1 /*=========================================================================
2 
3   Program:   Visualization Toolkit
4   Module:    vtkQuadraticQuad.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 "vtkQuadraticQuad.h"
16 
17 #include "vtkCellData.h"
18 #include "vtkDoubleArray.h"
19 #include "vtkMath.h"
20 #include "vtkObjectFactory.h"
21 #include "vtkPointData.h"
22 #include "vtkPoints.h"
23 #include "vtkQuad.h"
24 #include "vtkQuadraticEdge.h"
25 
26 vtkStandardNewMacro(vtkQuadraticQuad);
27 
28 //------------------------------------------------------------------------------
29 // Construct the quad with eight points.
vtkQuadraticQuad()30 vtkQuadraticQuad::vtkQuadraticQuad()
31 {
32   this->Edge = vtkQuadraticEdge::New();
33   this->Quad = vtkQuad::New();
34   this->PointData = vtkPointData::New();
35   this->CellData = vtkCellData::New();
36   this->CellScalars = vtkDoubleArray::New();
37   this->CellScalars->SetNumberOfTuples(9);
38   this->Scalars = vtkDoubleArray::New();
39   this->Scalars->SetNumberOfTuples(4);
40 
41   // We add a fictitious ninth point in order to process the cell. The ninth
42   // point is in the center of the cell.
43   this->Points->SetNumberOfPoints(9);
44   this->PointIds->SetNumberOfIds(9);
45   for (int i = 0; i < 9; i++)
46   {
47     this->Points->SetPoint(i, 0.0, 0.0, 0.0);
48     this->PointIds->SetId(i, 0);
49   }
50   this->Points->SetNumberOfPoints(8);
51   this->PointIds->SetNumberOfIds(8);
52 }
53 
54 //------------------------------------------------------------------------------
~vtkQuadraticQuad()55 vtkQuadraticQuad::~vtkQuadraticQuad()
56 {
57   this->Edge->Delete();
58   this->Quad->Delete();
59 
60   this->Scalars->Delete();
61   this->PointData->Delete();
62   this->CellData->Delete();
63   this->CellScalars->Delete();
64 }
65 //------------------------------------------------------------------------------
GetEdge(int edgeId)66 vtkCell* vtkQuadraticQuad::GetEdge(int edgeId)
67 {
68   edgeId = (edgeId < 0 ? 0 : (edgeId > 3 ? 3 : edgeId));
69   int p = (edgeId + 1) % 4;
70 
71   // load point id's
72   this->Edge->PointIds->SetId(0, this->PointIds->GetId(edgeId));
73   this->Edge->PointIds->SetId(1, this->PointIds->GetId(p));
74   this->Edge->PointIds->SetId(2, this->PointIds->GetId(edgeId + 4));
75 
76   // load coordinates
77   this->Edge->Points->SetPoint(0, this->Points->GetPoint(edgeId));
78   this->Edge->Points->SetPoint(1, this->Points->GetPoint(p));
79   this->Edge->Points->SetPoint(2, this->Points->GetPoint(edgeId + 4));
80 
81   return this->Edge;
82 }
83 
84 //------------------------------------------------------------------------------
85 
86 static int LinearQuads[4][4] = {
87   { 0, 4, 8, 7 },
88   { 4, 1, 5, 8 },
89   { 8, 5, 2, 6 },
90   { 7, 8, 6, 3 },
91 };
92 
Subdivide(double * weights)93 void vtkQuadraticQuad::Subdivide(double* weights)
94 {
95   int i, j;
96   double pc[3], x[3];
97 
98   pc[0] = pc[1] = 0.5;
99   vtkQuadraticQuad::InterpolationFunctions(pc, weights);
100 
101   double p[3];
102   x[0] = x[1] = x[2] = 0.0;
103   for (i = 0; i < 8; i++)
104   {
105     this->Points->GetPoint(i, p);
106     for (j = 0; j < 3; j++)
107     {
108       x[j] += p[j] * weights[i];
109     }
110   }
111   this->Points->SetPoint(8, x);
112 }
113 
114 //------------------------------------------------------------------------------
EvaluatePosition(const double * x,double closestPoint[3],int & subId,double pcoords[3],double & minDist2,double weights[])115 int vtkQuadraticQuad::EvaluatePosition(const double* x, double closestPoint[3], int& subId,
116   double pcoords[3], double& minDist2, double weights[])
117 {
118   double pc[3], dist2;
119   int ignoreId, i, returnStatus = 0, status;
120   double tempWeights[4];
121   double closest[3];
122 
123   // compute the midquad node
124   this->Subdivide(weights);
125 
126   // four linear quads are used
127   for (minDist2 = VTK_DOUBLE_MAX, i = 0; i < 4; i++)
128   {
129     this->Quad->Points->SetPoint(0, this->Points->GetPoint(LinearQuads[i][0]));
130     this->Quad->Points->SetPoint(1, this->Points->GetPoint(LinearQuads[i][1]));
131     this->Quad->Points->SetPoint(2, this->Points->GetPoint(LinearQuads[i][2]));
132     this->Quad->Points->SetPoint(3, this->Points->GetPoint(LinearQuads[i][3]));
133 
134     status = this->Quad->EvaluatePosition(x, closest, ignoreId, pc, dist2, tempWeights);
135     if (status != -1 && dist2 < minDist2)
136     {
137       returnStatus = status;
138       minDist2 = dist2;
139       subId = i;
140       pcoords[0] = pc[0];
141       pcoords[1] = pc[1];
142     }
143   }
144 
145   // adjust parametric coordinates
146   if (returnStatus != -1)
147   {
148     if (subId == 0)
149     {
150       pcoords[0] /= 2.0;
151       pcoords[1] /= 2.0;
152     }
153     else if (subId == 1)
154     {
155       pcoords[0] = 0.5 + (pcoords[0] / 2.0);
156       pcoords[1] /= 2.0;
157     }
158     else if (subId == 2)
159     {
160       pcoords[0] = 0.5 + (pcoords[0] / 2.0);
161       pcoords[1] = 0.5 + (pcoords[1] / 2.0);
162     }
163     else
164     {
165       pcoords[0] /= 2.0;
166       pcoords[1] = 0.5 + (pcoords[1] / 2.0);
167     }
168     pcoords[2] = 0.0;
169     if (closestPoint != nullptr)
170     {
171       // Compute both closestPoint and weights
172       this->EvaluateLocation(subId, pcoords, closestPoint, weights);
173     }
174     else
175     {
176       // Compute weights only
177       vtkQuadraticQuad::InterpolationFunctions(pcoords, weights);
178     }
179   }
180 
181   return returnStatus;
182 }
183 //------------------------------------------------------------------------------
EvaluateLocation(int & vtkNotUsed (subId),const double pcoords[3],double x[3],double * weights)184 void vtkQuadraticQuad::EvaluateLocation(
185   int& vtkNotUsed(subId), const double pcoords[3], double x[3], double* weights)
186 {
187   int i, j;
188   double pt[3];
189 
190   vtkQuadraticQuad::InterpolationFunctions(pcoords, weights);
191 
192   x[0] = x[1] = x[2] = 0.0;
193   for (i = 0; i < 8; i++)
194   {
195     this->Points->GetPoint(i, pt);
196     for (j = 0; j < 3; j++)
197     {
198       x[j] += pt[j] * weights[i];
199     }
200   }
201 }
202 
203 //------------------------------------------------------------------------------
CellBoundary(int subId,const double pcoords[3],vtkIdList * pts)204 int vtkQuadraticQuad::CellBoundary(int subId, const double pcoords[3], vtkIdList* pts)
205 {
206   return this->Quad->CellBoundary(subId, pcoords, pts);
207 }
208 
209 static double MidPoints[1][3] = { { 0.5, 0.5, 0.0 } };
210 
211 //------------------------------------------------------------------------------
InterpolateAttributes(vtkPointData * inPd,vtkCellData * inCd,vtkIdType cellId,vtkDataArray * cellScalars)212 void vtkQuadraticQuad::InterpolateAttributes(
213   vtkPointData* inPd, vtkCellData* inCd, vtkIdType cellId, vtkDataArray* cellScalars)
214 {
215   int numMidPts, i, j;
216   double weights[20];
217   double x[3];
218   double s;
219 
220   // Copy point and cell attribute data, first make sure it's empty:
221   this->PointData->Initialize();
222   this->CellData->Initialize();
223   // Make sure to copy ALL arrays. These field data have to be
224   // identical to the input field data. Otherwise, CopyData
225   // that occurs later may not work because the output field
226   // data was initialized (CopyAllocate) with the input field
227   // data.
228   this->PointData->CopyAllOn();
229   this->CellData->CopyAllOn();
230   this->PointData->CopyAllocate(inPd, 9);
231   this->CellData->CopyAllocate(inCd, 4);
232 
233   // copy the point data over into point ids 0->7
234   for (i = 0; i < 8; i++)
235   {
236     this->PointData->CopyData(inPd, this->PointIds->GetId(i), i);
237     this->CellScalars->SetValue(i, cellScalars->GetTuple1(i));
238   }
239   // copy the cell data over to the linear cell
240   this->CellData->CopyData(inCd, cellId, 0);
241 
242   // Interpolate new values
243   double p[3];
244   this->Points->Resize(9);
245   this->CellScalars->Resize(9);
246   for (numMidPts = 0; numMidPts < 1; numMidPts++)
247   {
248     vtkQuadraticQuad::InterpolationFunctions(MidPoints[numMidPts], weights);
249 
250     x[0] = x[1] = x[2] = 0.0;
251     s = 0.0;
252     for (i = 0; i < 8; i++)
253     {
254       this->Points->GetPoint(i, p);
255       for (j = 0; j < 3; j++)
256       {
257         x[j] += p[j] * weights[i];
258       }
259       s += cellScalars->GetTuple1(i) * weights[i];
260     }
261     this->Points->SetPoint(8 + numMidPts, x);
262     this->CellScalars->SetValue(8 + numMidPts, s);
263     this->PointData->InterpolatePoint(inPd, 8 + numMidPts, this->PointIds, weights);
264   }
265 }
266 
267 //------------------------------------------------------------------------------
Contour(double value,vtkDataArray * cellScalars,vtkIncrementalPointLocator * locator,vtkCellArray * verts,vtkCellArray * lines,vtkCellArray * polys,vtkPointData * inPd,vtkPointData * outPd,vtkCellData * inCd,vtkIdType cellId,vtkCellData * outCd)268 void vtkQuadraticQuad::Contour(double value, vtkDataArray* cellScalars,
269   vtkIncrementalPointLocator* locator, vtkCellArray* verts, vtkCellArray* lines,
270   vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId,
271   vtkCellData* outCd)
272 {
273   // interpolate point and cell data
274   this->InterpolateAttributes(inPd, inCd, cellId, cellScalars);
275 
276   // contour each linear quad separately
277   for (int i = 0; i < 4; i++)
278   {
279     for (int j = 0; j < 4; j++) // for each of the four vertices of the linear quad
280     {
281       this->Quad->Points->SetPoint(j, this->Points->GetPoint(LinearQuads[i][j]));
282       this->Quad->PointIds->SetId(j, LinearQuads[i][j]);
283       this->Scalars->SetValue(j, this->CellScalars->GetValue(LinearQuads[i][j]));
284     }
285 
286     this->Quad->Contour(value, this->Scalars, locator, verts, lines, polys, this->PointData, outPd,
287       this->CellData, i, outCd);
288   }
289 }
290 //------------------------------------------------------------------------------
291 // Clip this quadratic quad using scalar value provided. Like contouring,
292 // except that it cuts the quad to produce other quads and triangles.
Clip(double value,vtkDataArray * cellScalars,vtkIncrementalPointLocator * locator,vtkCellArray * polys,vtkPointData * inPd,vtkPointData * outPd,vtkCellData * inCd,vtkIdType cellId,vtkCellData * outCd,int insideOut)293 void vtkQuadraticQuad::Clip(double value, vtkDataArray* cellScalars,
294   vtkIncrementalPointLocator* locator, vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd,
295   vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd, int insideOut)
296 {
297   // interpolate point and cell data
298   this->InterpolateAttributes(inPd, inCd, cellId, cellScalars);
299 
300   // contour each linear quad separately
301   for (int i = 0; i < 4; i++)
302   {
303     for (int j = 0; j < 4; j++) // for each of the four vertices of the linear quad
304     {
305       this->Quad->Points->SetPoint(j, this->Points->GetPoint(LinearQuads[i][j]));
306       this->Quad->PointIds->SetId(j, LinearQuads[i][j]);
307       this->Scalars->SetValue(j, this->CellScalars->GetValue(LinearQuads[i][j]));
308     }
309 
310     this->Quad->Clip(value, this->Scalars, locator, polys, this->PointData, outPd, this->CellData,
311       i, outCd, insideOut);
312   }
313 }
314 
315 //------------------------------------------------------------------------------
316 // Line-line intersection. Intersection has to occur within [0,1] parametric
317 // coordinates and with specified tolerance.
IntersectWithLine(const double * p1,const double * p2,double tol,double & t,double * x,double * pcoords,int & subId)318 int vtkQuadraticQuad::IntersectWithLine(
319   const double* p1, const double* p2, double tol, double& t, double* x, double* pcoords, int& subId)
320 {
321   int subTest, i;
322   subId = 0;
323   double weights[8];
324 
325   // first define the midquad point
326   this->Subdivide(weights);
327 
328   // intersect the four linear quads
329   for (i = 0; i < 4; i++)
330   {
331     this->Quad->Points->SetPoint(0, this->Points->GetPoint(LinearQuads[i][0]));
332     this->Quad->Points->SetPoint(1, this->Points->GetPoint(LinearQuads[i][1]));
333     this->Quad->Points->SetPoint(2, this->Points->GetPoint(LinearQuads[i][2]));
334     this->Quad->Points->SetPoint(3, this->Points->GetPoint(LinearQuads[i][3]));
335 
336     if (this->Quad->IntersectWithLine(p1, p2, tol, t, x, pcoords, subTest))
337     {
338       return 1;
339     }
340   }
341 
342   return 0;
343 }
344 
345 //------------------------------------------------------------------------------
Triangulate(int vtkNotUsed (index),vtkIdList * ptIds,vtkPoints * pts)346 int vtkQuadraticQuad::Triangulate(int vtkNotUsed(index), vtkIdList* ptIds, vtkPoints* pts)
347 {
348   pts->Reset();
349   ptIds->Reset();
350 
351   // Create six linear triangles: one at each corner and two
352   // to cover the remaining quadrilateral.
353 
354   // First the corner vertices
355   ptIds->InsertId(0, this->PointIds->GetId(0));
356   ptIds->InsertId(1, this->PointIds->GetId(4));
357   ptIds->InsertId(2, this->PointIds->GetId(7));
358   pts->InsertPoint(0, this->Points->GetPoint(0));
359   pts->InsertPoint(1, this->Points->GetPoint(4));
360   pts->InsertPoint(2, this->Points->GetPoint(7));
361 
362   ptIds->InsertId(3, this->PointIds->GetId(4));
363   ptIds->InsertId(4, this->PointIds->GetId(1));
364   ptIds->InsertId(5, this->PointIds->GetId(5));
365   pts->InsertPoint(3, this->Points->GetPoint(4));
366   pts->InsertPoint(4, this->Points->GetPoint(1));
367   pts->InsertPoint(5, this->Points->GetPoint(5));
368 
369   ptIds->InsertId(6, this->PointIds->GetId(5));
370   ptIds->InsertId(7, this->PointIds->GetId(2));
371   ptIds->InsertId(8, this->PointIds->GetId(6));
372   pts->InsertPoint(6, this->Points->GetPoint(5));
373   pts->InsertPoint(7, this->Points->GetPoint(2));
374   pts->InsertPoint(8, this->Points->GetPoint(6));
375 
376   ptIds->InsertId(9, this->PointIds->GetId(6));
377   ptIds->InsertId(10, this->PointIds->GetId(3));
378   ptIds->InsertId(11, this->PointIds->GetId(7));
379   pts->InsertPoint(9, this->Points->GetPoint(6));
380   pts->InsertPoint(10, this->Points->GetPoint(3));
381   pts->InsertPoint(11, this->Points->GetPoint(7));
382 
383   // Now the two remaining triangles
384   // Choose the triangulation that minimizes the edge length
385   // across the cell.
386   double x4[3], x5[3], x6[3], x7[3];
387   this->Points->GetPoint(4, x4);
388   this->Points->GetPoint(5, x5);
389   this->Points->GetPoint(6, x6);
390   this->Points->GetPoint(7, x7);
391 
392   if (vtkMath::Distance2BetweenPoints(x4, x6) <= vtkMath::Distance2BetweenPoints(x5, x7))
393   {
394     ptIds->InsertId(12, this->PointIds->GetId(4));
395     ptIds->InsertId(13, this->PointIds->GetId(6));
396     ptIds->InsertId(14, this->PointIds->GetId(7));
397     pts->InsertPoint(12, this->Points->GetPoint(4));
398     pts->InsertPoint(13, this->Points->GetPoint(6));
399     pts->InsertPoint(14, this->Points->GetPoint(7));
400 
401     ptIds->InsertId(15, this->PointIds->GetId(4));
402     ptIds->InsertId(16, this->PointIds->GetId(5));
403     ptIds->InsertId(17, this->PointIds->GetId(6));
404     pts->InsertPoint(15, this->Points->GetPoint(4));
405     pts->InsertPoint(16, this->Points->GetPoint(5));
406     pts->InsertPoint(17, this->Points->GetPoint(6));
407   }
408   else
409   {
410     ptIds->InsertId(12, this->PointIds->GetId(5));
411     ptIds->InsertId(13, this->PointIds->GetId(6));
412     ptIds->InsertId(14, this->PointIds->GetId(7));
413     pts->InsertPoint(12, this->Points->GetPoint(5));
414     pts->InsertPoint(13, this->Points->GetPoint(6));
415     pts->InsertPoint(14, this->Points->GetPoint(7));
416 
417     ptIds->InsertId(15, this->PointIds->GetId(5));
418     ptIds->InsertId(16, this->PointIds->GetId(7));
419     ptIds->InsertId(17, this->PointIds->GetId(4));
420     pts->InsertPoint(15, this->Points->GetPoint(5));
421     pts->InsertPoint(16, this->Points->GetPoint(7));
422     pts->InsertPoint(17, this->Points->GetPoint(4));
423   }
424 
425   return 1;
426 }
427 
428 //------------------------------------------------------------------------------
Derivatives(int vtkNotUsed (subId),const double pcoords[3],const double * values,int dim,double * derivs)429 void vtkQuadraticQuad::Derivatives(
430   int vtkNotUsed(subId), const double pcoords[3], const double* values, int dim, double* derivs)
431 {
432   double sum[2], p[3];
433   double functionDerivs[16];
434   double *J[3], J0[3], J1[3], J2[3];
435   double *JI[3], JI0[3], JI1[3], JI2[3];
436 
437   vtkQuadraticQuad::InterpolationDerivs(pcoords, functionDerivs);
438 
439   // Compute transposed Jacobian and inverse Jacobian
440   J[0] = J0;
441   J[1] = J1;
442   J[2] = J2;
443   JI[0] = JI0;
444   JI[1] = JI1;
445   JI[2] = JI2;
446   for (int k = 0; k < 3; k++)
447   {
448     J0[k] = J1[k] = 0.0;
449   }
450 
451   for (int i = 0; i < 8; i++)
452   {
453     this->Points->GetPoint(i, p);
454     for (int j = 0; j < 2; j++)
455     {
456       for (int k = 0; k < 3; k++)
457       {
458         J[j][k] += p[k] * functionDerivs[j * 8 + i];
459       }
460     }
461   }
462 
463   // Compute third row vector in transposed Jacobian and normalize it, so that Jacobian determinant
464   // stays the same.
465   vtkMath::Cross(J0, J1, J2);
466   if (vtkMath::Normalize(J2) == 0.0 || !vtkMath::InvertMatrix(J, JI, 3)) // degenerate
467   {
468     for (int j = 0; j < dim; j++)
469     {
470       for (int i = 0; i < 3; i++)
471       {
472         derivs[j * dim + i] = 0.0;
473       }
474     }
475     return;
476   }
477 
478   // Loop over "dim" derivative values. For each set of values,
479   // compute derivatives
480   // in local system and then transform into modelling system.
481   // First compute derivatives in local x'-y' coordinate system
482   for (int j = 0; j < dim; j++)
483   {
484     sum[0] = sum[1] = 0.0;
485     for (int i = 0; i < 8; i++) // loop over interp. function derivatives
486     {
487       sum[0] += functionDerivs[i] * values[dim * i + j];
488       sum[1] += functionDerivs[8 + i] * values[dim * i + j];
489     }
490     //    dBydx = sum[0]*JI[0][0] + sum[1]*JI[0][1];
491     //    dBydy = sum[0]*JI[1][0] + sum[1]*JI[1][1];
492 
493     // Transform into global system (dot product with global axes)
494     derivs[3 * j] = sum[0] * JI[0][0] + sum[1] * JI[0][1];
495     derivs[3 * j + 1] = sum[0] * JI[1][0] + sum[1] * JI[1][1];
496     derivs[3 * j + 2] = sum[0] * JI[2][0] + sum[1] * JI[2][1];
497   }
498 }
499 
500 //------------------------------------------------------------------------------
501 // Compute interpolation functions. The first four nodes are the corner
502 // vertices; the others are mid-edge nodes.
InterpolationFunctions(const double pcoords[3],double weights[8])503 void vtkQuadraticQuad::InterpolationFunctions(const double pcoords[3], double weights[8])
504 {
505   double r = pcoords[0];
506   double s = pcoords[1];
507 
508   // midedge weights
509   weights[4] = 4 * r * (1.0 - r) * (1.0 - s);
510   weights[5] = 4 * r * (1.0 - s) * s;
511   weights[6] = 4 * r * (1.0 - r) * s;
512   weights[7] = 4 * (1.0 - r) * (1.0 - s) * s;
513 
514   // corner
515   weights[0] = (1.0 - r) * (1.0 - s) - 0.5 * (weights[4] + weights[7]);
516   weights[1] = r * (1.0 - s) - 0.5 * (weights[4] + weights[5]);
517   weights[2] = r * s - 0.5 * (weights[5] + weights[6]);
518   weights[3] = (1.0 - r) * s - 0.5 * (weights[6] + weights[7]);
519 }
520 
521 //------------------------------------------------------------------------------
522 // Derivatives in parametric space.
InterpolationDerivs(const double pcoords[3],double derivs[16])523 void vtkQuadraticQuad::InterpolationDerivs(const double pcoords[3], double derivs[16])
524 {
525   // Coordinate conversion
526   double r = pcoords[0];
527   double s = pcoords[1];
528 
529   // Derivatives in the r-direction
530   // midedge
531   derivs[4] = 4 * (1.0 - s) * (1.0 - 2 * r);
532   derivs[5] = 4 * (1.0 - s) * s;
533   derivs[6] = 4 * s * (1.0 - 2 * r);
534   derivs[7] = -4 * (1.0 - s) * s;
535   derivs[0] = -(1.0 - s) - 0.5 * (derivs[4] + derivs[7]);
536   derivs[1] = (1.0 - s) - 0.5 * (derivs[4] + derivs[5]);
537   derivs[2] = s - 0.5 * (derivs[5] + derivs[6]);
538   derivs[3] = -s - 0.5 * (derivs[6] + derivs[7]);
539 
540   // Derivatives in the s-direction
541   // midedge
542   derivs[12] = -4 * r * (1.0 - r);
543   derivs[13] = 4 * r * (1.0 - 2 * s);
544   derivs[14] = 4 * r * (1.0 - r);
545   derivs[15] = 4 * (1.0 - r) * (1.0 - 2 * s);
546   derivs[8] = -(1.0 - r) - 0.5 * (derivs[12] + derivs[15]);
547   derivs[9] = -r - 0.5 * (derivs[12] + derivs[13]);
548   derivs[10] = r - 0.5 * (derivs[13] + derivs[14]);
549   derivs[11] = (1.0 - r) - 0.5 * (derivs[14] + derivs[15]);
550 }
551 
552 //------------------------------------------------------------------------------
553 static double vtkQQuadCellPCoords[24] = {
554   0.0, 0.0, 0.0, //
555   1.0, 0.0, 0.0, //
556   1.0, 1.0, 0.0, //
557   0.0, 1.0, 0.0, //
558   0.5, 0.0, 0.0, //
559   1.0, 0.5, 0.0, //
560   0.5, 1.0, 0.0, //
561   0.0, 0.5, 0.0  //
562 };
GetParametricCoords()563 double* vtkQuadraticQuad::GetParametricCoords()
564 {
565   return vtkQQuadCellPCoords;
566 }
567 
568 //------------------------------------------------------------------------------
PrintSelf(ostream & os,vtkIndent indent)569 void vtkQuadraticQuad::PrintSelf(ostream& os, vtkIndent indent)
570 {
571   this->Superclass::PrintSelf(os, indent);
572 
573   os << indent << "Edge:\n";
574   this->Edge->PrintSelf(os, indent.GetNextIndent());
575   os << indent << "Quad:\n";
576   this->Quad->PrintSelf(os, indent.GetNextIndent());
577   os << indent << "Scalars:\n";
578   this->Scalars->PrintSelf(os, indent.GetNextIndent());
579 }
580