ATLAS Offline Software
VolumeIntersection.cxx
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1 /*
2  Copyright (C) 2002-2024 CERN for the benefit of the ATLAS collaboration
3 */
4 
6 // VolumeConverter.cxx, (c) ATLAS Detector software
8 
9 #include "TrkDetDescrGeoModelCnv/VolumeIntersection.h"
10 
11 #include "GeoPrimitives/GeoPrimitivesHelpers.h"
12 
13 // Trk
14 #include "TrkVolumes/BevelledCylinderVolumeBounds.h"
15 #include "TrkVolumes/BoundarySurface.h"
16 #include "TrkVolumes/CombinedVolumeBounds.h"
17 #include "TrkVolumes/CuboidVolumeBounds.h"
18 #include "TrkVolumes/CylinderVolumeBounds.h"
19 #include "TrkVolumes/DoubleTrapezoidVolumeBounds.h"
20 #include "TrkVolumes/PrismVolumeBounds.h"
21 #include "TrkVolumes/SimplePolygonBrepVolumeBounds.h"
22 #include "TrkVolumes/SubtractedVolumeBounds.h"
23 #include "TrkVolumes/TrapezoidVolumeBounds.h"
24 
25 // GeoModel
26 #include "GeoModelKernel/GeoShapeShift.h"
27 #include "GeoModelKernel/GeoShapeUnion.h"
28 #include "GeoModelKernel/GeoTrd.h"
29 
30 // STL
31 #include <iostream>
32 namespace{
33  Amg::Transform3D* makeTransform(const Amg::Transform3D& trf) {
34  return std::make_unique<Amg::Transform3D>(trf).release();
35  }
36 }
37 std::pair<bool, std::unique_ptr<Trk::Volume>>
38 Trk::VolumeIntersection::intersect(const Volume& volA,
39  const Volume& volB) {
40 
41  // if combination of shifted polygons, calculable
42  Trk::PolygonCache pgA = polygonXY(volA);
43  Trk::PolygonCache pgB = polygonXY(volB);
44 
45  if (pgA.nVtx > 0 && pgB.nVtx > 0) {
46  // check orientation of xy face
47  Amg::Vector3D a0 = pgA.vertices[1] - pgA.vertices[0];
48  Amg::Vector3D a1 = pgA.vertices[2] - pgA.vertices[1];
49  Amg::Vector3D b0 = pgB.vertices[1] - pgB.vertices[0];
50  Amg::Vector3D b1 = pgB.vertices[2] - pgB.vertices[1];
51 
52  if (std::abs((a0.cross(a1).unit()).dot(b0.cross(b1).unit())) < 1.e-3) {
53  if (std::abs((a0.cross(a1).unit()).dot(b1)) < 1.e-3)
54  pgB = polygonXY(volB, 1); // xy -> yz, only if cuboid-like
55  else if (std::abs((a0.cross(a1).unit()).dot(b0)) < 1.e-3)
56  pgB = polygonXY(volB, 2); // xy -> zx, only if cuboid-like
57  // new check orientation of xy face
58  b0 = pgB.vertices[1] - pgB.vertices[0];
59  b1 = pgB.vertices[2] - pgB.vertices[1];
60  }
61  if (std::abs(std::abs((a0.cross(a1).unit()).dot(b0.cross(b1).unit())) -
62  1.) > 1.e-3) {
63  return std::make_pair(false, nullptr);
64  }
65 
66  Amg::Transform3D trf{Amg::Transform3D::Identity()};
67  const Amg::Vector3D norm = a0.cross(a1).unit();
68  if (norm.z() != 1.) { // rotate to align with z axis
69  trf = Amg::getRotateY3D(-norm.theta()) *
70  Amg::getRotateZ3D(-norm.phi());
71  for (Amg::Vector3D& vertex : pgA.vertices) {
72  vertex = trf * vertex;
73  }
74  for (Amg::Vector3D& vertex : pgB.vertices) {
75  vertex = trf * vertex;
76  }
77  pgA.center = trf * pgA.center;
78  pgB.center = trf * pgB.center;
79  }
80  // overlap in z
81  pgA.minZ = std::min(pgA.vertices[0].z(),
82  2 * pgA.center.z() - pgA.vertices[0].z());
83  pgA.maxZ = std::max(pgA.vertices[0].z(),
84  2 * pgA.center.z() - pgA.vertices[0].z());
85  pgB.minZ = std::min(pgB.vertices[0].z(),
86  2 * pgB.center.z() - pgB.vertices[0].z());
87  pgB.maxZ = std::max(pgB.vertices[0].z(),
88  2 * pgB.center.z() - pgB.vertices[0].z());
89 
90  if (pgA.minZ > pgB.maxZ || pgB.minZ > pgA.maxZ) {
91  return std::make_pair(true, nullptr);
92  } // no overlap in z
93 
94  Trk::PolygonCache result = intersectPgon(pgA, pgB);
95  std::unique_ptr<Trk::Volume> overlap;
96  if (result.nVtx > 0) {
97  auto spb = std::make_unique<Trk::SimplePolygonBrepVolumeBounds>(result.xyVertices, 0.5 * (result.maxZ - result.minZ));
98  Amg::Transform3D transf = trf.inverse() *
99  Amg::Translation3D(0., 0., 0.5 * (result.maxZ + result.minZ));
100  overlap = std::make_unique<Trk::Volume>(makeTransform(transf), spb.release());
101  }
102  return std::make_pair(true, std::move(overlap));
103  } // end shifted polygons
104 
105  return std::make_pair(false, nullptr);
106 }
107 
108 Trk::PolygonCache Trk::VolumeIntersection::intersectPgon(
109  Trk::PolygonCache& pgA, Trk::PolygonCache& pgB) {
110 
111  // retrieve xy vertices (size+1)
112  for (const Amg::Vector3D& vtx : pgA.vertices)
113  pgA.xyVertices.emplace_back(vtx.x(), vtx.y());
114  pgA.xyVertices.emplace_back(pgA.vertices.front().x(), pgA.vertices.front().y());
115  for (const Amg::Vector3D& vtx : pgB.vertices)
116  pgB.xyVertices.emplace_back(vtx.x(), vtx.y());
117  pgB.xyVertices.emplace_back(pgB.vertices.front().x(), pgB.vertices.front().y());
118  // find common
119  for (const std::pair<double, double>& vtx : pgA.xyVertices) {
120  pgA.commonVertices.push_back(inside(vtx, pgB.xyVertices));
121  }
122  for (const std::pair<double, double>& vtx : pgB.xyVertices) {
123  pgB.commonVertices.push_back(inside(vtx, pgA.xyVertices));
124  }
125  // edges
126  for (int ia = 0; ia < pgA.nVtx; ia++) {
127  pgA.edges.emplace_back(
128  pgA.xyVertices[ia + 1].first - pgA.xyVertices[ia].first,
129  pgA.xyVertices[ia + 1].second - pgA.xyVertices[ia].second);
130  }
131  for (int ib = 0; ib < pgB.nVtx; ib++) {
132  pgB.edges.emplace_back(
133  pgB.xyVertices[ib + 1].first - pgB.xyVertices[ib].first,
134  pgB.xyVertices[ib + 1].second - pgB.xyVertices[ib].second);
135  }
136  // edge intersections
137  std::vector<Trk::EdgeCross> edge_cross;
138  for (int ia = 0; ia < pgA.nVtx; ia++) {
139  for (int ib = 0; ib < pgB.nVtx; ib++) {
140  double rs = det(pgA.edges[ia], pgB.edges[ib], false);
141  double qps = det(pgB.xyVertices[ib], pgB.edges[ib], false) -
142  det(pgA.xyVertices[ia], pgB.edges[ib], false);
143  double rpq = det(pgA.edges[ia], pgA.xyVertices[ia], false) -
144  det(pgA.edges[ia], pgB.xyVertices[ib], false);
145  if (rs == 0 && rpq == 0) {
146  double t0 =
147  det(pgA.edges[ia], pgA.edges[ia], true) > 0
148  ? (det(pgB.xyVertices[ib], pgA.edges[ia], true) -
149  det(pgA.xyVertices[ia], pgA.edges[ia], true)) /
150  det(pgA.edges[ia], pgA.edges[ia], true)
151  : 0;
152  double t1 =
153  det(pgA.edges[ia], pgA.edges[ia], true) > 0
154  ? t0 + det(pgB.edges[ib], pgA.edges[ia], true) /
155  det(pgA.edges[ia], pgA.edges[ia], true)
156  : 0;
157  if (t0 > 0 && t0 < 1.)
158  edge_cross.emplace_back(
159  std::make_pair(ia, ib), std::make_pair(t0, -1));
160  if (t1 > 0 && t1 < 1.)
161  edge_cross.emplace_back(
162  std::make_pair(ia, ib), std::make_pair(t1, -1));
163  } else if (rs != 0 && qps / rs > 0 && qps / rs < 1 &&
164  rpq / rs > 0 && rpq / rs < 1) {
165  edge_cross.emplace_back(std::make_pair(ia, ib),
166  std::make_pair(qps / rs, rpq / rs));
167  }
168  }
169  }
170  // collect new vertices : first in edge-crossing format
171  std::vector<Trk::EdgeCross> setVtx;
172  for (int ia = 0; ia < pgA.nVtx; ia++) {
173  if (pgA.commonVertices[ia])
174  setVtx.emplace_back(std::make_pair(ia, -1),
175  std::make_pair(0., -1.));
176  for (const Trk::EdgeCross& ie : edge_cross) {
177  if (ie.edge_id.first == ia) {
178  if (!setVtx.empty() && setVtx.back().edge_id.first == ia &&
179  setVtx.back().edge_pos.first > ie.edge_pos.first)
180  setVtx.insert(setVtx.end() - 1, ie);
181  else
182  setVtx.push_back(ie);
183  }
184  } // loop over edge crossings
185  }
186  // insert common vertices from polygonB
187  for (int ib = 0; ib < pgB.nVtx; ib++) {
188  if (pgB.commonVertices[ib]) {
189  int nlow = ib == 0 ? pgB.nVtx : ib - 1;
190  // find entry with nearest intersection along edge
191  std::vector<Trk::EdgeCross>::iterator it = setVtx.begin();
192  std::vector<Trk::EdgeCross>::iterator itb = setVtx.end();
193  while (it != setVtx.end()) {
194  if ((*it).edge_id.second == nlow) {
195  if (itb == setVtx.end() ||
196  (*it).edge_pos.second > (*itb).edge_pos.second)
197  itb = it;
198  }
199  ++it;
200  }
201  setVtx.insert(
202  itb, Trk::EdgeCross(
203  std::make_pair(ib, -2),
204  std::make_pair(
205  0., -1.))); // -2 indicates vertex coming from B
206  }
207  }
208 
209  // TODO verify the ordering
210 
211  // calculate position of vertices and fill the cache
212  Trk::PolygonCache pgon;
213  pgon.minZ = std::max(pgA.minZ, pgB.minZ);
214  pgon.maxZ = std::min(pgA.maxZ, pgB.maxZ);
215  pgon.nVtx = setVtx.size() < 3 ? 0 : setVtx.size();
216 
217  if (pgon.nVtx < 3)
218  return pgon;
219 
220  for (auto vtx : setVtx) {
221  if (vtx.edge_id.second == -1)
222  pgon.xyVertices.push_back(pgA.xyVertices[vtx.edge_id.first]);
223  else if (vtx.edge_id.second == -2)
224  pgon.xyVertices.push_back(pgB.xyVertices[vtx.edge_id.first]);
225  else { // calculate intersection
226  Amg::Vector2D vpos{pgA.xyVertices[vtx.edge_id.first].first,
227  pgA.xyVertices[vtx.edge_id.first].second};
228  Amg::Vector2D vdir{pgA.edges[vtx.edge_id.first].first,
229  pgA.edges[vtx.edge_id.first].second};
230  Amg::Vector2D vint = vpos + vtx.edge_pos.first * vdir;
231  pgon.xyVertices.emplace_back(vint.x(), vint.y());
232  }
233  }
234 
235  return pgon;
236 }
237 
238 Trk::PolygonCache Trk::VolumeIntersection::polygonXY(const Trk::Volume& vol,
239  int swap) {
240 
241  const CuboidVolumeBounds* box =
242  dynamic_cast<const Trk::CuboidVolumeBounds*>(&(vol.volumeBounds()));
243  const TrapezoidVolumeBounds* trd =
244  dynamic_cast<const Trk::TrapezoidVolumeBounds*>(&(vol.volumeBounds()));
245  const DoubleTrapezoidVolumeBounds* trdd =
246  dynamic_cast<const Trk::DoubleTrapezoidVolumeBounds*>(
247  &(vol.volumeBounds()));
248  const PrismVolumeBounds* prism =
249  dynamic_cast<const Trk::PrismVolumeBounds*>(&(vol.volumeBounds()));
250  const SimplePolygonBrepVolumeBounds* spb =
251  dynamic_cast<const Trk::SimplePolygonBrepVolumeBounds*>(
252  &(vol.volumeBounds()));
253 
254  bool isPolygon = (box || trd || prism || spb || trdd);
255 
256  if (!isPolygon)
257  return Trk::PolygonCache{};
258 
259  Trk::PolygonCache cache;
260 
261  double hz = 0.;
262  std::vector<Amg::Vector3D> vtxLocal;
263 
264  if (swap > 0 &&
265  (box || (trd && trd->minHalflengthX() ==
266  trd->maxHalflengthX()))) { // swapping faces
267 
268  if (swap == 1) {
269  if (box) {
270  hz = box->halflengthX();
271  cache.nVtx = 4;
272  vtxLocal.emplace_back(box->halflengthX(), box->halflengthY(),
273  box->halflengthZ());
274  vtxLocal.emplace_back(box->halflengthX(), -box->halflengthY(),
275  box->halflengthZ());
276  vtxLocal.emplace_back(box->halflengthX(), -box->halflengthY(),
277  -box->halflengthZ());
278  vtxLocal.emplace_back(box->halflengthX(), box->halflengthY(),
279  -box->halflengthZ());
280  } else if (trd) {
281  hz = trd->minHalflengthX();
282  cache.nVtx = 4;
283  vtxLocal.emplace_back(trd->minHalflengthX(), trd->halflengthY(),
284  trd->halflengthZ());
285  vtxLocal.emplace_back(trd->minHalflengthX(),
286  -trd->halflengthY(), trd->halflengthZ());
287  vtxLocal.emplace_back(trd->maxHalflengthX(),
288  -trd->halflengthY(), -trd->halflengthZ());
289  vtxLocal.emplace_back(trd->maxHalflengthX(), trd->halflengthY(),
290  -trd->halflengthZ());
291  }
292  } else if (swap == 2) {
293  if (box) {
294  hz = box->halflengthY();
295  cache.nVtx = 4;
296  vtxLocal.emplace_back(box->halflengthX(), box->halflengthY(),
297  box->halflengthZ());
298  vtxLocal.emplace_back(-box->halflengthX(), box->halflengthY(),
299  box->halflengthZ());
300  vtxLocal.emplace_back(-box->halflengthX(), box->halflengthY(),
301  -box->halflengthZ());
302  vtxLocal.emplace_back(box->halflengthX(), box->halflengthY(),
303  -box->halflengthZ());
304  } else if (trd) {
305  hz = trd->halflengthY();
306  cache.nVtx = 4;
307  vtxLocal.emplace_back(trd->minHalflengthX(), trd->halflengthY(),
308  trd->halflengthZ());
309  vtxLocal.emplace_back(-trd->minHalflengthX(),
310  trd->halflengthY(), trd->halflengthZ());
311  vtxLocal.emplace_back(-trd->minHalflengthX(),
312  trd->halflengthY(), -trd->halflengthZ());
313  vtxLocal.emplace_back(trd->minHalflengthX(), trd->halflengthY(),
314  -trd->halflengthZ());
315  }
316  }
317  cache.hZ = hz;
318  cache.center = vol.transform().translation();
319 
320  for (const Amg::Vector3D& vtxloc : vtxLocal) {
321  Amg::Vector3D vtx = vol.transform() * vtxloc;
322  cache.vertices.push_back(std::move(vtx));
323  }
324  return cache;
325  } // end swap
326 
327  if (box) {
328  hz = box->halflengthZ();
329  cache.nVtx = 4;
330  vtxLocal.emplace_back(box->halflengthX(), box->halflengthY(),
331  box->halflengthZ());
332  vtxLocal.emplace_back(-box->halflengthX(), box->halflengthY(),
333  box->halflengthZ());
334  vtxLocal.emplace_back(-box->halflengthX(), -box->halflengthY(),
335  box->halflengthZ());
336  vtxLocal.emplace_back(box->halflengthX(), -box->halflengthY(),
337  box->halflengthZ());
338  } else if (trd) {
339  hz = trd->halflengthZ();
340  cache.nVtx = 4;
341  vtxLocal.emplace_back(trd->minHalflengthX(), -trd->halflengthY(),
342  trd->halflengthZ());
343  vtxLocal.emplace_back(-trd->minHalflengthX(), -trd->halflengthY(),
344  trd->halflengthZ());
345  vtxLocal.emplace_back(-trd->maxHalflengthX(), trd->halflengthY(),
346  trd->halflengthZ());
347  vtxLocal.emplace_back(trd->maxHalflengthX(), trd->halflengthY(),
348  trd->halflengthZ());
349  } else if (trdd) {
350  hz = trdd->halflengthZ();
351  cache.nVtx = 6;
352  vtxLocal.emplace_back(trdd->maxHalflengthX(), 2 * trdd->halflengthY2(),
353  trdd->halflengthZ());
354  vtxLocal.emplace_back(-trdd->maxHalflengthX(), 2 * trdd->halflengthY2(),
355  trdd->halflengthZ());
356  vtxLocal.emplace_back(-trdd->medHalflengthX(), 0., trdd->halflengthZ());
357  vtxLocal.emplace_back(-trdd->minHalflengthX(),
358  -2 * trdd->halflengthY1(), trdd->halflengthZ());
359  vtxLocal.emplace_back(trdd->minHalflengthX(), -2 * trdd->halflengthY1(),
360  trdd->halflengthZ());
361  vtxLocal.emplace_back(trdd->medHalflengthX(), 0., trdd->halflengthZ());
362  } else if (prism) {
363  hz = prism->halflengthZ();
364  const std::vector<std::pair<double, double>> vtcs = prism->xyVertices();
365  for (const auto& vtc : vtcs)
366  vtxLocal.emplace_back(vtc.first, vtc.second, prism->halflengthZ());
367  cache.nVtx = vtcs.size();
368  } else if (spb) {
369  hz = spb->halflengthZ();
370  const std::vector<std::pair<double, double>> vtcs = spb->xyVertices();
371  for (const auto& vtc : vtcs)
372  vtxLocal.emplace_back(vtc.first, vtc.second, spb->halflengthZ());
373  cache.nVtx = vtcs.size();
374  }
375 
376  cache.hZ = hz;
377  cache.center = vol.transform().translation();
378 
379  for (const Amg::Vector3D& vtxloc : vtxLocal) {
380  Amg::Vector3D vtx = vol.transform() * vtxloc;
381  cache.vertices.push_back(std::move(vtx));
382  }
383 
384  return cache;
385 }
386 
387 bool Trk::VolumeIntersection::inside(
388  const std::pair<double, double>& vtx,
389  const std::vector<std::pair<double, double>>& pgon) {
390 
391  // GM code
392  bool in = false;
393  size_t nv = pgon.size();
394  for (size_t i = 0, k = nv - 1; i < nv; k = i++) {
395  if ((pgon[i].second > vtx.second) != (pgon[k].second > vtx.second)) {
396  double ctg = (pgon[k].first - pgon[i].first) /
397  (pgon[k].second - pgon[i].second);
398  in ^= (vtx.first <
399  (vtx.second - pgon[i].second) * ctg + pgon[i].first);
400  }
401  }
402  return in;
403 }
404 
405 double Trk::VolumeIntersection::det(const std::pair<double, double>& a,
406  const std::pair<double, double>& b,
407  bool dot) {
408 
409  if (dot)
410  return (a.first * b.first + a.second * b.second);
411 
412  return (a.first * b.second - a.second * b.first);
413 }
414 
415 std::pair<bool, std::unique_ptr<Trk::Volume>>
416 Trk::VolumeIntersection::intersectApproximative(const Volume& volA,
417  const Volume& volB) {
418 
419  // if combination of shifted polygons, calculable
420  Trk::PolygonCache pgA = polygonXY(volA);
421  Trk::PolygonCache pgB = polygonXY(volB);
422 
423  const Trk::CylinderVolumeBounds *cylA{nullptr}, *cylB{nullptr};
424  if (pgA.nVtx == 0)
425  cylA = dynamic_cast<const Trk::CylinderVolumeBounds*>(
426  &(volA.volumeBounds()));
427  if (pgB.nVtx == 0)
428  cylB = dynamic_cast<const Trk::CylinderVolumeBounds*>(
429  &(volB.volumeBounds()));
430 
431  if (cylA && cylB) {
432  double distance_center = (volA.center() - volB.center()).norm();
433  if (distance_center >
434  std::hypot(cylA->outerRadius(), cylA->halflengthZ()) +
435  std::hypot(cylB->outerRadius(), cylB->halflengthZ())) {
436  return std::make_pair(true, nullptr);
437  }
438  }
439 
440  if (pgA.nVtx > 0 && pgB.nVtx > 0) {
441  // check orientation of xy face
442  Amg::Vector3D a0{pgA.vertices[1] - pgA.vertices[0]};
443  Amg::Vector3D a1{pgA.vertices[2] - pgA.vertices[1]};
444  Amg::Vector3D b0{pgB.vertices[1] - pgB.vertices[0]};
445  Amg::Vector3D b1{pgB.vertices[2] - pgB.vertices[1]};
446  if (std::abs((b0.cross(b1).unit()).dot(a0.cross(a1).unit())) < 1.e-3) {
447  if (std::abs((b0.cross(b1).unit()).dot(a1)) < 1.e-3)
448  pgA = polygonXY(volA, 1); // xy -> yz, only if cuboid-like
449  else if (std::abs((b0.cross(b1).unit()).dot(a0)) < 1.e-3)
450  pgA = polygonXY(volA, 2); // xy -> zx, only if cuboid-like
451  // new check orientation of xy face
452  a0 = pgA.vertices[1] - pgA.vertices[0];
453  a1 = pgA.vertices[2] - pgA.vertices[1];
454  }
455  if (std::abs(std::abs((b0.cross(b1).unit()).dot(a0.cross(a1).unit())) -
456  1.) > 1.e-3) {
457  return std::make_pair(false, nullptr);
458  }
459 
460  Amg::Transform3D trf{Amg::Transform3D::Identity()};
461  Amg::Vector3D norm = a0.cross(a1).unit();
462  if (norm.z() != 1.) { // rotate to align with z axis
463  trf = Amg::AngleAxis3D(-norm.theta(), Amg::Vector3D::UnitY()) *
464  Amg::AngleAxis3D(-norm.phi(), Amg::Vector3D::UnitZ());
465 
466  for (Amg::Vector3D& vtx : pgA.vertices) {
467  vtx = trf * vtx;
468  }
469  for (Amg::Vector3D& vtx : pgB.vertices) {
470  vtx = trf * vtx;
471  }
472  pgA.center = trf * pgA.center;
473  pgB.center = trf * pgB.center;
474  }
475  // overlap in z
476  pgA.minZ = std::min(pgA.vertices[0].z(),
477  2 * pgA.center.z() - pgA.vertices[0].z());
478  pgA.maxZ = std::max(pgA.vertices[0].z(),
479  2 * pgA.center.z() - pgA.vertices[0].z());
480  pgB.minZ = std::min(pgB.vertices[0].z(),
481  2 * pgB.center.z() - pgB.vertices[0].z());
482  pgB.maxZ = std::max(pgB.vertices[0].z(),
483  2 * pgB.center.z() - pgB.vertices[0].z());
484 
485  if (pgA.minZ > pgB.maxZ || pgB.minZ > pgA.maxZ) {
486  return std::make_pair(true, nullptr);
487  } // no overlap in z
488 
489  Trk::PolygonCache result = intersectPgon(pgA, pgB);
490  std::unique_ptr<Trk::Volume> overlap{};
491  if (result.nVtx > 0) {
492  auto spb = std::make_unique<Trk::SimplePolygonBrepVolumeBounds>(result.xyVertices,
493  0.5 * (result.maxZ - result.minZ));
494  Amg::Transform3D transf = trf.inverse() *
495  Amg::Translation3D(0., 0., 0.5 * (result.maxZ + result.minZ));
496  overlap = std::make_unique<Trk::Volume>(makeTransform(transf), spb.release());
497  }
498  return std::make_pair(true, std::move(overlap));
499  } // end shifted polygons
500 
501  return std::make_pair(false, nullptr);
502 }
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