1 /*=========================================================================
2
3 Program: Visualization Toolkit
4 Module: vtkQuad.cxx
5
6 Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
7 All rights reserved.
8 See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
9
10 This software is distributed WITHOUT ANY WARRANTY; without even
11 the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
12 PURPOSE. See the above copyright notice for more information.
13
14 =========================================================================*/
15 #include "vtkQuad.h"
16
17 #include "vtkObjectFactory.h"
18 #include "vtkCellArray.h"
19 #include "vtkCellData.h"
20 #include "vtkLine.h"
21 #include "vtkTriangle.h"
22 #include "vtkMath.h"
23 #include "vtkPlane.h"
24 #include "vtkPointData.h"
25 #include "vtkIncrementalPointLocator.h"
26 #include "vtkPoints.h"
27
28 vtkStandardNewMacro(vtkQuad);
29
30 static const double VTK_DIVERGED = 1.e6;
31
32 //----------------------------------------------------------------------------
33 // Construct the quad with four points.
vtkQuad()34 vtkQuad::vtkQuad()
35 {
36 this->Points->SetNumberOfPoints(4);
37 this->PointIds->SetNumberOfIds(4);
38 for (int i = 0; i < 4; i++)
39 {
40 this->Points->SetPoint(i, 0.0, 0.0, 0.0);
41 this->PointIds->SetId(i,0);
42 }
43 this->Line = vtkLine::New();
44 this->Triangle = vtkTriangle::New();
45 }
46
47 //----------------------------------------------------------------------------
~vtkQuad()48 vtkQuad::~vtkQuad()
49 {
50 this->Line->Delete();
51 this->Triangle->Delete();
52 }
53
54 //----------------------------------------------------------------------------
55 static const int VTK_QUAD_MAX_ITERATION=20;
56 static const double VTK_QUAD_CONVERGED=1.e-04;
57
ComputeNormal(vtkQuad * self,double pt1[3],double pt2[3],double pt3[3],double n[3])58 inline static void ComputeNormal(vtkQuad *self, double pt1[3], double pt2[3],
59 double pt3[3], double n[3])
60 {
61 vtkTriangle::ComputeNormal (pt1, pt2, pt3, n);
62
63 // If first three points are co-linear, then use fourth point
64 //
65 double pt4[3];
66 if ( n[0] == 0.0 && n[1] == 0.0 && n[2] == 0.0 )
67 {
68 self->Points->GetPoint(3,pt4);
69 vtkTriangle::ComputeNormal (pt2, pt3, pt4, n);
70 }
71 }
72
73 //----------------------------------------------------------------------------
EvaluatePosition(double x[3],double * closestPoint,int & subId,double pcoords[3],double & dist2,double * weights)74 int vtkQuad::EvaluatePosition(double x[3], double* closestPoint,
75 int& subId, double pcoords[3],
76 double& dist2, double *weights)
77 {
78 int i, j;
79 double pt1[3], pt2[3], pt3[3], pt[3], n[3];
80 double det;
81 double maxComponent;
82 int idx=0, indices[2];
83 int iteration, converged;
84 double params[2];
85 double fcol[2], rcol[2], scol[2], cp[3];
86 double derivs[8];
87
88 subId = 0;
89 pcoords[0] = pcoords[1] = params[0] = params[1] = 0.5;
90
91 // Get normal for quadrilateral
92 //
93 this->Points->GetPoint(0, pt1);
94 this->Points->GetPoint(1, pt2);
95 this->Points->GetPoint(2, pt3);
96 ComputeNormal (this, pt1, pt2, pt3, n);
97
98 // Project point to plane
99 //
100 vtkPlane::ProjectPoint(x,pt1,n,cp);
101
102 // Construct matrices. Since we have over determined system, need to find
103 // which 2 out of 3 equations to use to develop equations. (Any 2 should
104 // work since we've projected point to plane.)
105 //
106 for (maxComponent=0.0, i=0; i<3; i++)
107 {
108 if (fabs(n[i]) > maxComponent)
109 {
110 maxComponent = fabs(n[i]);
111 idx = i;
112 }
113 }
114 for (j=0, i=0; i<3; i++)
115 {
116 if ( i != idx )
117 {
118 indices[j++] = i;
119 }
120 }
121
122 // Use Newton's method to solve for parametric coordinates
123 //
124 for (iteration=converged=0; !converged
125 && (iteration < VTK_QUAD_MAX_ITERATION);
126 iteration++)
127 {
128 // calculate element interpolation functions and derivatives
129 //
130 this->InterpolationFunctions(pcoords, weights);
131 this->InterpolationDerivs(pcoords, derivs);
132
133 // calculate newton functions
134 //
135 for (i=0; i<2; i++)
136 {
137 fcol[i] = rcol[i] = scol[i] = 0.0;
138 }
139 for (i=0; i<4; i++)
140 {
141 this->Points->GetPoint(i, pt);
142 for (j=0; j<2; j++)
143 {
144 fcol[j] += pt[indices[j]] * weights[i];
145 rcol[j] += pt[indices[j]] * derivs[i];
146 scol[j] += pt[indices[j]] * derivs[i+4];
147 }
148 }
149
150 for (j=0; j<2; j++)
151 {
152 fcol[j] -= cp[indices[j]];
153 }
154
155 // compute determinants and generate improvements
156 //
157 if ( (det=vtkMath::Determinant2x2(rcol,scol)) == 0.0 )
158 {
159 return -1;
160 }
161
162 pcoords[0] = params[0] - vtkMath::Determinant2x2 (fcol,scol) / det;
163 pcoords[1] = params[1] - vtkMath::Determinant2x2 (rcol,fcol) / det;
164
165 // check for convergence
166 //
167 if ( ((fabs(pcoords[0]-params[0])) < VTK_QUAD_CONVERGED) &&
168 ((fabs(pcoords[1]-params[1])) < VTK_QUAD_CONVERGED) )
169 {
170 converged = 1;
171 }
172 // Test for bad divergence (S.Hirschberg 11.12.2001)
173 else if ((fabs(pcoords[0]) > VTK_DIVERGED) ||
174 (fabs(pcoords[1]) > VTK_DIVERGED))
175 {
176 return -1;
177 }
178
179 // if not converged, repeat
180 //
181 else
182 {
183 params[0] = pcoords[0];
184 params[1] = pcoords[1];
185 }
186 }
187
188 // if not converged, set the parametric coordinates to arbitrary values
189 // outside of element
190 //
191 if ( !converged )
192 {
193 return -1;
194 }
195
196 this->InterpolationFunctions(pcoords, weights);
197
198 if ( pcoords[0] >= -0.001 && pcoords[0] <= 1.001 &&
199 pcoords[1] >= -0.001 && pcoords[1] <= 1.001 )
200 {
201 if (closestPoint)
202 {
203 dist2 =
204 vtkMath::Distance2BetweenPoints(cp,x); //projection distance
205 closestPoint[0] = cp[0];
206 closestPoint[1] = cp[1];
207 closestPoint[2] = cp[2];
208 }
209 return 1;
210 }
211 else
212 {
213 double t;
214 double pt4[3];
215
216 if (closestPoint)
217 {
218 this->Points->GetPoint(3, pt4);
219
220 if ( pcoords[0] < 0.0 && pcoords[1] < 0.0 )
221 {
222 dist2 = vtkMath::Distance2BetweenPoints(x,pt1);
223 for (i=0; i<3; i++)
224 {
225 closestPoint[i] = pt1[i];
226 }
227 }
228 else if ( pcoords[0] > 1.0 && pcoords[1] < 0.0 )
229 {
230 dist2 = vtkMath::Distance2BetweenPoints(x,pt2);
231 for (i=0; i<3; i++)
232 {
233 closestPoint[i] = pt2[i];
234 }
235 }
236 else if ( pcoords[0] > 1.0 && pcoords[1] > 1.0 )
237 {
238 dist2 = vtkMath::Distance2BetweenPoints(x,pt3);
239 for (i=0; i<3; i++)
240 {
241 closestPoint[i] = pt3[i];
242 }
243 }
244 else if ( pcoords[0] < 0.0 && pcoords[1] > 1.0 )
245 {
246 dist2 = vtkMath::Distance2BetweenPoints(x,pt4);
247 for (i=0; i<3; i++)
248 {
249 closestPoint[i] = pt4[i];
250 }
251 }
252 else if ( pcoords[0] < 0.0 )
253 {
254 dist2 = vtkLine::DistanceToLine(x,pt1,pt4,t,closestPoint);
255 }
256 else if ( pcoords[0] > 1.0 )
257 {
258 dist2 = vtkLine::DistanceToLine(x,pt2,pt3,t,closestPoint);
259 }
260 else if ( pcoords[1] < 0.0 )
261 {
262 dist2 = vtkLine::DistanceToLine(x,pt1,pt2,t,closestPoint);
263 }
264 else if ( pcoords[1] > 1.0 )
265 {
266 dist2 = vtkLine::DistanceToLine(x,pt3,pt4,t,closestPoint);
267 }
268 }
269 return 0;
270 }
271 }
272
273 //----------------------------------------------------------------------------
EvaluateLocation(int & vtkNotUsed (subId),double pcoords[3],double x[3],double * weights)274 void vtkQuad::EvaluateLocation(int& vtkNotUsed(subId), double pcoords[3],
275 double x[3], double *weights)
276 {
277 int i, j;
278 double pt[3];
279
280 this->InterpolationFunctions(pcoords, weights);
281
282 x[0] = x[1] = x[2] = 0.0;
283 for (i=0; i<4; i++)
284 {
285 this->Points->GetPoint(i, pt);
286 for (j=0; j<3; j++)
287 {
288 x[j] += pt[j] * weights[i];
289 }
290 }
291 }
292
293 //----------------------------------------------------------------------------
294 // Compute iso-parametric interpolation functions
295 //
InterpolationFunctions(double pcoords[3],double sf[4])296 void vtkQuad::InterpolationFunctions(double pcoords[3], double sf[4])
297 {
298 double rm, sm;
299
300 rm = 1. - pcoords[0];
301 sm = 1. - pcoords[1];
302
303 sf[0] = rm * sm;
304 sf[1] = pcoords[0] * sm;
305 sf[2] = pcoords[0] * pcoords[1];
306 sf[3] = rm * pcoords[1];
307 }
308
309 //----------------------------------------------------------------------------
InterpolationDerivs(double pcoords[3],double derivs[8])310 void vtkQuad::InterpolationDerivs(double pcoords[3], double derivs[8])
311 {
312 double rm, sm;
313
314 rm = 1. - pcoords[0];
315 sm = 1. - pcoords[1];
316
317 derivs[0] = -sm;
318 derivs[1] = sm;
319 derivs[2] = pcoords[1];
320 derivs[3] = -pcoords[1];
321 derivs[4] = -rm;
322 derivs[5] = -pcoords[0];
323 derivs[6] = pcoords[0];
324 derivs[7] = rm;
325 }
326
327 //----------------------------------------------------------------------------
CellBoundary(int vtkNotUsed (subId),double pcoords[3],vtkIdList * pts)328 int vtkQuad::CellBoundary(int vtkNotUsed(subId), double pcoords[3],
329 vtkIdList *pts)
330 {
331 double t1=pcoords[0]-pcoords[1];
332 double t2=1.0-pcoords[0]-pcoords[1];
333
334 pts->SetNumberOfIds(2);
335
336 // compare against two lines in parametric space that divide element
337 // into four pieces.
338 if ( t1 >= 0.0 && t2 >= 0.0 )
339 {
340 pts->SetId(0,this->PointIds->GetId(0));
341 pts->SetId(1,this->PointIds->GetId(1));
342 }
343
344 else if ( t1 >= 0.0 && t2 < 0.0 )
345 {
346 pts->SetId(0,this->PointIds->GetId(1));
347 pts->SetId(1,this->PointIds->GetId(2));
348 }
349
350 else if ( t1 < 0.0 && t2 < 0.0 )
351 {
352 pts->SetId(0,this->PointIds->GetId(2));
353 pts->SetId(1,this->PointIds->GetId(3));
354 }
355
356 else //( t1 < 0.0 && t2 >= 0.0 )
357 {
358 pts->SetId(0,this->PointIds->GetId(3));
359 pts->SetId(1,this->PointIds->GetId(0));
360 }
361
362 if ( pcoords[0] < 0.0 || pcoords[0] > 1.0 ||
363 pcoords[1] < 0.0 || pcoords[1] > 1.0 )
364 {
365 return 0;
366 }
367 else
368 {
369 return 1;
370 }
371 }
372
373 //----------------------------------------------------------------------------
374 // Marching (convex) quadrilaterals
375 //
376 static int edges[4][2] = { {0,1}, {1,2}, {3,2}, {0,3} };
377
378 typedef int EDGE_LIST;
379 typedef struct {
380 EDGE_LIST edges[5];
381 } LINE_CASES;
382
383 static LINE_CASES lineCases[] = {
384 {{-1, -1, -1, -1, -1}},
385 {{0, 3, -1, -1, -1}},
386 {{1, 0, -1, -1, -1}},
387 {{1, 3, -1, -1, -1}},
388 {{2, 1, -1, -1, -1}},
389 {{0, 3, 2, 1, -1}},
390 {{2, 0, -1, -1, -1}},
391 {{2, 3, -1, -1, -1}},
392 {{3, 2, -1, -1, -1}},
393 {{0, 2, -1, -1, -1}},
394 {{1, 0, 3, 2, -1}},
395 {{1, 2, -1, -1, -1}},
396 {{3, 1, -1, -1, -1}},
397 {{0, 1, -1, -1, -1}},
398 {{3, 0, -1, -1, -1}},
399 {{-1, -1, -1, -1, -1}}
400 };
401
402 //----------------------------------------------------------------------------
GetEdgeArray(int edgeId)403 int *vtkQuad::GetEdgeArray(int edgeId)
404 {
405 return edges[edgeId];
406 }
407
408 //----------------------------------------------------------------------------
Contour(double value,vtkDataArray * cellScalars,vtkIncrementalPointLocator * locator,vtkCellArray * verts,vtkCellArray * lines,vtkCellArray * vtkNotUsed (polys),vtkPointData * inPd,vtkPointData * outPd,vtkCellData * inCd,vtkIdType cellId,vtkCellData * outCd)409 void vtkQuad::Contour(double value, vtkDataArray *cellScalars,
410 vtkIncrementalPointLocator *locator,
411 vtkCellArray *verts,
412 vtkCellArray *lines,
413 vtkCellArray *vtkNotUsed(polys),
414 vtkPointData *inPd, vtkPointData *outPd,
415 vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd)
416 {
417 static int CASE_MASK[4] = {1,2,4,8};
418 LINE_CASES *lineCase;
419 EDGE_LIST *edge;
420 int i, j, index, *vert;
421 int newCellId;
422 vtkIdType pts[2];
423 int e1, e2;
424 double t, x1[3], x2[3], x[3], deltaScalar;
425 vtkIdType offset = verts->GetNumberOfCells();
426
427 // Build the case table
428 for ( i=0, index = 0; i < 4; i++)
429 {
430 if (cellScalars->GetComponent(i,0) >= value)
431 {
432 index |= CASE_MASK[i];
433 }
434 }
435
436 lineCase = lineCases + index;
437 edge = lineCase->edges;
438
439 for ( ; edge[0] > -1; edge += 2 )
440 {
441 for (i=0; i<2; i++) // insert line
442 {
443 vert = edges[edge[i]];
444 // calculate a preferred interpolation direction
445 deltaScalar = (cellScalars->GetComponent(vert[1],0)
446 - cellScalars->GetComponent(vert[0],0));
447 if (deltaScalar > 0)
448 {
449 e1 = vert[0]; e2 = vert[1];
450 }
451 else
452 {
453 e1 = vert[1]; e2 = vert[0];
454 deltaScalar = -deltaScalar;
455 }
456
457 // linear interpolation
458 if (deltaScalar == 0.0)
459 {
460 t = 0.0;
461 }
462 else
463 {
464 t = (value - cellScalars->GetComponent(e1,0)) / deltaScalar;
465 }
466
467 this->Points->GetPoint(e1, x1);
468 this->Points->GetPoint(e2, x2);
469
470 for (j=0; j<3; j++)
471 {
472 x[j] = x1[j] + t * (x2[j] - x1[j]);
473 }
474 if ( locator->InsertUniquePoint(x, pts[i]) )
475 {
476 if ( outPd )
477 {
478 vtkIdType p1 = this->PointIds->GetId(e1);
479 vtkIdType p2 = this->PointIds->GetId(e2);
480 outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
481 }
482 }
483 }
484 // check for degenerate line
485 if ( pts[0] != pts[1] )
486 {
487 newCellId = offset + lines->InsertNextCell(2,pts);
488 outCd->CopyData(inCd,cellId,newCellId);
489 }
490 }
491 }
492
493 //----------------------------------------------------------------------------
GetEdge(int edgeId)494 vtkCell *vtkQuad::GetEdge(int edgeId)
495 {
496 int edgeIdPlus1 = edgeId + 1;
497
498 if (edgeIdPlus1 > 3)
499 {
500 edgeIdPlus1 = 0;
501 }
502
503 // load point id's
504 this->Line->PointIds->SetId(0,this->PointIds->GetId(edgeId));
505 this->Line->PointIds->SetId(1,this->PointIds->GetId(edgeIdPlus1));
506
507 // load coordinates
508 this->Line->Points->SetPoint(0,this->Points->GetPoint(edgeId));
509 this->Line->Points->SetPoint(1,this->Points->GetPoint(edgeIdPlus1));
510
511 return this->Line;
512 }
513
514
515 //----------------------------------------------------------------------------
516 // Intersect plane; see whether point is in quadrilateral. This code
517 // splits the quad into two triangles and intersects them (because the
518 // quad may be non-planar).
519 //
IntersectWithLine(double p1[3],double p2[3],double tol,double & t,double x[3],double pcoords[3],int & subId)520 int vtkQuad::IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
521 double x[3], double pcoords[3], int& subId)
522 {
523 int diagonalCase;
524 double d1 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(0),
525 this->Points->GetPoint(2));
526 double d2 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(1),
527 this->Points->GetPoint(3));
528 subId = 0;
529
530 // Figure out how to uniquely tessellate the quad. Watch out for
531 // equivalent triangulations (i.e., the triangulation is equivalent
532 // no matter where the diagonal). In this case use the point ids as
533 // a tie breaker to insure unique triangulation across the quad.
534 //
535 if ( d1 == d2 ) //rare case; discriminate based on point id
536 {
537 int i, id, maxId=0, maxIdx=0;
538 for (i=0; i<4; i++) //find the maximum id
539 {
540 if ( (id=this->PointIds->GetId(i)) > maxId )
541 {
542 maxId = id;
543 maxIdx = i;
544 }
545 }
546 if ( maxIdx == 0 || maxIdx == 2) diagonalCase = 0;
547 else diagonalCase = 1;
548 }
549 else if ( d1 < d2 )
550 {
551 diagonalCase = 0;
552 }
553 else //d2 < d1
554 {
555 diagonalCase = 1;
556 }
557
558 // Note: in the following code the parametric coords must be adjusted to
559 // reflect the use of the triangle parametric coordinate system.
560 switch (diagonalCase)
561 {
562 case 0:
563 this->Triangle->Points->SetPoint(0,this->Points->GetPoint(0));
564 this->Triangle->Points->SetPoint(1,this->Points->GetPoint(1));
565 this->Triangle->Points->SetPoint(2,this->Points->GetPoint(2));
566 if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
567 {
568 pcoords[0] = pcoords[0] + pcoords[1];
569 return 1;
570 }
571 this->Triangle->Points->SetPoint(0,this->Points->GetPoint(2));
572 this->Triangle->Points->SetPoint(1,this->Points->GetPoint(3));
573 this->Triangle->Points->SetPoint(2,this->Points->GetPoint(0));
574 if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
575 {
576 pcoords[0] = 1.0 - (pcoords[0]+pcoords[1]);
577 pcoords[1] = 1.0 - pcoords[1];
578 return 1;
579 }
580 return 0;
581
582 case 1:
583 this->Triangle->Points->SetPoint(0,this->Points->GetPoint(0));
584 this->Triangle->Points->SetPoint(1,this->Points->GetPoint(1));
585 this->Triangle->Points->SetPoint(2,this->Points->GetPoint(3));
586 if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
587 {
588 return 1;
589 }
590 this->Triangle->Points->SetPoint(0,this->Points->GetPoint(2));
591 this->Triangle->Points->SetPoint(1,this->Points->GetPoint(3));
592 this->Triangle->Points->SetPoint(2,this->Points->GetPoint(1));
593 if (this->Triangle->IntersectWithLine(p1, p2, tol, t, x, pcoords, subId) )
594 {
595 pcoords[0] = 1.0 - pcoords[0];
596 pcoords[1] = 1.0 - pcoords[1];
597 return 1;
598 }
599
600 return 0;
601 }
602
603 return 0;
604 }
605
606 //----------------------------------------------------------------------------
Triangulate(int vtkNotUsed (index),vtkIdList * ptIds,vtkPoints * pts)607 int vtkQuad::Triangulate(int vtkNotUsed(index), vtkIdList *ptIds,
608 vtkPoints *pts)
609 {
610 double d1, d2;
611
612 pts->Reset();
613 ptIds->Reset();
614
615 // use minimum diagonal (Delaunay triangles) - assumed convex
616 d1 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(0),
617 this->Points->GetPoint(2));
618 d2 = vtkMath::Distance2BetweenPoints(this->Points->GetPoint(1),
619 this->Points->GetPoint(3));
620
621 if ( d1 <= d2 )
622 {
623 ptIds->InsertId(0,this->PointIds->GetId(0));
624 pts->InsertPoint(0,this->Points->GetPoint(0));
625 ptIds->InsertId(1,this->PointIds->GetId(1));
626 pts->InsertPoint(1,this->Points->GetPoint(1));
627 ptIds->InsertId(2,this->PointIds->GetId(2));
628 pts->InsertPoint(2,this->Points->GetPoint(2));
629
630 ptIds->InsertId(3,this->PointIds->GetId(0));
631 pts->InsertPoint(3,this->Points->GetPoint(0));
632 ptIds->InsertId(4,this->PointIds->GetId(2));
633 pts->InsertPoint(4,this->Points->GetPoint(2));
634 ptIds->InsertId(5,this->PointIds->GetId(3));
635 pts->InsertPoint(5,this->Points->GetPoint(3));
636 }
637 else
638 {
639 ptIds->InsertId(0,this->PointIds->GetId(0));
640 pts->InsertPoint(0,this->Points->GetPoint(0));
641 ptIds->InsertId(1,this->PointIds->GetId(1));
642 pts->InsertPoint(1,this->Points->GetPoint(1));
643 ptIds->InsertId(2,this->PointIds->GetId(3));
644 pts->InsertPoint(2,this->Points->GetPoint(3));
645
646 ptIds->InsertId(3,this->PointIds->GetId(1));
647 pts->InsertPoint(3,this->Points->GetPoint(1));
648 ptIds->InsertId(4,this->PointIds->GetId(2));
649 pts->InsertPoint(4,this->Points->GetPoint(2));
650 ptIds->InsertId(5,this->PointIds->GetId(3));
651 pts->InsertPoint(5,this->Points->GetPoint(3));
652 }
653
654 return 1;
655 }
656
657 //----------------------------------------------------------------------------
Derivatives(int vtkNotUsed (subId),double pcoords[3],double * values,int dim,double * derivs)658 void vtkQuad::Derivatives(int vtkNotUsed(subId), double pcoords[3],
659 double *values, int dim, double *derivs)
660 {
661 double v0[2], v1[2], v2[2], v3[2], v10[3], v20[3], lenX;
662 double x0[3], x1[3], x2[3], x3[3], n[3], vec20[3], vec30[3];
663 double *J[2], J0[2], J1[2];
664 double *JI[2], JI0[2], JI1[2];
665 double funcDerivs[8], sum[2], dBydx, dBydy;
666 int i, j;
667
668 // Project points of quad into 2D system
669 this->Points->GetPoint(0, x0);
670 this->Points->GetPoint(1, x1);
671 this->Points->GetPoint(2, x2);
672 ComputeNormal (this,x0, x1, x2, n);
673 this->Points->GetPoint(3, x3);
674
675 for (i=0; i < 3; i++)
676 {
677 v10[i] = x1[i] - x0[i];
678 vec20[i] = x2[i] - x0[i];
679 vec30[i] = x3[i] - x0[i];
680 }
681
682 vtkMath::Cross(n,v10,v20); //creates local y' axis
683
684 if ( (lenX=vtkMath::Normalize(v10)) <= 0.0
685 || vtkMath::Normalize(v20) <= 0.0 ) //degenerate
686 {
687 for ( j=0; j < dim; j++ )
688 {
689 for ( i=0; i < 3; i++ )
690 {
691 derivs[j*dim + i] = 0.0;
692 }
693 }
694 return;
695 }
696
697 v0[0] = v0[1] = 0.0; //convert points to 2D (i.e., local system)
698 v1[0] = lenX; v1[1] = 0.0;
699 v2[0] = vtkMath::Dot(vec20,v10);
700 v2[1] = vtkMath::Dot(vec20,v20);
701 v3[0] = vtkMath::Dot(vec30,v10);
702 v3[1] = vtkMath::Dot(vec30,v20);
703
704 this->InterpolationDerivs(pcoords, funcDerivs);
705
706 // Compute Jacobian and inverse Jacobian
707 J[0] = J0; J[1] = J1;
708 JI[0] = JI0; JI[1] = JI1;
709
710 J[0][0] = v0[0]*funcDerivs[0] + v1[0]*funcDerivs[1] +
711 v2[0]*funcDerivs[2] + v3[0]*funcDerivs[3];
712 J[0][1] = v0[1]*funcDerivs[0] + v1[1]*funcDerivs[1] +
713 v2[1]*funcDerivs[2] + v3[1]*funcDerivs[3];
714 J[1][0] = v0[0]*funcDerivs[4] + v1[0]*funcDerivs[5] +
715 v2[0]*funcDerivs[6] + v3[0]*funcDerivs[7];
716 J[1][1] = v0[1]*funcDerivs[4] + v1[1]*funcDerivs[5] +
717 v2[1]*funcDerivs[6] + v3[1]*funcDerivs[7];
718
719 // Compute inverse Jacobian, return if Jacobian is singular
720 if (!vtkMath::InvertMatrix(J,JI,2))
721 {
722 for ( j=0; j < dim; j++ )
723 {
724 for ( i=0; i < 3; i++ )
725 {
726 derivs[j*dim + i] = 0.0;
727 }
728 }
729 return;
730 }
731
732 // Loop over "dim" derivative values. For each set of values,
733 // compute derivatives
734 // in local system and then transform into modelling system.
735 // First compute derivatives in local x'-y' coordinate system
736 for ( j=0; j < dim; j++ )
737 {
738 sum[0] = sum[1] = 0.0;
739 for ( i=0; i < 4; i++) //loop over interp. function derivatives
740 {
741 sum[0] += funcDerivs[i] * values[dim*i + j];
742 sum[1] += funcDerivs[4 + i] * values[dim*i + j];
743 }
744 dBydx = sum[0]*JI[0][0] + sum[1]*JI[0][1];
745 dBydy = sum[0]*JI[1][0] + sum[1]*JI[1][1];
746
747 // Transform into global system (dot product with global axes)
748 derivs[3*j] = dBydx * v10[0] + dBydy * v20[0];
749 derivs[3*j + 1] = dBydx * v10[1] + dBydy * v20[1];
750 derivs[3*j + 2] = dBydx * v10[2] + dBydy * v20[2];
751 }
752 }
753
754 //----------------------------------------------------------------------------
755 // support quad clipping
756 typedef int QUAD_EDGE_LIST;
757 typedef struct {
758 QUAD_EDGE_LIST edges[14];
759 } QUAD_CASES;
760
761 static QUAD_CASES quadCases[] = {
762 {{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 0
763 {{ 3, 100, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 1
764 {{ 3, 101, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 2
765 {{ 4, 100, 101, 1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 3
766 {{ 3, 102, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
767 {{ 3, 100, 0, 3, 3, 102, 2, 1, 4, 0, 1, 2, 3, -1}}, // 5
768 {{ 4, 101, 102, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
769 {{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 102, 2, -1, -1}}, // 7
770 {{ 3, 103, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
771 {{ 4, 100, 0, 2, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
772 {{ 3, 101, 1, 0, 3, 103, 3, 2, 4, 0, 1, 2, 3, -1}}, // 10
773 {{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 103, -1, -1}}, // 11
774 {{ 4, 102, 103, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
775 {{ 3, 100, 0, 103, 3, 0, 1, 103, 3, 1, 102, 103, -1, -1}}, // 13
776 {{ 3, 0, 101, 102, 3, 0, 102, 3, 3, 102, 103, 3, -1, -1}}, // 14
777 {{ 4, 100, 101, 102, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
778 };
779
780 static QUAD_CASES quadCasesComplement[] = {
781 {{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 0
782 {{ 3, 100, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 1
783 {{ 3, 101, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 2
784 {{ 4, 100, 101, 1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 3
785 {{ 3, 102, 2, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 4
786 {{ 3, 100, 0, 3, 3, 102, 2, 1, -1, -1, -1, -1, -1, -1}}, // 5
787 {{ 4, 101, 102, 2, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 6
788 {{ 3, 100, 101, 3, 3, 101, 2, 3, 3, 101, 102, 2, -1, -1}}, // 7
789 {{ 3, 103, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 8
790 {{ 4, 100, 0, 2, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 9
791 {{ 3, 101, 1, 0, 3, 103, 3, 2, -1, -1, -1, -1, -1, -1}}, // 10
792 {{ 3, 100, 101, 1, 3, 100, 1, 2, 3, 100, 2, 103, -1, -1}}, // 11
793 {{ 4, 102, 103, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 12
794 {{ 3, 100, 0, 103, 3, 0, 1, 103, 3, 1, 102, 103, -1, -1}}, // 13
795 {{ 3, 0, 101, 102, 3, 0, 102, 3, 3, 102, 103, 3, -1, -1}}, // 14
796 {{ 4, 100, 101, 102, 103, -1, -1, -1, -1, -1, -1, -1, -1, -1}}, // 15
797 };
798
799 //----------------------------------------------------------------------------
800 // Clip this quad using scalar value provided. Like contouring, except
801 // that it cuts the quad to produce other quads and/or triangles.
Clip(double value,vtkDataArray * cellScalars,vtkIncrementalPointLocator * locator,vtkCellArray * polys,vtkPointData * inPd,vtkPointData * outPd,vtkCellData * inCd,vtkIdType cellId,vtkCellData * outCd,int insideOut)802 void vtkQuad::Clip(double value, vtkDataArray *cellScalars,
803 vtkIncrementalPointLocator *locator, vtkCellArray *polys,
804 vtkPointData *inPd, vtkPointData *outPd,
805 vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
806 int insideOut)
807 {
808 static int CASE_MASK[4] = {1,2,4,8};
809 QUAD_CASES *quadCase;
810 QUAD_EDGE_LIST *edge;
811 int i, j, index, *vert;
812 int e1, e2;
813 int newCellId;
814 vtkIdType pts[4];
815 int vertexId;
816 double t, x1[3], x2[3], x[3], deltaScalar;
817 double scalar0, scalar1, e1Scalar;
818
819 // Build the index into the case table
820 if ( insideOut )
821 {
822 for ( i=0, index = 0; i < 4; i++)
823 {
824 if (cellScalars->GetComponent(i,0) <= value)
825 {
826 index |= CASE_MASK[i];
827 }
828 }
829 // Select case based on the index and get the list of edges for this case
830 quadCase = quadCases + index;
831 }
832 else
833 {
834 for ( i=0, index = 0; i < 4; i++)
835 {
836 if (cellScalars->GetComponent(i,0) > value)
837 {
838 index |= CASE_MASK[i];
839 }
840 }
841 // Select case based on the index and get the list of edges for this case
842 quadCase = quadCasesComplement + index;
843 }
844
845 edge = quadCase->edges;
846
847 // generate each quad
848 for ( ; edge[0] > -1; edge += edge[0]+1 )
849 {
850 for (i=0; i < edge[0]; i++) // insert quad or triangle
851 {
852 // vertex exists, and need not be interpolated
853 if (edge[i+1] >= 100)
854 {
855 vertexId = edge[i+1] - 100;
856 this->Points->GetPoint(vertexId, x);
857 if ( locator->InsertUniquePoint(x, pts[i]) )
858 {
859 outPd->CopyData(inPd,this->PointIds->GetId(vertexId),pts[i]);
860 }
861 }
862
863 else //new vertex, interpolate
864 {
865 vert = edges[edge[i+1]];
866
867 // calculate a preferred interpolation direction
868 scalar0 = cellScalars->GetComponent(vert[0],0);
869 scalar1 = cellScalars->GetComponent(vert[1],0);
870 deltaScalar = scalar1 - scalar0;
871
872 if (deltaScalar > 0)
873 {
874 e1 = vert[0]; e2 = vert[1];
875 e1Scalar = scalar0;
876 }
877 else
878 {
879 e1 = vert[1]; e2 = vert[0];
880 e1Scalar = scalar1;
881 deltaScalar = -deltaScalar;
882 }
883
884 // linear interpolation
885 if (deltaScalar == 0.0)
886 {
887 t = 0.0;
888 }
889 else
890 {
891 t = (value - e1Scalar) / deltaScalar;
892 }
893
894 this->Points->GetPoint(e1, x1);
895 this->Points->GetPoint(e2, x2);
896
897 for (j=0; j<3; j++)
898 {
899 x[j] = x1[j] + t * (x2[j] - x1[j]);
900 }
901
902 if ( locator->InsertUniquePoint(x, pts[i]) )
903 {
904 vtkIdType p1 = this->PointIds->GetId(e1);
905 vtkIdType p2 = this->PointIds->GetId(e2);
906 outPd->InterpolateEdge(inPd,pts[i],p1,p2,t);
907 }
908 }
909 }
910 // check for degenerate output
911 if ( edge[0] == 3 ) //i.e., a triangle
912 {
913 if (pts[0] == pts[1] || pts[0] == pts[2] || pts[1] == pts[2] )
914 {
915 continue;
916 }
917 }
918 else // a quad
919 {
920 if ((pts[0] == pts[3] && pts[1] == pts[2]) ||
921 (pts[0] == pts[1] && pts[3] == pts[2]) )
922 {
923 continue;
924 }
925 }
926
927 newCellId = polys->InsertNextCell(edge[0],pts);
928 outCd->CopyData(inCd,cellId,newCellId);
929 }
930 }
931
932 //----------------------------------------------------------------------------
933 static double vtkQuadCellPCoords[12] = {0.0,0.0,0.0, 1.0,0.0,0.0,
934 1.0,1.0,0.0, 0.0,1.0,0.0};
GetParametricCoords()935 double *vtkQuad::GetParametricCoords()
936 {
937 return vtkQuadCellPCoords;
938 }
939
940 //----------------------------------------------------------------------------
PrintSelf(ostream & os,vtkIndent indent)941 void vtkQuad::PrintSelf(ostream& os, vtkIndent indent)
942 {
943 this->Superclass::PrintSelf(os,indent);
944
945 os << indent << "Line:\n";
946 this->Line->PrintSelf(os,indent.GetNextIndent());
947 os << indent << "Triangle:\n";
948 this->Triangle->PrintSelf(os,indent.GetNextIndent());
949 }
950