Chaste Commit::baa90ac2819b962188b7562f2326be23c47859a7
VoronoiVertexMeshGenerator.cpp
1/*
2
3Copyright (c) 2005-2024, University of Oxford.
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34*/
35
36#include "VoronoiVertexMeshGenerator.hpp"
37#include <boost/make_shared.hpp>
38#include <boost/shared_ptr.hpp>
39
40#if BOOST_VERSION >= 105200
41
42using boost::polygon::voronoi_builder;
43using boost::polygon::voronoi_diagram;
44typedef boost::polygon::point_data<int> boost_point;
45
47 unsigned numElementsY,
48 unsigned numRelaxationSteps,
49 double elementTargetArea)
50 : mpMesh(nullptr),
51 mpTorMesh(nullptr),
52 mNumElementsX(numElementsX),
53 mNumElementsY(numElementsY),
54 mNumRelaxationSteps(numRelaxationSteps),
55 mElementTargetArea(elementTargetArea),
56 mTol(1e-7),
57 mMaxExpectedNumSidesPerPolygon(17)
58{
59 this->ValidateInputAndSetMembers();
60 this->GenerateVoronoiMesh();
61}
62
63void VoronoiVertexMeshGenerator::GenerateVoronoiMesh()
64{
71 // Get initial seed locations
72 std::vector<c_vector<double, 2> > seed_locations = this->GetInitialPointLocations();
73 this->ValidateSeedLocations(seed_locations);
74
75 // We now create the initial Voronoi tessellation. This method updates mpMesh.
76 this->CreateVoronoiTessellation(seed_locations);
77
82 for (unsigned relaxation = 0 ; relaxation < mNumRelaxationSteps ; relaxation++)
83 {
84 seed_locations.clear();
85 seed_locations = this->GetElementCentroidsFromMesh();
86
87 this->CreateVoronoiTessellation(seed_locations);
88 }
89
90 // We need to modify the node locations to achieve the correct target average element area
91 double scale_factor = double(mMaxNumElems) * sqrt(mElementTargetArea);
92 for (unsigned node_idx = 0 ; node_idx < mpMesh->GetNumNodes() ; node_idx++)
93 {
94 c_vector<double, 2>& node_location = mpMesh->GetNode(node_idx)->rGetModifiableLocation();
95 node_location *= scale_factor;
96 }
97}
98
99boost::shared_ptr<MutableVertexMesh<2,2> > VoronoiVertexMeshGenerator::GetMesh()
100{
101 return mpMesh;
102}
103
104boost::shared_ptr<MutableVertexMesh<2,2> > VoronoiVertexMeshGenerator::GetMeshAfterReMesh()
105{
106 mpMesh->ReMesh();
107 return mpMesh;
108}
109
110boost::shared_ptr<Toroidal2dVertexMesh> VoronoiVertexMeshGenerator::GetToroidalMesh()
111{
112 /*
113 * METHOD OUTLINE:
114 *
115 * 1. Copy nodes and elements from mpMesh into a new MutableVertexMesh, so no data is shared between mpMesh and the
116 * nodes and elements we will be working with. There are no available copy constructors, so this is done from
117 * scratch.
118 *
119 * 2. Identify which nodes on the boundary are congruent to each other. This is done by recursively using the
120 * helper function CheckForCongruentNodes().
121 *
122 * 3. Create mpTorMesh by copying the subset of remaining nodes and all elements in the new MutableVertexMesh.
123 * Some elements have been modified to replace nodes by congruent partner nodes and some nodes have been deleted.
124 */
125
126 // The width and height of the mesh for periodicity purposes
127 double width = mNumElementsX * sqrt(mElementTargetArea);
128 double height = mNumElementsY * sqrt(mElementTargetArea);
129
130 // We need to construct new nodes and elements so we don't have mpTorMesh sharing data with mpMesh
131 std::vector<Node<2>*> new_nodes(mpMesh->GetNumNodes());
132 std::vector<VertexElement<2,2>*> new_elems(mpMesh->GetNumElements());
133
134 // Copy nodes
135 for (unsigned node_counter = 0 ; node_counter < mpMesh->GetNumNodes() ; node_counter++)
136 {
137 Node<2>* p_node_to_copy = mpMesh->GetNode(node_counter);
138
139 // Get all the information about the node we are copying
140 unsigned copy_index = p_node_to_copy->GetIndex();
141 bool copy_is_boundary = p_node_to_copy->IsBoundaryNode();
142 const c_vector<double, 2>& copy_location = p_node_to_copy->rGetLocation();
143
144 // There should not be any 'gaps' in node numbering, but we will assert just to make sure
145 assert(copy_index < mpMesh->GetNumNodes());
146
147 // Create a new node and place it in index order. Every node in a periodic mesh is non-boundary.
148 new_nodes[copy_index] = new Node<2>(copy_index, copy_location, copy_is_boundary);
149 }
150
151 // Copy elements
152 for (unsigned elem_counter = 0; elem_counter < mpMesh->GetNumElements(); elem_counter++)
153 {
154 VertexElement<2,2>* p_elem_to_copy = mpMesh->GetElement(elem_counter);
155
156 // Get the information relating to the element we are copying
157 unsigned copy_index = p_elem_to_copy->GetIndex();
158 unsigned copy_num_nodes = p_elem_to_copy->GetNumNodes();
159
160 // There should not be any 'gaps' in element numbering, but we will assert just to make sure
161 assert(copy_index < mpMesh->GetNumElements());
162
163 // The vertex element is created from a vector of nodes
164 std::vector<Node<2>*> nodes_this_elem;
165
166 // Loop through the nodes in p_elem_to_copy and add the corresponding nodes that we have already copied
167 for (unsigned node_local_idx = 0 ; node_local_idx < copy_num_nodes ; node_local_idx++)
168 {
169 Node<2>* p_local_node = p_elem_to_copy->GetNode(node_local_idx);
170 unsigned local_node_global_idx = p_local_node->GetIndex();
171 nodes_this_elem.push_back(new_nodes[local_node_global_idx]);
172 }
173
174 // Create a new node and place it in index order
175 new_elems[copy_index] = new VertexElement<2,2>(copy_index, nodes_this_elem);
176 }
177
178 // We can now create the mesh with new_elements and the subset of new_nodes
179 MutableVertexMesh<2,2>* p_temp_mesh = new MutableVertexMesh<2,2>(new_nodes, new_elems);
180
181 /*
182 * Recursively associate congruent nodes.
183 *
184 * For each node currently on the boundary, we loop through all other boundary nodes and check against all eight
185 * possible congruent locations. If any one coincides, we replace the identified node with its congruent partner,
186 * delete and remove the identified node from the mesh, and start again from scratch.
187 *
188 * If a node has no congruent partners, we simply mark it as non-boundary, as it is then a node that needs to appear
189 * in the final toroidal mesh.
190 *
191 * This recursion is guaranteed to terminate as the number of boundary nodes decreases by precisely one each time
192 * CheckForCongruentNodes() is called, and CheckForCongruentNodes() returns false if there are no boundary nodes.
193 */
194 bool re_check = true;
195
196 while (re_check)
197 {
198 re_check = this->CheckForCongruentNodes(p_temp_mesh, width, height);
199 }
200
201 // We now copy the nodes and elements into a new toroidal mesh, and delete p_temp_mesh
202 new_nodes.clear();
203 new_nodes.resize(p_temp_mesh->GetNumNodes());
204
205 new_elems.clear();
206 new_elems.resize(p_temp_mesh->GetNumElements());
207
208 // Copy nodes
209 for (unsigned node_counter = 0 ; node_counter < p_temp_mesh->GetNumNodes() ; node_counter++)
210 {
211 Node<2>* p_node_to_copy = p_temp_mesh->GetNode(node_counter);
212
213 // Get all the information about the node we are copying
214 unsigned copy_index = p_node_to_copy->GetIndex();
215 const c_vector<double, 2>& copy_location = p_node_to_copy->rGetLocation();
216
217 // No nodes should be boundary nodes
218 assert(!p_node_to_copy->IsBoundaryNode());
219
220 // There should not be any 'gaps' in node numbering, but we will assert just to make sure
221 assert(copy_index < p_temp_mesh->GetNumNodes());
222
223 // Create a new node and place it in index order. Every node in a periodic mesh is non-boundary.
224 new_nodes[copy_index] = new Node<2>(copy_index, copy_location, false);
225 }
226
227 // Copy elements
228 for (unsigned elem_counter = 0; elem_counter < p_temp_mesh->GetNumElements(); elem_counter++)
229 {
230 VertexElement<2,2>* p_elem_to_copy = p_temp_mesh->GetElement(elem_counter);
231
232 // Get the information relating to the element we are copying
233 unsigned copy_index = p_elem_to_copy->GetIndex();
234 unsigned copy_num_nodes = p_elem_to_copy->GetNumNodes();
235
236 // There should not be any 'gaps' in element numbering, but we will assert just to make sure
237 assert(copy_index < p_temp_mesh->GetNumElements());
238
239 // The vertex element is created from a vector of nodes
240 std::vector<Node<2>*> nodes_this_elem;
241
242 // Loop through the nodes in p_elem_to_copy and add the corresponding nodes that we have already copied
243 for (unsigned node_local_idx = 0 ; node_local_idx < copy_num_nodes ; node_local_idx++)
244 {
245 Node<2>* p_local_node = p_elem_to_copy->GetNode(node_local_idx);
246
247 unsigned local_node_global_idx = p_local_node->GetIndex();
248
249 nodes_this_elem.push_back(new_nodes[local_node_global_idx]);
250 }
251
252 // Create a new node and place it in index order
253 new_elems[copy_index] = new VertexElement<2,2>(copy_index, nodes_this_elem);
254 }
255
256 delete p_temp_mesh;
257
258 /*
259 * We now create the mesh with new_elements and new_nodes. We immediately call ReMesh() to tidy up any short edges.
260 *
261 * We then reposition all nodes to be within the box [0, width]x[0, height] to make mesh look nicer when visualised.
262 */
263 mpTorMesh = boost::make_shared<Toroidal2dVertexMesh>(width, height, new_nodes, new_elems);
264
265 mpTorMesh->ReMesh();
266
267 c_vector<double, 2> min_x_y;
268 min_x_y[0] = DBL_MAX;
269 min_x_y[1] = DBL_MAX;
270
271 // First loop is to calculate the correct offset, min_x_y
272 for (unsigned node_idx = 0 ; node_idx < mpTorMesh->GetNumNodes() ; node_idx++)
273 {
274 const c_vector<double, 2>& r_this_node_location = mpTorMesh->GetNode(node_idx)->rGetLocation();
275
276 if (r_this_node_location[0] < min_x_y[0])
277 {
278 min_x_y[0] = r_this_node_location[0];
279 }
280 if (r_this_node_location[1] < min_x_y[1])
281 {
282 min_x_y[1] = r_this_node_location[1];
283 }
284 }
285
286 // Second loop applies the offset, min_x_y, to each node in the mesh
287 for (unsigned node_idx = 0 ; node_idx < mpTorMesh->GetNumNodes() ; node_idx++)
288 {
289 mpTorMesh->GetNode(node_idx)->rGetModifiableLocation() -= min_x_y;
290 }
291
292 // Third loop is to reposition any nodes that are now outside the bounding rectangle
293 for (unsigned node_idx = 0 ; node_idx < mpTorMesh->GetNumNodes() ; node_idx++)
294 {
295 if (mpTorMesh->GetNode(node_idx)->rGetLocation()[0] >= width)
296 {
297 mpTorMesh->GetNode(node_idx)->rGetModifiableLocation()[0] -= width;
298 }
299 if (mpTorMesh->GetNode(node_idx)->rGetLocation()[1] >= height)
300 {
301 mpTorMesh->GetNode(node_idx)->rGetModifiableLocation()[1] -= height;
302 }
303 }
304
305 return mpTorMesh;
306}
307
308bool VoronoiVertexMeshGenerator::CheckForCongruentNodes(MutableVertexMesh<2,2>* pMesh, double width, double height)
309{
310 // First find all the current boundary nodes in pMesh
311 std::vector<Node<2>*> boundary_nodes;
312 for (unsigned node_idx = 0 ; node_idx < pMesh->GetNumNodes() ; node_idx++)
313 {
314 Node<2>* p_node = pMesh->GetNode(node_idx);
315
316 if (p_node->IsBoundaryNode())
317 {
318 boundary_nodes.push_back(p_node);
319 }
320 }
321
322 // If there are no boundary nodes, return false (we're done checking congruencies)
323 if (boundary_nodes.empty())
324 {
325 return false;
326 }
327
328 // Otherwise, calculate the eight possible congruent locations for the current node
329 Node<2>* p_node_a = *(boundary_nodes.begin());
330 c_vector<double, 2> node_a_pos = p_node_a->rGetLocation();
331 std::vector<c_vector<double,2> > congruent_locations(8, node_a_pos);
332
333 congruent_locations[0][0] += width;
334
335 congruent_locations[1][1] += height;
336
337 congruent_locations[2][0] -= width;
338
339 congruent_locations[3][1] -= height;
340
341 congruent_locations[4][0] += width;
342 congruent_locations[4][1] += height;
343
344 congruent_locations[5][0] -= width;
345 congruent_locations[5][1] += height;
346
347 congruent_locations[6][0] -= width;
348 congruent_locations[6][1] -= height;
349
350 congruent_locations[7][0] += width;
351 congruent_locations[7][1] -= height;
352
353 // Loop over all other boundary nodes
354 for (unsigned node_b_counter = 0; node_b_counter < boundary_nodes.size(); node_b_counter++)
355 {
356 // Get the index of the current boundary node, and the corresponding node from the mesh
357 unsigned node_b_idx = boundary_nodes[node_b_counter]->GetIndex();
358 Node<2>* p_mesh_node_b = pMesh->GetNode(node_b_idx);
359
360 if (p_node_a == p_mesh_node_b)
361 {
362 continue;
363 }
364
365 c_vector<double, 2> node_b_pos = p_mesh_node_b->rGetLocation();
366
367 // Loop over the eight possible congruent locations and check for coincidence of location
368 for (unsigned pos = 0 ; pos < congruent_locations.size() ; pos++)
369 {
370 if (norm_inf(node_b_pos - congruent_locations[pos]) < mTol)
371 {
372 // Once we find a congruent location, we replace that node in all containing elements
373 std::set<unsigned> containing_elems = p_mesh_node_b->rGetContainingElementIndices();
374
375 assert(containing_elems.size() > 0);
376
377 for (std::set<unsigned>::iterator it = containing_elems.begin() ; it != containing_elems.end() ; ++it)
378 {
379 VertexElement<2,2>* p_this_elem = pMesh->GetElement(*it);
380 unsigned local_idx = p_this_elem->GetNodeLocalIndex(p_mesh_node_b->GetIndex());
381
382 assert(local_idx < UINT_MAX);
383
384 p_this_elem->AddNode(p_node_a, local_idx);
385 p_this_elem->DeleteNode(local_idx);
386 }
387
388 // Delete the node_b and remove it from the mesh, and return true to start checking again from scratch
389 pMesh->DeleteNodePriorToReMesh(p_mesh_node_b->GetIndex());
390 pMesh->RemoveDeletedNodes();
391 return true;
392 }
393 }
394 }
395
396 /*
397 * If we have checked p_node_a against all node_b candidates and have not found a congruent location, p_node_a can
398 * be re-tagged as a non-boundary node, and so will not get checked again next time this function is called.
399 */
400 p_node_a->SetAsBoundaryNode(false);
401
402 return true;
403}
404
405std::vector<c_vector<double, 2> > VoronoiVertexMeshGenerator::GetInitialPointLocations()
406{
407 // Create a vector which contains mTotalNumElements spaces
408 std::vector<c_vector<double, 2> > seed_points(mTotalNumElements);
409
411
412 // Create the correct number of suitably scaled random numbers
413 for (unsigned point_idx = 0 ; point_idx < mTotalNumElements ; point_idx++)
414 {
415 seed_points[point_idx][0] = p_rand_gen->ranf() * mMultiplierInX;
416 seed_points[point_idx][1] = p_rand_gen->ranf() * mMultiplierInY;
417 }
418
419 return seed_points;
420}
421
422std::vector<c_vector<double, 2> > VoronoiVertexMeshGenerator::GetElementCentroidsFromMesh()
423{
424 assert(mpMesh->GetNumElements() == mNumElementsX * mNumElementsY);
425
426 std::vector<c_vector<double, 2> > element_centroids;
427
428 // Loop over all elements in the mesh
429 for (unsigned elem_idx = 0; elem_idx < mpMesh->GetNumElements(); elem_idx++)
430 {
431 // Get the current centroid of the element
432 c_vector<double, 2> this_centroid = mpMesh->GetCentroidOfElement(elem_idx);
433
440 // Account for possible wrap-around in the x-direction
441 if (this_centroid[0] < 0.0)
442 {
443 this_centroid[0] += mMultiplierInX;
444 }
445 else if (this_centroid[0] > mMultiplierInX)
446 {
447 this_centroid[0] -= mMultiplierInX;
448 }
449
450 // Account for possible wrap-around in the y-direction
451 if (this_centroid[1] < 0.0)
452 {
453 this_centroid[1] += mMultiplierInY;
454 }
455 else if (this_centroid[1] > mMultiplierInY)
456 {
457 this_centroid[1] -= mMultiplierInY;
458 }
459
460 element_centroids.push_back(this_centroid);
461 }
462
463 return element_centroids;
464}
465
466void VoronoiVertexMeshGenerator::CreateVoronoiTessellation(std::vector<c_vector<double, 2> >& rSeedLocations)
467{
468 // Clear the mesh nodes and elements, as they will be replaced in this method
469 std::vector<Node<2>*> nodes;
470 std::vector<VertexElement<2, 2>* > elements;
471
479 // Datatype is boost::polygon::point_data<int>
480 std::vector<boost_point> points;
481
482 // Take the locations and map them to integers in a subset of [0, INT_MAX/2] x [0, INT_MAX/2]
483 for (unsigned point_idx = 0 ; point_idx < rSeedLocations.size() ; point_idx++)
484 {
485 // Calculate the correct integer gridpoints
486 int point_x = int( floor( (rSeedLocations[point_idx][0] * mSamplingMultiplier) + 0.5) );
487 int point_y = int( floor( (rSeedLocations[point_idx][1] * mSamplingMultiplier) + 0.5) );
488
489 points.push_back( boost_point(point_x, point_y) );
490 }
491
492 // Define offset vectors for the 3 by 3 tessellation
493 std::vector<boost_point> offsets;
494 offsets.push_back( boost_point(-mMaxIntX, mMaxIntY) );
495 offsets.push_back( boost_point( 0, mMaxIntY) );
496 offsets.push_back( boost_point( mMaxIntX, mMaxIntY) );
497 offsets.push_back( boost_point( mMaxIntX, 0) );
498 offsets.push_back( boost_point( mMaxIntX, -mMaxIntY) );
499 offsets.push_back( boost_point( 0, -mMaxIntY) );
500 offsets.push_back( boost_point(-mMaxIntX, -mMaxIntY) );
501 offsets.push_back( boost_point(-mMaxIntX, 0) );
502
503 // Add all the points in the tessellation to the vector of boost points so in total there are 9 copies of each
504 // seed location, suitably tiled.
505 for (unsigned rep = 0; rep < offsets.size(); rep++)
506 {
507 boost_point offset = offsets[rep];
508 for (unsigned point_idx = 0; point_idx < rSeedLocations.size(); point_idx++)
509 {
510 boost_point new_point = boost_point(points[point_idx].x() + offset.x(), points[point_idx].y() + offset.y());
511 points.push_back(new_point);
512 }
513 }
514
530 // Construct the Voronoi tessellation of these 9 x mTotalNumElements points
531 voronoi_diagram<double> vd;
532 construct_voronoi(points.begin(), points.end(), &vd);
533
534 // Loop over the cells in the voronoi diagram to find nodes for our mesh
535 for (voronoi_diagram<double>::const_cell_iterator it = vd.cells().begin();
536 it != vd.cells().end();
537 ++it)
538 {
539 // Get a reference to the current cell
540 const voronoi_diagram<double>::cell_type& cell = *it;
541
542 // The cells we care about are exactly those whose source_index is less than the size of the locations vector
543 // (i.e. those cells in the central portion of the 3x3 tessellation of source points)
544 if (cell.source_index() < rSeedLocations.size())
545 {
546 // We create a vector of nodes, which will be used to create a MutableElement
547 std::vector<Node<2>*> nodes_this_elem;
548
549 // Loop over the edges of the current cell
550 const voronoi_diagram<double>::edge_type *edge = cell.incident_edge();
551
552 do
553 {
554 if (edge->is_primary())
555 {
556 // Calculate the location corresponding to the location of vertex0 of the current edge
557 double x_location = (edge->vertex0()->x()) / mSamplingMultiplier;
558 double y_location = (edge->vertex0()->y()) / mSamplingMultiplier;
559
560 // Create a node at this location. Default to non-boundary node; this will be updated later
561 Node<2>* p_this_node = new Node<2>(nodes.size(), false, x_location, y_location);
562
570 unsigned existing_node_idx = UINT_MAX;
571
572 for (unsigned node_idx = 0; node_idx < nodes.size(); node_idx++)
573 {
574 // Grab the existing node location
575 const c_vector<double, 2>& r_existing_node_location = nodes[node_idx]->rGetLocation();
576
577 // Equality here is determined entirely on coincidence of position
578 if (fabs(r_existing_node_location[0] - p_this_node->rGetLocation()[0]) < DBL_EPSILON)
579 {
580 if (fabs(r_existing_node_location[1] - p_this_node->rGetLocation()[1]) < DBL_EPSILON)
581 {
582 // If the nodes match, return the existing node index
583 existing_node_idx = node_idx;
584 }
585 }
586 }
587
588 if (existing_node_idx < UINT_MAX)
589 {
590 // The node was already in nodes vector, and its index is the variable 'existing_node'
591 nodes_this_elem.push_back(nodes[existing_node_idx]);
592 delete p_this_node;
593 }
594 else
595 {
596 // The node does not yet exist - we add it to the nodes vector
597 nodes.push_back(p_this_node);
598 nodes_this_elem.push_back(p_this_node);
599 }
600
601 // Move to the next edge
602 edge = edge->next();
603 }
604
605 } while (edge != cell.incident_edge());
606
607 // Add a new VertexElement to the mElements vector
608 elements.push_back(new VertexElement<2,2>(elements.size(), nodes_this_elem));
609 }
610 }
611
612 // Loop over the cells in the voronoi diagram to identify boundary nodes
613 for (voronoi_diagram<double>::const_cell_iterator it = vd.cells().begin();
614 it != vd.cells().end();
615 ++it)
616 {
617 // Get a reference to the current cell
618 const voronoi_diagram<double>::cell_type& cell = *it;
619
620 // The cells we care about are exactly those whose source_index is greater than the size of the locations vector
621 // (i.e. those cells in the outside eight portions of the 3x3 tessellation of source points)
622 if (cell.source_index() >= rSeedLocations.size())
623 {
624 // Loop over the edges of the current cell
625 const voronoi_diagram<double>::edge_type *edge = cell.incident_edge();
626
627 do
628 {
629 /*
630 * Break out of the do-while if there is an infinite edge; we needn't care about cells at the very edge.
631 */
632 if (edge->is_infinite())
633 {
634 break;
635 }
636
637 if (edge->is_primary())
638 {
639 c_vector<double, 2> vertex_location;
640
641 // Get the location of vertex0 of the current edge
642 vertex_location[0] = (edge->vertex0()->x()) / mSamplingMultiplier;
643 vertex_location[1] = (edge->vertex0()->y()) / mSamplingMultiplier;
644
645 /*
646 * Check whether this location coincides with one of our nodes; if it does, it must be a boundary
647 * node
648 */
649 for (unsigned node_idx = 0 ; node_idx < nodes.size() ; node_idx++)
650 {
651 // Grab the existing node location
652 const c_vector<double, 2>& r_existing_node_location = nodes[node_idx]->rGetLocation();
653
654 // Equality here is determined entirely on coincidence of position
655 if (fabs(r_existing_node_location[0] - vertex_location[0]) < DBL_EPSILON)
656 {
657 if (fabs(r_existing_node_location[1] - vertex_location[1]) < DBL_EPSILON)
658 {
659 // If the locations match, tag the node as being on the boundary
660 nodes[node_idx]->SetAsBoundaryNode(true);
661 }
662 }
663 }
664 // Move to the next edge
665 edge = edge->next();
666 }
667
668 } while (edge != cell.incident_edge());
669 }
670 }
671
672 // Create a new mesh with the current vector of nodes and elements
673 if (mpMesh)
674 {
675 mpMesh.reset();
676 }
677 mpMesh = boost::make_shared<MutableVertexMesh<2,2> >(nodes, elements);
678}
679
680void VoronoiVertexMeshGenerator::ValidateInputAndSetMembers()
681{
682 // Validate inputs
683 if ((mNumElementsX < 2) || (mNumElementsY < 2))
684 {
685 EXCEPTION("Need at least 2 by 2 cells");
686 }
687
688 if (mElementTargetArea <= 0.0)
689 {
690 EXCEPTION("Specified target area must be strictly positive");
691 }
692
693 // The total number of elements requested
694 mTotalNumElements = mNumElementsX * mNumElementsY;
695
696 // Max of the numbers of elements across and up
697 mMaxNumElems = std::max(mNumElementsX, mNumElementsY);
698
699 // The multipliers necessary in x and y to ensure all seed points are in [0,1]x[0,1]
700 mMultiplierInX = double(mNumElementsX) / double(mMaxNumElems);
701 mMultiplierInY = double(mNumElementsY) / double(mMaxNumElems);
702
703 // Floating point representation of INT_MAX/2
704 mSamplingMultiplier = 0.5 * double(INT_MAX);
705
706 // The max integer that a seed point could be mapped to when discretising
707 mMaxIntX = int( floor( (mMultiplierInX * mSamplingMultiplier) + 0.5 ) );
708 mMaxIntY = int( floor( (mMultiplierInY * mSamplingMultiplier) + 0.5 ) );
709}
710
711void VoronoiVertexMeshGenerator::ValidateSeedLocations(std::vector<c_vector<double, 2> >& rSeedLocations)
712{
713 unsigned num_seeds = rSeedLocations.size();
714
715 /*
716 * Seeds at least 1.0 / mSamplingMultiplier apart from each other
717 * are acceptable; the 1.5 term below could just as well be any
718 * number that is strictly greater than 1.0.
719 */
720 double safe_distance = 1.5 / mSamplingMultiplier;
721
722 // If we find a seed that needs to move position, we will move it and start checking again from the beginning
723 bool recheck = true;
724
725 while (recheck)
726 {
727 // If no seeds needs moving (as is overwhelmingly likely), we do not need to check again
728 recheck = false;
729
730 // We check each seed against every other, without double counting
731 for (unsigned seed_idx_one = 0; seed_idx_one < num_seeds; seed_idx_one++)
732 {
733 for (unsigned seed_idx_two = seed_idx_one + 1; seed_idx_two < num_seeds; seed_idx_two++)
734 {
735 // We get the distance between the two seeds currently being considered
736 c_vector<double, 2> one_to_two = rSeedLocations[seed_idx_two] - rSeedLocations[seed_idx_one];
737 double distance = norm_2(one_to_two);
738
739 if (distance < safe_distance)
740 {
741 // We will now need to re-check
742 recheck = true;
743
744 /*
745 * If the distance is non-zero, we will move the second seed away along the line joining the two
746 * seeds until it's at the safe distance. If the distance is somehow zero, we will just move the
747 * x-location of the second seed by the safe distance.
748 *
749 * In all cases, we also need to ensure the new location is within the boundary box.
750 */
751 if (distance > DBL_EPSILON)
752 {
753 double multiplier = safe_distance / distance;
754 rSeedLocations[seed_idx_two] += (one_to_two * multiplier);
755
756 rSeedLocations[seed_idx_two][0] = fmod(rSeedLocations[seed_idx_two][0] + mMultiplierInX, mMultiplierInX);
757 rSeedLocations[seed_idx_two][1] = fmod(rSeedLocations[seed_idx_two][1] + mMultiplierInX, mMultiplierInX);
758 }
759 else
760 {
761 rSeedLocations[seed_idx_two][0] += safe_distance;
762 rSeedLocations[seed_idx_two][0] = fmod(rSeedLocations[seed_idx_two][0], mMultiplierInX);
763 }
764 }
765 }
766
767 // We will re-check now rather than finishing the outer loop first
768 if (recheck)
769 {
770 break;
771 }
772 }
773 }
774}
775
776std::vector<double> VoronoiVertexMeshGenerator::GetPolygonDistribution()
777{
778 assert(mpMesh != nullptr);
779
780 // Number of elements in the mesh
781 unsigned num_elems = mpMesh->GetNumElements();
782
783 // Store the number of each class of polygons
784 std::vector<unsigned> num_polygons(mMaxExpectedNumSidesPerPolygon - 2, 0);
785
786 // Container to return the polygon distribution
787 std::vector<double> polygon_dist;
788
789 // Loop over elements in the mesh to get the number of each class of polygon
790 for (unsigned elem_idx = 0; elem_idx < num_elems; elem_idx++)
791 {
792 unsigned num_nodes_this_elem = mpMesh->GetElement(elem_idx)->GetNumNodes();
793
794 // All polygons are assumed to have 3, 4, 5, ..., mMaxExpectedNumSidesPerPolygon sides
795 assert(num_nodes_this_elem > 2);
796 assert(num_nodes_this_elem <= mMaxExpectedNumSidesPerPolygon);
797
798 // Increment correct place in counter - triangles in place 0, squares in 1, etc
799 num_polygons[num_nodes_this_elem - 3]++;
800 }
801
802 // Loop over the vector of polygon numbers and calculate the distribution vector to return
803 unsigned elems_accounted_for = 0;
804 for (unsigned polygon = 0 ; polygon < num_polygons.size() ; polygon++)
805 {
806 elems_accounted_for += num_polygons[polygon];
807
808 polygon_dist.push_back(static_cast<double>(num_polygons[polygon]) / static_cast<double>(num_elems));
809
810 // Only fill the vector of polygon distributions to the point where there are none of higher class in the mesh
811 if (elems_accounted_for == num_elems)
812 {
813 break;
814 }
815 }
816
817 return polygon_dist;
818}
819
820double VoronoiVertexMeshGenerator::GetAreaCoefficientOfVariation()
821{
822 assert(mpMesh != nullptr);
823
824 // Number of elements in the mesh, and check there are at least two
825 unsigned num_elems = mpMesh->GetNumElements();
826 assert(num_elems > 1);
827
828 double var = 0.0;
829
830 // Loop over elements in the mesh to get the contributions to the variance
831 for (unsigned elem_idx = 0 ; elem_idx < num_elems ; elem_idx++)
832 {
833 double deviation = mpMesh->GetVolumeOfElement(elem_idx) - mElementTargetArea;
834 var += deviation * deviation;
835 }
836
837 var /= static_cast<double>(num_elems - 1);
838
839 return sqrt(var) / mElementTargetArea;
840}
841
842void VoronoiVertexMeshGenerator::RefreshSeedsAndRegenerateMesh()
843{
844 this->GenerateVoronoiMesh();
845}
846
847void VoronoiVertexMeshGenerator::SetMaxExpectedNumSidesPerPolygon(unsigned maxExpectedNumSidesPerPolygon)
848{
849 mMaxExpectedNumSidesPerPolygon = maxExpectedNumSidesPerPolygon;
850}
851
852unsigned VoronoiVertexMeshGenerator::GetMaxExpectedNumSidesPerPolygon()
853{
854 return mMaxExpectedNumSidesPerPolygon;
855}
856
857#endif // BOOST_VERSION >= 105200
858#if BOOST_VERSION < 105200
859
865{
866 EXCEPTION("This is a dummy class. Build with Boost version 1.52 or above for functionality.");
867}
868
869#endif // BOOST_VERSION < 105200
#define EXCEPTION(message)
Node< SPACE_DIM > * GetNode(unsigned localIndex) const
unsigned GetNumNodes() const
unsigned GetIndex() const
Node< SPACE_DIM > * GetNode(unsigned index) const
void DeleteNode(const unsigned &rIndex)
unsigned GetNodeLocalIndex(unsigned globalIndex) const
void AddNode(Node< SPACE_DIM > *pNode, const unsigned &rIndex)
unsigned GetNumNodes() const
void DeleteNodePriorToReMesh(unsigned index)
unsigned GetNumElements() const
Definition Node.hpp:59
std::set< unsigned > & rGetContainingElementIndices()
Definition Node.cpp:300
const c_vector< double, SPACE_DIM > & rGetLocation() const
Definition Node.cpp:139
bool IsBoundaryNode() const
Definition Node.cpp:164
unsigned GetIndex() const
Definition Node.cpp:158
void SetAsBoundaryNode(bool value=true)
Definition Node.cpp:127
static RandomNumberGenerator * Instance()
VertexElement< ELEMENT_DIM, SPACE_DIM > * GetElement(unsigned index) const