& p ) const
1676 {
1677  G4double safe=0.0,safeRMin,safeRMax,safePhi,safeTheta;
1678  G4double rho2,rds,rho;
1679  G4double cosPsi;
1680  G4double pTheta,dTheta1,dTheta2;
1681  rho2=p.x()*p.x()+p.y()*p.y();
1682  rds=std::sqrt(rho2+p.z()*p.z());
1683  rho=std::sqrt(rho2);
1684 
1685  //
1686  // Distance to r shells
1687  //
1688  if (fRmin)
1689  {
1690  safeRMin=fRmin-rds;
1691  safeRMax=rds-fRmax;
1692  if (safeRMin>safeRMax)
1693  {
1694  safe=safeRMin;
1695  }
1696  else
1697  {
1698  safe=safeRMax;
1699  }
1700  }
1701  else
1702  {
1703  safe=rds-fRmax;
1704  }
1705 
1706  //
1707  // Distance to phi extent
1708  //
1709  if (!fFullPhiSphere && rho)
1710  {
1711  // Psi=angle from central phi to point
1712  //
1713  cosPsi=(p.x()*cosCPhi+p.y()*sinCPhi)/rho;
1714  if (cosPsi<std::cos(hDPhi))
1715  {
1716  // Point lies outside phi range
1717  //
1718  if ((p.y()*cosCPhi-p.x()*sinCPhi)<=0)
1719  {
1720  safePhi=std::fabs(p.x()*sinSPhi-p.y()*cosSPhi);
1721  }
1722  else
1723  {
1724  safePhi=std::fabs(p.x()*sinEPhi-p.y()*cosEPhi);
1725  }
1726  if (safePhi>safe) { safe=safePhi; }
1727  }
1728  }
1729  //
1730  // Distance to Theta extent
1731  //
1732  if ((rds!=0.0) && (!fFullThetaSphere))
1733  {
1734  pTheta=std::acos(p.z()/rds);
1735  if (pTheta<0) { pTheta+=pi; }
1736  dTheta1=fSTheta-pTheta;
1737  dTheta2=pTheta-eTheta;
1738  if (dTheta1>dTheta2)
1739  {
1740  if (dTheta1>=0) // WHY ???????????
1741  {
1742  safeTheta=rds*std::sin(dTheta1);
1743  if (safe<=safeTheta)
1744  {
1745  safe=safeTheta;
1746  }
1747  }
1748  }
1749  else
1750  {
1751  if (dTheta2>=0)
1752  {
1753  safeTheta=rds*std::sin(dTheta2);
1754  if (safe<=safeTheta)
1755  {
1756  safe=safeTheta;
1757  }
1758  }
1759  }
1760  }
1761 
1762  if (safe<0) { safe=0; }
1763  return safe;
1764 }
1765 
1767 //
1768 // Calculate distance to surface of shape from 'inside', allowing for tolerance
1769 // - Only Calc rmax intersection if no valid rmin intersection
1770 
1771 G4double G4Sphere::DistanceToOut( const G4ThreeVector& p,
1772  const G4ThreeVector& v,
1773  const G4bool calcNorm,
1774  G4bool *validNorm,
1775  G4ThreeVector *n ) const
1776 {
1777  G4double snxt = kInfinity; // snxt is default return value
1778  G4double sphi= kInfinity,stheta= kInfinity;
1779  ESide side=kNull,sidephi=kNull,sidetheta=kNull;
1780 
1781  const G4double halfRmaxTolerance = fRmaxTolerance*0.5;
1782  const G4double halfRminTolerance = fRminTolerance*0.5;
1783  const G4double Rmax_plus = fRmax + halfRmaxTolerance;
1784  const G4double Rmin_minus = (fRmin) ? fRmin-halfRminTolerance : 0;
1785  G4double t1,t2;
1786  G4double b,c,d;
1787 
1788  // Variables for phi intersection:
1789 
1790  G4double pDistS,compS,pDistE,compE,sphi2,vphi;
1791 
1792  G4double rho2,rad2,pDotV2d,pDotV3d;
1793 
1794  G4double xi,yi,zi; // Intersection point
1795 
1796  // Theta precals
1797  //
1798  G4double rhoSecTheta;
1799  G4double dist2STheta, dist2ETheta, distTheta;
1800  G4double d2,sd;
1801 
1802  // General Precalcs
1803  //
1804  rho2 = p.x()*p.x()+p.y()*p.y();
1805  rad2 = rho2+p.z()*p.z();
1806 
1807  pDotV2d = p.x()*v.x()+p.y()*v.y();
1808  pDotV3d = pDotV2d+p.z()*v.z();
1809 
1810  // Radial Intersections from G4Sphere::DistanceToIn
1811  //
1812  // Outer spherical shell intersection
1813  // - Only if outside tolerant fRmax
1814  // - Check for if inside and outer G4Sphere heading through solid (-> 0)
1815  // - No intersect -> no intersection with G4Sphere
1816  //
1817  // Shell eqn: x^2+y^2+z^2=RSPH^2
1818  //
1819  // => (px+svx)^2+(py+svy)^2+(pz+svz)^2=R^2
1820  //
1821  // => (px^2+py^2+pz^2) +2sd(pxvx+pyvy+pzvz)+sd^2(vx^2+vy^2+vz^2)=R^2
1822  // => rad2 +2sd(pDotV3d) +sd^2 =R^2
1823  //
1824  // => sd=-pDotV3d+-std::sqrt(pDotV3d^2-(rad2-R^2))
1825 
1826  if( (rad2 <= Rmax_plus*Rmax_plus) && (rad2 >= Rmin_minus*Rmin_minus) )
1827  {
1828  c = rad2 - fRmax*fRmax;
1829 
1830  if (c < fRmaxTolerance*fRmax)
1831  {
1832  // Within tolerant Outer radius
1833  //
1834  // The test is
1835  // rad - fRmax < 0.5*kRadTolerance
1836  // => rad < fRmax + 0.5*kRadTol
1837  // => rad2 < (fRmax + 0.5*kRadTol)^2
1838  // => rad2 < fRmax^2 + 2.*0.5*fRmax*kRadTol + 0.25*kRadTol*kRadTol
1839  // => rad2 - fRmax^2 <~ fRmax*kRadTol
1840 
1841  d2 = pDotV3d*pDotV3d - c;
1842 
1843  if( (c >- fRmaxTolerance*fRmax) // on tolerant surface
1844  && ((pDotV3d >=0) || (d2 < 0)) ) // leaving outside from Rmax
1845  // not re-entering
1846  {
1847  if(calcNorm)
1848  {
1849  *validNorm = true ;
1850  *n = G4ThreeVector(p.x()/fRmax,p.y()/fRmax,p.z()/fRmax) ;
1851  }
1852  return snxt = 0;
1853  }
1854  else
1855  {
1856  snxt = -pDotV3d+std::sqrt(d2); // second root since inside Rmax
1857  side = kRMax ;
1858  }
1859  }
1860 
1861  // Inner spherical shell intersection:
1862  // Always first >=0 root, because would have passed
1863  // from outside of Rmin surface .
1864 
1865  if (fRmin)
1866  {
1867  c = rad2 - fRmin*fRmin;
1868  d2 = pDotV3d*pDotV3d - c;
1869 
1870  if (c >- fRminTolerance*fRmin) // 2.0 * (0.5*kRadTolerance) * fRmin
1871  {
1872  if ( (c < fRminTolerance*fRmin) // leaving from Rmin
1873  && (d2 >= fRminTolerance*fRmin) && (pDotV3d < 0) )
1874  {
1875  if(calcNorm) { *validNorm = false; } // Rmin surface is concave
1876  return snxt = 0 ;
1877  }
1878  else
1879  {
1880  if ( d2 >= 0. )
1881  {
1882  sd = -pDotV3d-std::sqrt(d2);
1883 
1884  if ( sd >= 0. ) // Always intersect Rmin first
1885  {
1886  snxt = sd ;
1887  side = kRMin ;
1888  }
1889  }
1890  }
1891  }
1892  }
1893  }
1894 
1895  // Theta segment intersection
1896 
1897  if ( !fFullThetaSphere )
1898  {
1899  // Intersection with theta surfaces
1900  //
1901  // Known failure cases:
1902  // o Inside tolerance of stheta surface, skim
1903  // ~parallel to cone and Hit & enter etheta surface [& visa versa]
1904  //
1905  // To solve: Check 2nd root of etheta surface in addition to stheta
1906  //
1907  // o start/end theta is exactly pi/2
1908  //
1909  // Intersections with cones
1910  //
1911  // Cone equation: x^2+y^2=z^2tan^2(t)
1912  //
1913  // => (px+svx)^2+(py+svy)^2=(pz+svz)^2tan^2(t)
1914  //
1915  // => (px^2+py^2-pz^2tan^2(t))+2sd(pxvx+pyvy-pzvztan^2(t))
1916  // + sd^2(vx^2+vy^2-vz^2tan^2(t)) = 0
1917  //
1918  // => sd^2(1-vz^2(1+tan^2(t))+2sd(pdotv2d-pzvztan^2(t))
1919  // + (rho2-pz^2tan^2(t)) = 0
1920  //
1921 
1922  if(fSTheta) // intersection with first cons
1923  {
1924  if( std::fabs(tanSTheta) > 5./kAngTolerance ) // kons is plane z=0
1925  {
1926  if( v.z() > 0. )
1927  {
1928  if ( std::fabs( p.z() ) <= halfRmaxTolerance )
1929  {
1930  if(calcNorm)
1931  {
1932  *validNorm = true;
1933  *n = G4ThreeVector(0.,0.,1.);
1934  }
1935  return snxt = 0 ;
1936  }
1937  stheta = -p.z()/v.z();
1938  sidetheta = kSTheta;
1939  }
1940  }
1941  else // kons is not plane
1942  {
1943  t1 = 1-v.z()*v.z()*(1+tanSTheta2);
1944  t2 = pDotV2d-p.z()*v.z()*tanSTheta2; // ~vDotN if p on cons
1945  dist2STheta = rho2-p.z()*p.z()*tanSTheta2; // t3
1946 
1947  distTheta = std::sqrt(rho2)-p.z()*tanSTheta;
1948 
1949  if( std::fabs(t1) < halfAngTolerance ) // 1st order equation,
1950  { // v parallel to kons
1951  if( v.z() > 0. )
1952  {
1953  if(std::fabs(distTheta) < halfRmaxTolerance) // p on surface
1954  {
1955  if( (fSTheta < halfpi) && (p.z() > 0.) )
1956  {
1957  if( calcNorm ) { *validNorm = false; }
1958  return snxt = 0.;
1959  }
1960  else if( (fSTheta > halfpi) && (p.z() <= 0) )
1961  {
1962  if( calcNorm )
1963  {
1964  *validNorm = true;
1965  if (rho2)
1966  {
1967  rhoSecTheta = std::sqrt(rho2*(1+tanSTheta2));
1968 
1969  *n = G4ThreeVector( p.x()/rhoSecTheta,
1970  p.y()/rhoSecTheta,
1971  std::sin(fSTheta) );
1972  }
1973  else *n = G4ThreeVector(0.,0.,1.);
1974  }
1975  return snxt = 0.;
1976  }
1977  }
1978  stheta = -0.5*dist2STheta/t2;
1979  sidetheta = kSTheta;
1980  }
1981  } // 2nd order equation, 1st root of fSTheta cone,
1982  else // 2nd if 1st root -ve
1983  {
1984  if( std::fabs(distTheta) < halfRmaxTolerance )
1985  {
1986  if( (fSTheta > halfpi) && (t2 >= 0.) ) // leave
1987  {
1988  if( calcNorm )
1989  {
1990  *validNorm = true;
1991  if (rho2)
1992  {
1993  rhoSecTheta = std::sqrt(rho2*(1+tanSTheta2));
1994 
1995  *n = G4ThreeVector( p.x()/rhoSecTheta,
1996  p.y()/rhoSecTheta,
1997  std::sin(fSTheta) );
1998  }
1999  else { *n = G4ThreeVector(0.,0.,1.); }
2000  }
2001  return snxt = 0.;
2002  }
2003  else if( (fSTheta < halfpi) && (t2 < 0.) && (p.z() >=0.) ) // leave
2004  {
2005  if( calcNorm ) { *validNorm = false; }
2006  return snxt = 0.;
2007  }
2008  }
2009  b = t2/t1;
2010  c = dist2STheta/t1;
2011  d2 = b*b - c ;
2012 
2013  if ( d2 >= 0. )
2014  {
2015  d = std::sqrt(d2);
2016 
2017  if( fSTheta > halfpi )
2018  {
2019  sd = -b - d; // First root
2020 
2021  if ( ((std::fabs(s) < halfRmaxTolerance) && (t2 < 0.))
2022  || (sd < 0.) || ( (sd > 0.) && (p.z() + sd*v.z() > 0.) ) )
2023  {
2024  sd = -b + d ; // 2nd root
2025  }
2026  if( (sd > halfRmaxTolerance) && (p.z() + sd*v.z() <= 0.) )
2027  {
2028  stheta = sd;
2029  sidetheta = kSTheta;
2030  }
2031  }
2032  else // sTheta < pi/2, concave surface, no normal
2033  {
2034  sd = -b - d; // First root
2035 
2036  if ( ( (std::fabs(sd) < halfRmaxTolerance) && (t2 >= 0.) )
2037  || (sd < 0.) || ( (sd > 0.) && (p.z() + sd*v.z() < 0.) ) )
2038  {
2039  sd = -b + d ; // 2nd root
2040  }
2041  if( (sd > halfRmaxTolerance) && (p.z() + sd*v.z() >= 0.) )
2042  {
2043  stheta = sd;
2044  sidetheta = kSTheta;
2045  }
2046  }
2047  }
2048  }
2049  }
2050  }
2051  if (eTheta < pi) // intersection with second cons
2052  {
2053  if( std::fabs(tanETheta) > 5./kAngTolerance ) // kons is plane z=0
2054  {
2055  if( v.z() < 0. )
2056  {
2057  if ( std::fabs( p.z() ) <= halfRmaxTolerance )
2058  {
2059  if(calcNorm)
2060  {
2061  *validNorm = true;
2062  *n = G4ThreeVector(0.,0.,-1.);
2063  }
2064  return snxt = 0 ;
2065  }
2066  sd = -p.z()/v.z();
2067 
2068  if( sd < stheta )
2069  {
2070  stheta = sd;
2071  sidetheta = kETheta;
2072  }
2073  }
2074  }
2075  else // kons is not plane
2076  {
2077  t1 = 1-v.z()*v.z()*(1+tanETheta2);
2078  t2 = pDotV2d-p.z()*v.z()*tanETheta2; // ~vDotN if p on cons
2079  dist2ETheta = rho2-p.z()*p.z()*tanETheta2; // t3
2080 
2081  distTheta = std::sqrt(rho2)-p.z()*tanETheta;
2082 
2083  if( std::fabs(t1) < halfAngTolerance ) // 1st order equation,
2084  { // v parallel to kons
2085  if( v.z() < 0. )
2086  {
2087  if(std::fabs(distTheta) < halfRmaxTolerance) // p on surface
2088  {
2089  if( (eTheta > halfpi) && (p.z() < 0.) )
2090  {
2091  if( calcNorm ) { *validNorm = false; }
2092  return snxt = 0.;
2093  }
2094  else if ( (eTheta < halfpi) && (p.z() >= 0) )
2095  {
2096  if( calcNorm )
2097  {
2098  *validNorm = true;
2099  if (rho2)
2100  {
2101  rhoSecTheta = std::sqrt(rho2*(1+tanETheta2));
2102  *n = G4ThreeVector( p.x()/rhoSecTheta,
2103  p.y()/rhoSecTheta,
2104  -sinETheta );
2105  }
2106  else { *n = G4ThreeVector(0.,0.,-1.); }
2107  }
2108  return snxt = 0.;
2109  }
2110  }
2111  sd = -0.5*dist2ETheta/t2;
2112 
2113  if( sd < stheta )
2114  {
2115  stheta = sd;
2116  sidetheta = kETheta;
2117  }
2118  }
2119  } // 2nd order equation, 1st root of fSTheta cone
2120  else // 2nd if 1st root -ve
2121  {
2122  if ( std::fabs(distTheta) < halfRmaxTolerance )
2123  {
2124  if( (eTheta < halfpi) && (t2 >= 0.) ) // leave
2125  {
2126  if( calcNorm )
2127  {
2128  *validNorm = true;
2129  if (rho2)
2130  {
2131  rhoSecTheta = std::sqrt(rho2*(1+tanETheta2));
2132  *n = G4ThreeVector( p.x()/rhoSecTheta,
2133  p.y()/rhoSecTheta,
2134  -sinETheta );
2135  }
2136  else *n = G4ThreeVector(0.,0.,-1.);
2137  }
2138  return snxt = 0.;
2139  }
2140  else if ( (eTheta > halfpi)
2141  && (t2 < 0.) && (p.z() <=0.) ) // leave
2142  {
2143  if( calcNorm ) { *validNorm = false; }
2144  return snxt = 0.;
2145  }
2146  }
2147  b = t2/t1;
2148  c = dist2ETheta/t1;
2149  d2 = b*b - c ;
2150  if ( (d2 <halfRmaxTolerance) && (d2 > -halfRmaxTolerance) )
2151  {
2152  d2 = 0.;
2153  }
2154  if ( d2 >= 0. )
2155  {
2156  d = std::sqrt(d2);
2157 
2158  if( eTheta < halfpi )
2159  {
2160  sd = -b - d; // First root
2161 
2162  if( ((std::fabs(sd) < halfRmaxTolerance) && (t2 < 0.))
2163  || (sd < 0.) )
2164  {
2165  sd = -b + d ; // 2nd root
2166  }
2167  if( sd > halfRmaxTolerance )
2168  {
2169  if( sd < stheta )
2170  {
2171  stheta = sd;
2172  sidetheta = kETheta;
2173  }
2174  }
2175  }
2176  else // sTheta+fDTheta > pi/2, concave surface, no normal
2177  {
2178  sd = -b - d; // First root
2179 
2180  if ( ((std::fabs(sd) < halfRmaxTolerance) && (t2 >= 0.))
2181  || (sd < 0.)
2182  || ( (sd > 0.) && (p.z() + sd*v.z() > halfRmaxTolerance) ) )
2183  {
2184  sd = -b + d ; // 2nd root
2185  }
2186  if ( ( sd>halfRmaxTolerance )
2187  && ( p.z()+sd*v.z() <= halfRmaxTolerance ) )
2188  {
2189  if( sd < stheta )
2190  {
2191  stheta = sd;
2192  sidetheta = kETheta;
2193  }
2194  }
2195  }
2196  }
2197  }
2198  }
2199  }
2200 
2201  } // end theta intersections
2202 
2203  // Phi Intersection
2204 
2205  if ( !fFullPhiSphere )
2206  {
2207  if ( p.x() || p.y() ) // Check if on z axis (rho not needed later)
2208  {
2209  // pDist -ve when inside
2210 
2211  pDistS=p.x()*sinSPhi-p.y()*cosSPhi;
2212  pDistE=-p.x()*sinEPhi+p.y()*cosEPhi;
2213 
2214  // Comp -ve when in direction of outwards normal
2215 
2216  compS = -sinSPhi*v.x()+cosSPhi*v.y() ;
2217  compE = sinEPhi*v.x()-cosEPhi*v.y() ;
2218  sidephi = kNull ;
2219 
2220  if ( (pDistS <= 0) && (pDistE <= 0) )
2221  {
2222  // Inside both phi *full* planes
2223 
2224  if ( compS < 0 )
2225  {
2226  sphi = pDistS/compS ;
2227  xi = p.x()+sphi*v.x() ;
2228  yi = p.y()+sphi*v.y() ;
2229 
2230  // Check intersection with correct half-plane (if not -> no intersect)
2231  //
2232  if( (std::fabs(xi)<=kCarTolerance) && (std::fabs(yi)<=kCarTolerance) )
2233  {
2234  vphi = std::atan2(v.y(),v.x());
2235  sidephi = kSPhi;
2236  if ( ( (fSPhi-halfAngTolerance) <= vphi)
2237  && ( (ePhi+halfAngTolerance) >= vphi) )
2238  {
2239  sphi = kInfinity;
2240  }
2241  }
2242  else if ( ( yi*cosCPhi - xi*sinCPhi ) >= 0 )
2243  {
2244  sphi=kInfinity;
2245  }
2246  else
2247  {
2248  sidephi = kSPhi ;
2249  if ( pDistS > -halfCarTolerance) { sphi = 0; } // Leave by sphi
2250  }
2251  }
2252  else { sphi = kInfinity; }
2253 
2254  if ( compE < 0 )
2255  {
2256  sphi2=pDistE/compE ;
2257  if (sphi2 < sphi) // Only check further if < starting phi intersection
2258  {
2259  xi = p.x()+sphi2*v.x() ;
2260  yi = p.y()+sphi2*v.y() ;
2261 
2262  // Check intersection with correct half-plane
2263  //
2264  if ( (std::fabs(xi)<=kCarTolerance)
2265  && (std::fabs(yi)<=kCarTolerance))
2266  {
2267  // Leaving via ending phi
2268  //
2269  vphi = std::atan2(v.y(),v.x()) ;
2270 
2271  if( !((fSPhi-halfAngTolerance <= vphi)
2272  &&(fSPhi+fDPhi+halfAngTolerance >= vphi)) )
2273  {
2274  sidephi = kEPhi;
2275  if ( pDistE <= -halfCarTolerance ) { sphi = sphi2; }
2276  else { sphi = 0.0; }
2277  }
2278  }
2279  else if ((yi*cosCPhi-xi*sinCPhi)>=0) // Leaving via ending phi
2280  {
2281  sidephi = kEPhi ;
2282  if ( pDistE <= -halfCarTolerance )
2283  {
2284  sphi=sphi2;
2285  }
2286  else
2287  {
2288  sphi = 0 ;
2289  }
2290  }
2291  }
2292  }
2293  }
2294  else if ((pDistS >= 0) && (pDistE >= 0)) // Outside both *full* phi planes
2295  {
2296  if ( pDistS <= pDistE )
2297  {
2298  sidephi = kSPhi ;
2299  }
2300  else
2301  {
2302  sidephi = kEPhi ;
2303  }
2304  if ( fDPhi > pi )
2305  {
2306  if ( (compS < 0) && (compE < 0) ) { sphi = 0; }
2307  else { sphi = kInfinity; }
2308  }
2309  else
2310  {
2311  // if towards both >=0 then once inside (after error)
2312  // will remain inside
2313 
2314  if ( (compS >= 0) && (compE >= 0) ) { sphi = kInfinity; }
2315  else { sphi = 0; }
2316  }
2317  }
2318  else if ( (pDistS > 0) && (pDistE < 0) )
2319  {
2320  // Outside full starting plane, inside full ending plane
2321 
2322  if ( fDPhi > pi )
2323  {
2324  if ( compE < 0 )
2325  {
2326  sphi = pDistE/compE ;
2327  xi = p.x() + sphi*v.x() ;
2328  yi = p.y() + sphi*v.y() ;
2329 
2330  // Check intersection in correct half-plane
2331  // (if not -> not leaving phi extent)
2332  //
2333  if( (std::fabs(xi)<=kCarTolerance)&&(std::fabs(yi)<=kCarTolerance) )
2334  {
2335  vphi = std::atan2(v.y(),v.x());
2336  sidephi = kSPhi;
2337  if ( ( (fSPhi-halfAngTolerance) <= vphi)
2338  && ( (ePhi+halfAngTolerance) >= vphi) )
2339  {
2340  sphi = kInfinity;
2341  }
2342  }
2343  else if ( ( yi*cosCPhi - xi*sinCPhi ) <= 0 )
2344  {
2345  sphi = kInfinity ;
2346  }
2347  else // Leaving via Ending phi
2348  {
2349  sidephi = kEPhi ;
2350  if ( pDistE > -halfCarTolerance ) { sphi = 0.; }
2351  }
2352  }
2353  else
2354  {
2355  sphi = kInfinity ;
2356  }
2357  }
2358  else
2359  {
2360  if ( compS >= 0 )
2361  {
2362  if ( compE < 0 )
2363  {
2364  sphi = pDistE/compE ;
2365  xi = p.x() + sphi*v.x() ;
2366  yi = p.y() + sphi*v.y() ;
2367 
2368  // Check intersection in correct half-plane
2369  // (if not -> remain in extent)
2370  //
2371  if( (std::fabs(xi)<=kCarTolerance)
2372  && (std::fabs(yi)<=kCarTolerance) )
2373  {
2374  vphi = std::atan2(v.y(),v.x());
2375  sidephi = kSPhi;
2376  if ( ( (fSPhi-halfAngTolerance) <= vphi)
2377  && ( (ePhi+halfAngTolerance) >= vphi) )
2378  {
2379  sphi = kInfinity;
2380  }
2381  }
2382  else if ( ( yi*cosCPhi - xi*sinCPhi) <= 0 )
2383  {
2384  sphi=kInfinity;
2385  }
2386  else // otherwise leaving via Ending phi
2387  {
2388  sidephi = kEPhi ;
2389  }
2390  }
2391  else sphi=kInfinity;
2392  }
2393  else // leaving immediately by starting phi
2394  {
2395  sidephi = kSPhi ;
2396  sphi = 0 ;
2397  }
2398  }
2399  }
2400  else
2401  {
2402  // Must be pDistS < 0 && pDistE > 0
2403  // Inside full starting plane, outside full ending plane
2404 
2405  if ( fDPhi > pi )
2406  {
2407  if ( compS < 0 )
2408  {
2409  sphi=pDistS/compS;
2410  xi=p.x()+sphi*v.x();
2411  yi=p.y()+sphi*v.y();
2412 
2413  // Check intersection in correct half-plane
2414  // (if not -> not leaving phi extent)
2415  //
2416  if( (std::fabs(xi)<=kCarTolerance)&&(std::fabs(yi)<=kCarTolerance) )
2417  {
2418  vphi = std::atan2(v.y(),v.x()) ;
2419  sidephi = kSPhi;
2420  if ( ( (fSPhi-halfAngTolerance) <= vphi)
2421  && ( (ePhi+halfAngTolerance) >= vphi) )
2422  {
2423  sphi = kInfinity;
2424  }
2425  }
2426  else if ( ( yi*cosCPhi - xi*sinCPhi ) >= 0 )
2427  {
2428  sphi = kInfinity ;
2429  }
2430  else // Leaving via Starting phi
2431  {
2432  sidephi = kSPhi ;
2433  if ( pDistS > -halfCarTolerance ) { sphi = 0; }
2434  }
2435  }
2436  else
2437  {
2438  sphi = kInfinity ;
2439  }
2440  }
2441  else
2442  {
2443  if ( compE >= 0 )
2444  {
2445  if ( compS < 0 )
2446  {
2447  sphi = pDistS/compS ;
2448  xi = p.x()+sphi*v.x() ;
2449  yi = p.y()+sphi*v.y() ;
2450 
2451  // Check intersection in correct half-plane
2452  // (if not -> remain in extent)
2453  //
2454  if( (std::fabs(xi)<=kCarTolerance)
2455  && (std::fabs(yi)<=kCarTolerance))
2456  {
2457  vphi = std::atan2(v.y(),v.x()) ;
2458  sidephi = kSPhi;
2459  if ( ( (fSPhi-halfAngTolerance) <= vphi)
2460  && ( (ePhi+halfAngTolerance) >= vphi) )
2461  {
2462  sphi = kInfinity;
2463  }
2464  }
2465  else if ( ( yi*cosCPhi - xi*sinCPhi ) >= 0 )
2466  {
2467  sphi = kInfinity ;
2468  }
2469  else // otherwise leaving via Starting phi
2470  {
2471  sidephi = kSPhi ;
2472  }
2473  }
2474  else
2475  {
2476  sphi = kInfinity ;
2477  }
2478  }
2479  else // leaving immediately by ending
2480  {
2481  sidephi = kEPhi ;
2482  sphi = 0 ;
2483  }
2484  }
2485  }
2486  }
2487  else
2488  {
2489  // On z axis + travel not || to z axis -> if phi of vector direction
2490  // within phi of shape, Step limited by rmax, else Step =0
2491 
2492  if ( v.x() || v.y() )
2493  {
2494  vphi = std::atan2(v.y(),v.x()) ;
2495  if ((fSPhi-halfAngTolerance < vphi) && (vphi < ePhi+halfAngTolerance))
2496  {
2497  sphi = kInfinity;
2498  }
2499  else
2500  {
2501  sidephi = kSPhi ; // arbitrary
2502  sphi = 0 ;
2503  }
2504  }
2505  else // travel along z - no phi intersection
2506  {
2507  sphi = kInfinity ;
2508  }
2509  }
2510  if ( sphi < snxt ) // Order intersecttions
2511  {
2512  snxt = sphi ;
2513  side = sidephi ;
2514  }
2515  }
2516  if (stheta < snxt ) // Order intersections
2517  {
2518  snxt = stheta ;
2519  side = sidetheta ;
2520  }
2521 
2522  if (calcNorm) // Output switch operator
2523  {
2524  switch( side )
2525  {
2526  case kRMax:
2527  xi=p.x()+snxt*v.x();
2528  yi=p.y()+snxt*v.y();
2529  zi=p.z()+snxt*v.z();
2530  *n=G4ThreeVector(xi/fRmax,yi/fRmax,zi/fRmax);
2531  *validNorm=true;
2532  break;
2533 
2534  case kRMin:
2535  *validNorm=false; // Rmin is concave
2536  break;
2537 
2538  case kSPhi:
2539  if ( fDPhi <= pi ) // Normal to Phi-
2540  {
2541  *n=G4ThreeVector(sinSPhi,-cosSPhi,0);
2542  *validNorm=true;
2543  }
2544  else { *validNorm=false; }
2545  break ;
2546 
2547  case kEPhi:
2548  if ( fDPhi <= pi ) // Normal to Phi+
2549  {
2550  *n=G4ThreeVector(-sinEPhi,cosEPhi,0);
2551  *validNorm=true;
2552  }
2553  else { *validNorm=false; }
2554  break;
2555 
2556  case kSTheta:
2557  if( fSTheta == halfpi )
2558  {
2559  *n=G4ThreeVector(0.,0.,1.);
2560  *validNorm=true;
2561  }
2562  else if ( fSTheta > halfpi )
2563  {
2564  xi = p.x() + snxt*v.x();
2565  yi = p.y() + snxt*v.y();
2566  rho2=xi*xi+yi*yi;
2567  if (rho2)
2568  {
2569  rhoSecTheta = std::sqrt(rho2*(1+tanSTheta2));
2570  *n = G4ThreeVector( xi/rhoSecTheta, yi/rhoSecTheta,
2571  -tanSTheta/std::sqrt(1+tanSTheta2));
2572  }
2573  else
2574  {
2575  *n = G4ThreeVector(0.,0.,1.);
2576  }
2577  *validNorm=true;
2578  }
2579  else { *validNorm=false; } // Concave STheta cone
2580  break;
2581 
2582  case kETheta:
2583  if( eTheta == halfpi )
2584  {
2585  *n = G4ThreeVector(0.,0.,-1.);
2586  *validNorm = true;
2587  }
2588  else if ( eTheta < halfpi )
2589  {
2590  xi=p.x()+snxt*v.x();
2591  yi=p.y()+snxt*v.y();
2592  rho2=xi*xi+yi*yi;
2593  if (rho2)
2594  {
2595  rhoSecTheta = std::sqrt(rho2*(1+tanETheta2));
2596  *n = G4ThreeVector( xi/rhoSecTheta, yi/rhoSecTheta,
2597  -tanETheta/std::sqrt(1+tanETheta2) );
2598  }
2599  else
2600  {
2601  *n = G4ThreeVector(0.,0.,-1.);
2602  }
2603  *validNorm=true;
2604  }
2605  else { *validNorm=false; } // Concave ETheta cone
2606  break;
2607 
2608  default:
2609  G4cout << G4endl;
2610  DumpInfo();
2611  std::ostringstream message;
2612  G4int oldprc = message.precision(16);
2613  message << "Undefined side for valid surface normal to solid."
2614  << G4endl
2615  << "Position:" << G4endl << G4endl
2616  << "p.x() = " << p.x()/mm << " mm" << G4endl
2617  << "p.y() = " << p.y()/mm << " mm" << G4endl
2618  << "p.z() = " << p.z()/mm << " mm" << G4endl << G4endl
2619  << "Direction:" << G4endl << G4endl
2620  << "v.x() = " << v.x() << G4endl
2621  << "v.y() = " << v.y() << G4endl
2622  << "v.z() = " << v.z() << G4endl << G4endl
2623  << "Proposed distance :" << G4endl << G4endl
2624  << "snxt = " << snxt/mm << " mm" << G4endl;
2625  message.precision(oldprc);
2626  G4Exception("G4Sphere::DistanceToOut(p,v,..)",
2627  "GeomSolids1002", JustWarning, message);
2628  break;
2629  }
2630  }
2631  if (snxt == kInfinity)
2632  {
2633  G4cout << G4endl;
2634  DumpInfo();
2635  std::ostringstream message;
2636  G4int oldprc = message.precision(16);
2637  message << "Logic error: snxt = kInfinity ???" << G4endl
2638  << "Position:" << G4endl << G4endl
2639  << "p.x() = " << p.x()/mm << " mm" << G4endl
2640  << "p.y() = " << p.y()/mm << " mm" << G4endl
2641  << "p.z() = " << p.z()/mm << " mm" << G4endl << G4endl
2642  << "Rp = "<< std::sqrt( p.x()*p.x()+p.y()*p.y()+p.z()*p.z() )/mm
2643  << " mm" << G4endl << G4endl
2644  << "Direction:" << G4endl << G4endl
2645  << "v.x() = " << v.x() << G4endl
2646  << "v.y() = " << v.y() << G4endl
2647  << "v.z() = " << v.z() << G4endl << G4endl
2648  << "Proposed distance :" << G4endl << G4endl
2649  << "snxt = " << snxt/mm << " mm" << G4endl;
2650  message.precision(oldprc);
2651  G4Exception("G4Sphere::DistanceToOut(p,v,..)",
2652  "GeomSolids1002", JustWarning, message);
2653  }
2654 
2655  return snxt;
2656 }
2657 
2659 //
2660 // Calculate distance (<=actual) to closest surface of shape from inside
2661 
2662 G4double G4Sphere::DistanceToOut( const G4ThreeVector& p ) const
2663 {
2664  G4double safe=0.0,safeRMin,safeRMax,safePhi,safeTheta;
2665  G4double rho2,rds,rho;
2666  G4double pTheta,dTheta1 = kInfinity,dTheta2 = kInfinity;
2667  rho2=p.x()*p.x()+p.y()*p.y();
2668  rds=std::sqrt(rho2+p.z()*p.z());
2669  rho=std::sqrt(rho2);
2670 
2671 #ifdef G4CSGDEBUG
2672  if( Inside(p) == kOutside )
2673  {
2674  G4int old_prc = G4cout.precision(16);
2675  G4cout << G4endl;
2676  DumpInfo();
2677  G4cout << "Position:" << G4endl << G4endl ;
2678  G4cout << "p.x() = " << p.x()/mm << " mm" << G4endl ;
2679  G4cout << "p.y() = " << p.y()/mm << " mm" << G4endl ;
2680  G4cout << "p.z() = " << p.z()/mm << " mm" << G4endl << G4endl ;
2681  G4cout.precision(old_prc) ;
2682  G4Exception("G4Sphere::DistanceToOut(p)",
2683  "GeomSolids1002", JustWarning, "Point p is outside !?" );
2684  }
2685 #endif
2686 
2687  // Distance to r shells
2688  //
2689  safeRMax = fRmax-rds;
2690  safe = safeRMax;
2691  if (fRmin)
2692  {
2693  safeRMin = rds-fRmin;
2694  safe = std::min( safeRMin, safeRMax );
2695  }
2696 
2697  // Distance to phi extent
2698  //
2699  if ( !fFullPhiSphere )
2700  {
2701  if (rho>0.0)
2702  {
2703  if ((p.y()*cosCPhi-p.x()*sinCPhi)<=0)
2704  {
2705  safePhi=-(p.x()*sinSPhi-p.y()*cosSPhi);
2706  }
2707  else
2708  {
2709  safePhi=(p.x()*sinEPhi-p.y()*cosEPhi);
2710  }
2711  }
2712  else
2713  {
2714  safePhi = 0.0; // Distance to both Phi surfaces (extended)
2715  }
2716  // Both cases above can be improved - in case fRMin > 0.0
2717  // although it may be costlier (good for precise, not fast version)
2718 
2719  safe= std::min(safe, safePhi);
2720  }
2721 
2722  // Distance to Theta extent
2723  //
2724  if ( !fFullThetaSphere )
2725  {
2726  if( rds > 0.0 )
2727  {
2728  pTheta=std::acos(p.z()/rds);
2729  if (pTheta<0) { pTheta+=pi; }
2730  if(fSTheta>0.)
2731  { dTheta1=pTheta-fSTheta;}
2732  if(eTheta<pi)
2733  { dTheta2=eTheta-pTheta;}
2734 
2735  safeTheta=rds*std::sin(std::min(dTheta1, dTheta2) );
2736  }
2737  else
2738  {
2739  safeTheta= 0.0;
2740  // An improvement will be to return negative answer if outside (TODO)
2741  }
2742  safe = std::min( safe, safeTheta );
2743  }
2744 
2745  if (safe<0.0) { safe=0; }
2746  // An improvement to return negative answer if outside (TODO)
2747 
2748  return safe;
2749 }
2750 
2752 //
2753 // G4EntityType
2754 
2755 G4GeometryType G4Sphere::GetEntityType() const
2756 {
2757  return G4String("G4Sphere");
2758 }
2759 
2761 //
2762 // Make a clone of the object
2763 //
2764 G4VSolid* G4Sphere::Clone() const
2765 {
2766  return new G4Sphere(*this);
2767 }
2768 
2770 //
2771 // Stream object contents to an output stream
2772 
2773 std::ostream& G4Sphere::StreamInfo( std::ostream& os ) const
2774 {
2775  G4int oldprc = os.precision(16);
2776  os << "-----------------------------------------------------------\n"
2777  << " *** Dump for solid - " << GetName() << " ***\n"
2778  << " ===================================================\n"
2779  << " Solid type: G4Sphere\n"
2780  << " Parameters: \n"
2781  << " inner radius: " << fRmin/mm << " mm \n"
2782  << " outer radius: " << fRmax/mm << " mm \n"
2783  << " starting phi of segment : " << fSPhi/degree << " degrees \n"
2784  << " delta phi of segment : " << fDPhi/degree << " degrees \n"
2785  << " starting theta of segment: " << fSTheta/degree << " degrees \n"
2786  << " delta theta of segment : " << fDTheta/degree << " degrees \n"
2787  << "-----------------------------------------------------------\n";
2788  os.precision(oldprc);
2789 
2790  return os;
2791 }
2792 
2794 //
2795 // GetPointOnSurface
2796 
2797 G4ThreeVector G4Sphere::GetPointOnSurface() const
2798 {
2799  G4double zRand, aOne, aTwo, aThr, aFou, aFiv, chose, phi, sinphi, cosphi;
2800  G4double height1, height2, slant1, slant2, costheta, sintheta, rRand;
2801 
2802  height1 = (fRmax-fRmin)*cosSTheta;
2803  height2 = (fRmax-fRmin)*cosETheta;
2804  slant1 = std::sqrt(sqr((fRmax - fRmin)*sinSTheta) + height1*height1);
2805  slant2 = std::sqrt(sqr((fRmax - fRmin)*sinETheta) + height2*height2);
2806  rRand = GetRadiusInRing(fRmin,fRmax);
2807 
2808  aOne = fRmax*fRmax*fDPhi*(cosSTheta-cosETheta);
2809  aTwo = fRmin*fRmin*fDPhi*(cosSTheta-cosETheta);
2810  aThr = fDPhi*((fRmax + fRmin)*sinSTheta)*slant1;
2811  aFou = fDPhi*((fRmax + fRmin)*sinETheta)*slant2;
2812  aFiv = 0.5*fDTheta*(fRmax*fRmax-fRmin*fRmin);
2813 
2814  phi = G4RandFlat::shoot(fSPhi, ePhi);
2815  cosphi = std::cos(phi);
2816  sinphi = std::sin(phi);
2817  costheta = G4RandFlat::shoot(cosETheta,cosSTheta);
2818  sintheta = std::sqrt(1.-sqr(costheta));
2819 
2820  if(fFullPhiSphere) { aFiv = 0; }
2821  if(fSTheta == 0) { aThr=0; }
2822  if(eTheta == pi) { aFou = 0; }
2823  if(fSTheta == halfpi) { aThr = pi*(fRmax*fRmax-fRmin*fRmin); }
2824  if(eTheta == halfpi) { aFou = pi*(fRmax*fRmax-fRmin*fRmin); }
2825 
2826  chose = G4RandFlat::shoot(0.,aOne+aTwo+aThr+aFou+2.*aFiv);
2827  if( (chose>=0.) && (chose<aOne) )
2828  {
2829  return G4ThreeVector(fRmax*sintheta*cosphi,
2830  fRmax*sintheta*sinphi, fRmax*costheta);
2831  }
2832  else if( (chose>=aOne) && (chose<aOne+aTwo) )
2833  {
2834  return G4ThreeVector(fRmin*sintheta*cosphi,
2835  fRmin*sintheta*sinphi, fRmin*costheta);
2836  }
2837  else if( (chose>=aOne+aTwo) && (chose<aOne+aTwo+aThr) )
2838  {
2839  if (fSTheta != halfpi)
2840  {
2841  zRand = G4RandFlat::shoot(fRmin*cosSTheta,fRmax*cosSTheta);
2842  return G4ThreeVector(tanSTheta*zRand*cosphi,
2843  tanSTheta*zRand*sinphi,zRand);
2844  }
2845  else
2846  {
2847  return G4ThreeVector(rRand*cosphi, rRand*sinphi, 0.);
2848  }
2849  }
2850  else if( (chose>=aOne+aTwo+aThr) && (chose<aOne+aTwo+aThr+aFou) )
2851  {
2852  if(eTheta != halfpi)
2853  {
2854  zRand = G4RandFlat::shoot(fRmin*cosETheta, fRmax*cosETheta);
2855  return G4ThreeVector (tanETheta*zRand*cosphi,
2856  tanETheta*zRand*sinphi,zRand);
2857  }
2858  else
2859  {
2860  return G4ThreeVector(rRand*cosphi, rRand*sinphi, 0.);
2861  }
2862  }
2863  else if( (chose>=aOne+aTwo+aThr+aFou) && (chose<aOne+aTwo+aThr+aFou+aFiv) )
2864  {
2865  return G4ThreeVector(rRand*sintheta*cosSPhi,
2866  rRand*sintheta*sinSPhi,rRand*costheta);
2867  }
2868  else
2869  {
2870  return G4ThreeVector(rRand*sintheta*cosEPhi,
2871  rRand*sintheta*sinEPhi,rRand*costheta);
2872  }
2873 }
2874 
2876 //
2877 // GetSurfaceArea
2878 
2879 G4double G4Sphere::GetSurfaceArea()
2880 {
2881  if(fSurfaceArea != 0.) {;}
2882  else
2883  {
2884  G4double Rsq=fRmax*fRmax;
2885  G4double rsq=fRmin*fRmin;
2886 
2887  fSurfaceArea = fDPhi*(rsq+Rsq)*(cosSTheta - cosETheta);
2888  if(!fFullPhiSphere)
2889  {
2890  fSurfaceArea = fSurfaceArea + fDTheta*(Rsq-rsq);
2891  }
2892  if(fSTheta >0)
2893  {
2894  G4double acos1=std::acos( std::pow(sinSTheta,2) * std::cos(fDPhi)
2895  + std::pow(cosSTheta,2));
2896  if(fDPhi>pi)
2897  {
2898  fSurfaceArea = fSurfaceArea + 0.5*(Rsq-rsq)*(twopi-acos1);
2899  }
2900  else
2901  {
2902  fSurfaceArea = fSurfaceArea + 0.5*(Rsq-rsq)*acos1;
2903  }
2904  }
2905  if(eTheta < pi)
2906  {
2907  G4double acos2=std::acos( std::pow(sinETheta,2) * std::cos(fDPhi)
2908  + std::pow(cosETheta,2));
2909  if(fDPhi>pi)
2910  {
2911  fSurfaceArea = fSurfaceArea + 0.5*(Rsq-rsq)*(twopi-acos2);
2912  }
2913  else
2914  {
2915  fSurfaceArea = fSurfaceArea + 0.5*(Rsq-rsq)*acos2;
2916  }
2917  }
2918  }
2919  return fSurfaceArea;
2920 }
2921 
2923 //
2924 // Methods for visualisation
2925 
2926 G4VisExtent G4Sphere::GetExtent() const
2927 {
2928  return G4VisExtent(-fRmax, fRmax,-fRmax, fRmax,-fRmax, fRmax );
2929 }
2930 
2931 
2932 void G4Sphere::DescribeYourselfTo ( G4VGraphicsScene& scene ) const
2933 {
2934  scene.AddSolid (*this);
2935 }
2936 
2937 G4Polyhedron* G4Sphere::CreatePolyhedron () const
2938 {
2939  return new G4PolyhedronSphere (fRmin, fRmax, fSPhi, fDPhi, fSTheta, fDTheta);
2940 }
2941 
2942 #endif
G4BoundingEnvelope::CalculateExtent
G4bool CalculateExtent(const EAxis pAxis, const G4VoxelLimits &pVoxelLimits, const G4Transform3D &pTransform3D, G4double &pMin, G4double &pMax) const
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G4Sphere::CheckThetaAngles
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Definition: G4Sphere.hh:237
G4Sphere::Inside
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G4double GetCosStartPhi() const
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static G4bool DiskExtent(G4double rmin, G4double rmax, G4double startPhi, G4double delPhi, G4TwoVector &pmin, G4TwoVector &pmax)
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G4double DistanceToOut(const G4ThreeVector &p, const G4ThreeVector &v, const G4bool calcNorm=G4bool(false), G4bool *validNorm=0, G4ThreeVector *n=0) const
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brief Return the smallest of the two arguments
Definition: G4INCLGlobals.hh:117
kEPhi
Definition: G4Cons.cc:75
G4Sphere::GetInnerRadius
G4double GetInnerRadius() const
kNRMax
Definition: G4Cons.cc:79
G4Sphere::cosHDPhiIT
G4double cosHDPhiIT
Definition: G4Sphere.hh:241
다음에 의해 생성됨 :   doxygen 1.8.5