Actual source code: plexrefregular.c

  1: #include <petsc/private/dmplextransformimpl.h>

  3: /* Regular Refinment of Hybrid Meshes

  5:    We would like to express regular refinement as a small set of rules that can be applied on every point of the Plex
  6:    to automatically generate a refined Plex. In fact, we would like these rules to be general enough to encompass other
  7:    transformations, such as changing from one type of cell to another, as simplex to hex.

  9:    To start, we can create a function that takes an original cell type and returns the number of new cells replacing it
 10:    and the types of the new cells.

 12:    We need the group multiplication table for group actions from the dihedral group for each cell type.

 14:    We need an operator which takes in a cell, and produces a new set of cells with new faces and correct orientations. I think
 15:    we can just write this operator for faces with identity, and then compose the face orientation actions to get the actual
 16:    (face, orient) pairs for each subcell.
 17: */

 19: /*@
 20:   DMPlexRefineRegularGetAffineFaceTransforms - Gets the affine map from the reference face cell to each face in the given cell

 22:   Input Parameters:
 23: + cr - The DMPlexCellRefiner object
 24: - ct - The cell type

 26:   Output Parameters:
 27: + Nf   - The number of faces for this cell type
 28: . v0   - The translation of the first vertex for each face
 29: . J    - The Jacobian for each face (map from original cell to subcell)
 30: . invJ - The inverse Jacobian for each face
 31: - detJ - The determinant of the Jacobian for each face

 33:   Note: The Jacobian and inverse Jacboian will be rectangular, and the inverse is really a generalized inverse.
 34: $         v0 + j x_face = x_cell
 35: $    invj (x_cell - v0) = x_face

 37:   Level: developer

 39: .seealso: DMPlexCellRefinerGetAffineTransforms(), Create()
 40: @*/
 41: PetscErrorCode DMPlexRefineRegularGetAffineFaceTransforms(DMPlexTransform tr, DMPolytopeType ct, PetscInt *Nf, PetscReal *v0[], PetscReal *J[], PetscReal *invJ[], PetscReal *detJ[])
 42: {
 43:   /*
 44:    2
 45:    |\
 46:    | \
 47:    |  \
 48:    |   \
 49:    |    \
 50:    |     \
 51:    |      \
 52:    2       1
 53:    |        \
 54:    |         \
 55:    |          \
 56:    0---0-------1
 57:    v0[Nf][dc]:       3 x 2
 58:    J[Nf][df][dc]:    3 x 1 x 2
 59:    invJ[Nf][dc][df]: 3 x 2 x 1
 60:    detJ[Nf]:         3
 61:    */
 62:   static PetscReal tri_v0[]   = {0.0, -1.0,  0.0, 0.0,  -1.0,  0.0};
 63:   static PetscReal tri_J[]    = {1.0, 0.0,  -1.0, 1.0,   0.0, -1.0};
 64:   static PetscReal tri_invJ[] = {1.0, 0.0,  -0.5, 0.5,   0.0, -1.0};
 65:   static PetscReal tri_detJ[] = {1.0,  1.414213562373095,  1.0};
 66:   /*
 67:    3---------2---------2
 68:    |                   |
 69:    |                   |
 70:    |                   |
 71:    3                   1
 72:    |                   |
 73:    |                   |
 74:    |                   |
 75:    0---------0---------1

 77:    v0[Nf][dc]:       4 x 2
 78:    J[Nf][df][dc]:    4 x 1 x 2
 79:    invJ[Nf][dc][df]: 4 x 2 x 1
 80:    detJ[Nf]:         4
 81:    */
 82:   static PetscReal quad_v0[]   = {0.0, -1.0,  1.0, 0.0,   0.0, 1.0  -1.0,  0.0};
 83:   static PetscReal quad_J[]    = {1.0, 0.0,   0.0, 1.0,  -1.0, 0.0,  0.0, -1.0};
 84:   static PetscReal quad_invJ[] = {1.0, 0.0,   0.0, 1.0,  -1.0, 0.0,  0.0, -1.0};
 85:   static PetscReal quad_detJ[] = {1.0,  1.0,  1.0,  1.0};

 87:   switch (ct) {
 88:     case DM_POLYTOPE_TRIANGLE:      if (Nf) *Nf = 3; if (v0) *v0 = tri_v0;  if (J) *J = tri_J;  if (invJ) *invJ = tri_invJ;  if (detJ) *detJ = tri_detJ;  break;
 89:     case DM_POLYTOPE_QUADRILATERAL: if (Nf) *Nf = 4; if (v0) *v0 = quad_v0; if (J) *J = quad_J; if (invJ) *invJ = quad_invJ; if (detJ) *detJ = quad_detJ; break;
 90:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unsupported polytope type %s", DMPolytopeTypes[ct]);
 91:   }
 92:   return 0;
 93: }

 95: /*@
 96:   DMPlexRefineRegularGetAffineTransforms - Gets the affine map from the reference cell to each subcell

 98:   Input Parameters:
 99: + cr - The DMPlexCellRefiner object
100: - ct - The cell type

102:   Output Parameters:
103: + Nc   - The number of subcells produced from this cell type
104: . v0   - The translation of the first vertex for each subcell
105: . J    - The Jacobian for each subcell (map from reference cell to subcell)
106: - invJ - The inverse Jacobian for each subcell

108:   Level: developer

110: .seealso: DMPlexRefineRegularGetAffineFaceTransforms(), DMPLEXREFINEREGULAR
111: @*/
112: PetscErrorCode DMPlexRefineRegularGetAffineTransforms(DMPlexTransform tr, DMPolytopeType ct, PetscInt *Nc, PetscReal *v0[], PetscReal *J[], PetscReal *invJ[])
113: {
114:   /*
115:    2
116:    |\
117:    | \
118:    |  \
119:    |   \
120:    | C  \
121:    |     \
122:    |      \
123:    2---1---1
124:    |\  D  / \
125:    | 2   0   \
126:    |A \ /  B  \
127:    0---0-------1
128:    */
129:   static PetscReal tri_v0[]   = {-1.0, -1.0,  0.0, -1.0,  -1.0, 0.0,  0.0, -1.0};
130:   static PetscReal tri_J[]    = {0.5, 0.0,
131:                                  0.0, 0.5,

133:                                  0.5, 0.0,
134:                                  0.0, 0.5,

136:                                  0.5, 0.0,
137:                                  0.0, 0.5,

139:                                  0.0, -0.5,
140:                                  0.5,  0.5};
141:   static PetscReal tri_invJ[] = {2.0, 0.0,
142:                                  0.0, 2.0,

144:                                  2.0, 0.0,
145:                                  0.0, 2.0,

147:                                  2.0, 0.0,
148:                                  0.0, 2.0,

150:                                  2.0,  2.0,
151:                                 -2.0,  0.0};
152:     /*
153:      3---------2---------2
154:      |         |         |
155:      |    D    2    C    |
156:      |         |         |
157:      3----3----0----1----1
158:      |         |         |
159:      |    A    0    B    |
160:      |         |         |
161:      0---------0---------1
162:      */
163:   static PetscReal quad_v0[]   = {-1.0, -1.0,  0.0, -1.0,  0.0, 0.0,  -1.0, 0.0};
164:   static PetscReal quad_J[]    = {0.5, 0.0,
165:                                   0.0, 0.5,

167:                                   0.5, 0.0,
168:                                   0.0, 0.5,

170:                                   0.5, 0.0,
171:                                   0.0, 0.5,

173:                                   0.5, 0.0,
174:                                   0.0, 0.5};
175:   static PetscReal quad_invJ[] = {2.0, 0.0,
176:                                   0.0, 2.0,

178:                                   2.0, 0.0,
179:                                   0.0, 2.0,

181:                                   2.0, 0.0,
182:                                   0.0, 2.0,

184:                                   2.0, 0.0,
185:                                   0.0, 2.0};
186:     /*
187:      Bottom (viewed from top)    Top
188:      1---------2---------2       7---------2---------6
189:      |         |         |       |         |         |
190:      |    B    2    C    |       |    H    2    G    |
191:      |         |         |       |         |         |
192:      3----3----0----1----1       3----3----0----1----1
193:      |         |         |       |         |         |
194:      |    A    0    D    |       |    E    0    F    |
195:      |         |         |       |         |         |
196:      0---------0---------3       4---------0---------5
197:      */
198:   static PetscReal hex_v0[]   = {-1.0, -1.0, -1.0,  -1.0,  0.0, -1.0,  0.0, 0.0, -1.0,   0.0, -1.0, -1.0,
199:                                  -1.0, -1.0,  0.0,   0.0, -1.0,  0.0,  0.0, 0.0,  0.0,  -1.0,  0.0,  0.0};
200:   static PetscReal hex_J[]    = {0.5, 0.0, 0.0,
201:                                  0.0, 0.5, 0.0,
202:                                  0.0, 0.0, 0.5,

204:                                  0.5, 0.0, 0.0,
205:                                  0.0, 0.5, 0.0,
206:                                  0.0, 0.0, 0.5,

208:                                  0.5, 0.0, 0.0,
209:                                  0.0, 0.5, 0.0,
210:                                  0.0, 0.0, 0.5,

212:                                  0.5, 0.0, 0.0,
213:                                  0.0, 0.5, 0.0,
214:                                  0.0, 0.0, 0.5,

216:                                  0.5, 0.0, 0.0,
217:                                  0.0, 0.5, 0.0,
218:                                  0.0, 0.0, 0.5,

220:                                  0.5, 0.0, 0.0,
221:                                  0.0, 0.5, 0.0,
222:                                  0.0, 0.0, 0.5,

224:                                  0.5, 0.0, 0.0,
225:                                  0.0, 0.5, 0.0,
226:                                  0.0, 0.0, 0.5,

228:                                  0.5, 0.0, 0.0,
229:                                  0.0, 0.5, 0.0,
230:                                  0.0, 0.0, 0.5};
231:   static PetscReal hex_invJ[] = {2.0, 0.0, 0.0,
232:                                  0.0, 2.0, 0.0,
233:                                  0.0, 0.0, 2.0,

235:                                  2.0, 0.0, 0.0,
236:                                  0.0, 2.0, 0.0,
237:                                  0.0, 0.0, 2.0,

239:                                  2.0, 0.0, 0.0,
240:                                  0.0, 2.0, 0.0,
241:                                  0.0, 0.0, 2.0,

243:                                  2.0, 0.0, 0.0,
244:                                  0.0, 2.0, 0.0,
245:                                  0.0, 0.0, 2.0,

247:                                  2.0, 0.0, 0.0,
248:                                  0.0, 2.0, 0.0,
249:                                  0.0, 0.0, 2.0,

251:                                  2.0, 0.0, 0.0,
252:                                  0.0, 2.0, 0.0,
253:                                  0.0, 0.0, 2.0,

255:                                  2.0, 0.0, 0.0,
256:                                  0.0, 2.0, 0.0,
257:                                  0.0, 0.0, 2.0,

259:                                  2.0, 0.0, 0.0,
260:                                  0.0, 2.0, 0.0,
261:                                  0.0, 0.0, 2.0};

263:   switch (ct) {
264:     case DM_POLYTOPE_TRIANGLE:      if (Nc) *Nc = 4; if (v0) *v0 = tri_v0;  if (J) *J = tri_J;  if (invJ) *invJ = tri_invJ;  break;
265:     case DM_POLYTOPE_QUADRILATERAL: if (Nc) *Nc = 4; if (v0) *v0 = quad_v0; if (J) *J = quad_J; if (invJ) *invJ = quad_invJ; break;
266:     case DM_POLYTOPE_HEXAHEDRON:    if (Nc) *Nc = 8; if (v0) *v0 = hex_v0;  if (J) *J = hex_J;  if (invJ) *invJ = hex_invJ;  break;
267:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Unsupported polytope type %s", DMPolytopeTypes[ct]);
268:   }
269:   return 0;
270: }

272: #if 0
273: static PetscErrorCode DMPlexCellRefinerGetCellVertices_Regular(DMPlexCellRefiner cr, DMPolytopeType ct, PetscInt *Nv, PetscReal *subcellV[])
274: {
275:   static PetscReal seg_v[]  = {-1.0,  0.0,  1.0};
276:   static PetscReal tri_v[]  = {-1.0, -1.0,  1.0, -1.0,  -1.0, 1.0,  0.0, -1.0,  0.0, 0.0,  -1.0, 0.0};
277:   static PetscReal quad_v[] = {-1.0, -1.0,  1.0, -1.0,   1.0, 1.0,  -1.0, 1.0,  0.0, -1.0,  1.0, 0.0,   0.0, 1.0,  -1.0, 0.0,  0.0, 0.0};
278:   static PetscReal tet_v[]  = {-1.0, -1.0, -1.0,   0.0, -1.0, -1.0,   1.0, -1.0, -1.0,
279:                                -1.0,  0.0, -1.0,   0.0,  0.0, -1.0,  -1.0,  1.0, -1.0,
280:                                -1.0, -1.0,  0.0,   0.0, -1.0,  0.0,  -1.0,  0.0,  0.0,  -1.0, -1.0,  1.0};
281:   static PetscReal hex_v[]  = {-1.0, -1.0, -1.0,   0.0, -1.0, -1.0,   1.0, -1.0, -1.0,
282:                                -1.0,  0.0, -1.0,   0.0,  0.0, -1.0,   1.0,  0.0, -1.0,
283:                                -1.0,  1.0, -1.0,   0.0,  1.0, -1.0,   1.0,  1.0, -1.0,
284:                                -1.0, -1.0,  0.0,   0.0, -1.0,  0.0,   1.0, -1.0,  0.0,
285:                                -1.0,  0.0,  0.0,   0.0,  0.0,  0.0,   1.0,  0.0,  0.0,
286:                                -1.0,  1.0,  0.0,   0.0,  1.0,  0.0,   1.0,  1.0,  0.0,
287:                                -1.0, -1.0,  1.0,   0.0, -1.0,  1.0,   1.0, -1.0,  1.0,
288:                                -1.0,  0.0,  1.0,   0.0,  0.0,  1.0,   1.0,  0.0,  1.0,
289:                                -1.0,  1.0,  1.0,   0.0,  1.0,  1.0,   1.0,  1.0,  1.0};

291:   switch (ct) {
292:     case DM_POLYTOPE_SEGMENT:       *Nv =  3; *subcellV = seg_v;  break;
293:     case DM_POLYTOPE_TRIANGLE:      *Nv =  6; *subcellV = tri_v;  break;
294:     case DM_POLYTOPE_QUADRILATERAL: *Nv =  9; *subcellV = quad_v; break;
295:     case DM_POLYTOPE_TETRAHEDRON:   *Nv = 10; *subcellV = tet_v;  break;
296:     case DM_POLYTOPE_HEXAHEDRON:    *Nv = 27; *subcellV = hex_v;  break;
297:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No subcell vertices for cell type %s", DMPolytopeTypes[ct]);
298:   }
299:   return 0;
300: }

302: static PetscErrorCode DMPlexCellRefinerGetSubcellVertices_Regular(DMPlexCellRefiner cr, DMPolytopeType ct, DMPolytopeType rct, PetscInt r, PetscInt *Nv, PetscInt *subcellV[])
303: {
304:   static PetscInt seg_v[]  = {0, 1, 1, 2};
305:   static PetscInt tri_v[]  = {0, 3, 5,  3, 1, 4,  5, 4, 2,  3, 4, 5};
306:   static PetscInt quad_v[] = {0, 4, 8, 7,  4, 1, 5, 8,  8, 5, 2, 6,  7, 8, 6, 3};
307:   static PetscInt tet_v[]  = {0, 3, 1, 6,  3, 2, 4, 8,  1, 4, 5, 7,  6, 8, 7, 9,
308:                               1, 6, 3, 7,  8, 4, 3, 7,  7, 3, 1, 4,  7, 3, 8, 6};
309:   static PetscInt hex_v[]  = {0,  3,  4,  1,  9, 10, 13, 12,   3,  6,  7,  4, 12, 13, 16, 15,   4,  7,  8,  5, 13, 14, 17, 16,   1,  4 , 5 , 2, 10, 11, 14, 13,
310:                               9, 12, 13, 10, 18, 19, 22, 21,  10, 13, 14, 11, 19, 20, 23, 22,  13, 16, 17, 14, 22, 23, 26, 25,  12, 15, 16, 13, 21, 22, 25, 24};

313:   switch (ct) {
314:     case DM_POLYTOPE_SEGMENT:       *Nv = 2; *subcellV = &seg_v[r*(*Nv)];  break;
315:     case DM_POLYTOPE_TRIANGLE:      *Nv = 3; *subcellV = &tri_v[r*(*Nv)];  break;
316:     case DM_POLYTOPE_QUADRILATERAL: *Nv = 4; *subcellV = &quad_v[r*(*Nv)]; break;
317:     case DM_POLYTOPE_TETRAHEDRON:   *Nv = 4; *subcellV = &tet_v[r*(*Nv)];  break;
318:     case DM_POLYTOPE_HEXAHEDRON:    *Nv = 8; *subcellV = &hex_v[r*(*Nv)];  break;
319:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "No subcell vertices for cell type %s", DMPolytopeTypes[ct]);
320:   }
321:   return 0;
322: }
323: #endif

325: static PetscErrorCode DMPlexTransformView_Regular(DMPlexTransform tr, PetscViewer viewer)
326: {
327:   PetscBool      isascii;

331:   PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &isascii);
332:   if (isascii) {
333:     const char *name;

335:     PetscObjectGetName((PetscObject) tr, &name);
336:     PetscViewerASCIIPrintf(viewer, "Regular refinement %s\n", name ? name : "");
337:   } else {
338:     SETERRQ(PetscObjectComm((PetscObject) tr), PETSC_ERR_SUP, "Viewer type %s not yet supported for DMPlexTransform writing", ((PetscObject) viewer)->type_name);
339:   }
340:   return 0;
341: }

343: static PetscErrorCode DMPlexTransformSetUp_Regular(DMPlexTransform tr)
344: {
345:   return 0;
346: }

348: static PetscErrorCode DMPlexTransformDestroy_Regular(DMPlexTransform tr)
349: {
350:   DMPlexRefine_Regular *f = (DMPlexRefine_Regular *) tr->data;

352:   PetscFree(f);
353:   return 0;
354: }

356: PetscErrorCode DMPlexTransformGetSubcellOrientation_Regular(DMPlexTransform tr, DMPolytopeType sct, PetscInt sp, PetscInt so, DMPolytopeType tct, PetscInt r, PetscInt o, PetscInt *rnew, PetscInt *onew)
357: {
358:   static PetscInt seg_seg[] = {1, -1, 0, -1,
359:                                0,  0, 1,  0};
360:   static PetscInt tri_seg[] = {2, -1, 1, -1, 0, -1,
361:                                1, -1, 0, -1, 2, -1,
362:                                0, -1, 2, -1, 1, -1,
363:                                0,  0, 1,  0, 2,  0,
364:                                1,  0, 2,  0, 0,  0,
365:                                2,  0, 0,  0, 1,  0};
366:   static PetscInt tri_tri[] = {1, -3, 0, -3, 2, -3, 3, -2,
367:                                0, -2, 2, -2, 1, -2, 3, -1,
368:                                2, -1, 1, -1, 0, -1, 3, -3,
369:                                0,  0, 1,  0, 2,  0, 3,  0,
370:                                1,  1, 2,  1, 0,  1, 3,  1,
371:                                2,  2, 0,  2, 1,  2, 3,  2};
372:   static PetscInt quad_seg[]  = {1, 0, 0, 0, 3, 0, 2, 0,
373:                                  0, 0, 3, 0, 2, 0, 1, 0,
374:                                  3, 0, 2, 0, 1, 0, 0, 0,
375:                                  2, 0, 1, 0, 0, 0, 3, 0,
376:                                  0, 0, 1, 0, 2, 0, 3, 0,
377:                                  1, 0, 2, 0, 3, 0, 0, 0,
378:                                  2, 0, 3, 0, 0, 0, 1, 0,
379:                                  3, 0, 0, 0, 1, 0, 2, 0};
380:   static PetscInt quad_quad[] = {2, -4, 1, -4, 0, -4, 3, -4,
381:                                  1, -3, 0, -3, 3, -3, 2, -3,
382:                                  0, -2, 3, -2, 2, -2, 1, -2,
383:                                  3, -1, 2, -1, 1, -1, 0, -1,
384:                                  0,  0, 1,  0, 2,  0, 3,  0,
385:                                  1,  1, 2,  1, 3,  1, 0,  1,
386:                                  2,  2, 3,  2, 0,  2, 1,  2,
387:                                  3,  3, 0,  3, 1,  3, 2,  3};
388:   static PetscInt tseg_seg[]  = {0, -1,
389:                                  0,  0,
390:                                  0,  0,
391:                                  0, -1};
392:   static PetscInt tseg_tseg[] = {1, -2, 0, -2,
393:                                  1, -1, 0, -1,
394:                                  0,  0, 1,  0,
395:                                  0,  1, 1,  1};
396:   static PetscInt tet_seg[]   = {0, -1,
397:                                  0,  0,
398:                                  0,  0,
399:                                  0, -1,
400:                                  0,  0,
401:                                  0,  0,
402:                                  0,  0,
403:                                  0,  0,
404:                                  0,  0,
405:                                  0,  0,
406:                                  0,  0,
407:                                  0,  0,
408:                                  0,  0,
409:                                  0,  0,
410:                                  0,  0,
411:                                  0,  0,
412:                                  0,  0,
413:                                  0,  0,
414:                                  0, -1,
415:                                  0,  0,
416:                                  0,  0,
417:                                  0, -1,
418:                                  0,  0,
419:                                  0,  0};
420:   static PetscInt tet_tri[]   = {2, -1, 3, -1, 1, -3, 0, -2, 6, 1, 7, -3, 5, 2, 4, -3,
421:                                  3, -1, 1, -1, 2, -3, 0, -1, 4, 0, 5, 0, 6, 0, 7, 0,
422:                                  1, -1, 2, -1, 3, -3, 0, -3, 4, 0, 5, 0, 6, 0, 7, 0,
423:                                  3, -2, 2, -3, 0, -1, 1, -1, 7, -3, 6, 1, 4, 2, 5, -3,
424:                                  2, -3, 0, -2, 3, -1, 1, -3, 4, 0, 5, 0, 6, 0, 7, 0,
425:                                  0, -2, 3, -2, 2, -2, 1, -2, 4, 0, 5, 0, 6, 0, 7, 0,
426:                                  0, -1, 1, -2, 3, -2, 2, -2, 7, 1, 6, -3, 5, -3, 4, 2,
427:                                  1, -2, 3, -3, 0, -3, 2, -1, 4, 0, 5, 0, 6, 0, 7, 0,
428:                                  3, -3, 0, -1, 1, -1, 2, -3, 4, 0, 5, 0, 6, 0, 7, 0,
429:                                  1, -3, 0, -3, 2, -1, 3, -3, 6, -3, 7, 1, 4, -3, 5, 2,
430:                                  0, -3, 2, -2, 1, -2, 3, -2, 4, 0, 5, 0, 6, 0, 7, 0,
431:                                  2, -2, 1, -3, 0, -2, 3, -1, 4, 0, 5, 0, 6, 0, 7, 0,
432:                                  0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0,
433:                                  1, 0, 2, 2, 0, 1, 3, 1, 4, 0, 5, 0, 6, 0, 7, 0,
434:                                  2, 2, 0, 0, 1, 1, 3, 2, 4, 0, 5, 0, 6, 0, 7, 0,
435:                                  1, 2, 0, 1, 3, 1, 2, 2, 5, 0, 4, 0, 7, -1, 6, -1,
436:                                  0, 1, 3, 0, 1, 0, 2, 0, 4, 0, 5, 0, 6, 0, 7, 0,
437:                                  3, 0, 1, 2, 0, 2, 2, 1, 4, 0, 5, 0, 6, 0, 7, 0,
438:                                  2, 0, 3, 2, 0, 0, 1, 1, 4, -2, 5, -2, 7, 0, 6, 0,
439:                                  3, 2, 0, 2, 2, 1, 1, 2, 4, 0, 5, 0, 6, 0, 7, 0,
440:                                  0, 2, 2, 0, 3, 0, 1, 0, 4, 0, 5, 0, 6, 0, 7, 0,
441:                                  3, 1, 2, 1, 1, 2, 0, 2, 5, -2, 4, -2, 6, -1, 7, -1,
442:                                  2, 1, 1, 1, 3, 2, 0, 0, 4, 0, 5, 0, 6, 0, 7, 0,
443:                                  1, 1, 3, 1, 2, 2, 0, 1, 4, 0, 5, 0, 6, 0, 7, 0};
444:   static PetscInt tet_tet[]   = {2, -12, 3, -12, 1, -12, 0, -12, 6, -9, 7, -9, 5, -12, 4, -12,
445:                                  3, -11, 1, -11, 2, -11, 0, -11, 4, 0, 5, 0, 6, 0, 7, 0,
446:                                  1, -10, 2, -10, 3, -10, 0, -10, 4, 0, 5, 0, 6, 0, 7, 0,
447:                                  3, -9, 2, -9, 0, -9, 1, -9, 7, -9, 6, -9, 4, -12, 5, -12,
448:                                  2, -8, 0, -8, 3, -8, 1, -8, 4, 0, 5, 0, 6, 0, 7, 0,
449:                                  0, -7, 3, -7, 2, -7, 1, -7, 4, 0, 5, 0, 6, 0, 7, 0,
450:                                  0, -6, 1, -6, 3, -6, 2, -6, 4, -3, 5, -3, 7, -6, 6, -6,
451:                                  1, -5, 3, -5, 0, -5, 2, -5, 4, 0, 5, 0, 6, 0, 7, 0,
452:                                  3, -4, 0, -4, 1, -4, 2, -4, 4, 0, 5, 0, 6, 0, 7, 0,
453:                                  1, -3, 0, -3, 2, -3, 3, -3, 5, -3, 4, -3, 6, -6, 7, -6,
454:                                  0, -2, 2, -2, 1, -2, 3, -2, 4, 0, 5, 0, 6, 0, 7, 0,
455:                                  2, -1, 1, -1, 0, -1, 3, -1, 4, 0, 5, 0, 6, 0, 7, 0,
456:                                  0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0,
457:                                  1, 1, 2, 1, 0, 1, 3, 1, 4, 0, 5, 0, 6, 0, 7, 0,
458:                                  2, 2, 0, 2, 1, 2, 3, 2, 4, 0, 5, 0, 6, 0, 7, 0,
459:                                  1, 3, 0, 3, 3, 3, 2, 3, 5, 0, 4, 0, 7, 0, 6, 0,
460:                                  0, 4, 3, 4, 1, 4, 2, 4, 4, 0, 5, 0, 6, 0, 7, 0,
461:                                  3, 5, 1, 5, 0, 5, 2, 5, 4, 0, 5, 0, 6, 0, 7, 0,
462:                                  2, 6, 3, 6, 0, 6, 1, 6, 6, 6, 7, 6, 4, 6, 5, 6,
463:                                  3, 7, 0, 7, 2, 7, 1, 7, 4, 0, 5, 0, 6, 0, 7, 0,
464:                                  0, 8, 2, 8, 3, 8, 1, 8, 4, 0, 5, 0, 6, 0, 7, 0,
465:                                  3, 9, 2, 9, 1, 9, 0, 9, 7, 6, 6, 6, 5, 6, 4, 6,
466:                                  2, 10, 1, 10, 3, 10, 0, 10, 4, 0, 5, 0, 6, 0, 7, 0,
467:                                  1, 11, 3, 11, 2, 11, 0, 11, 4, 0, 5, 0, 6, 0, 7, 0};
468:   static PetscInt hex_seg[]   = {2, 0, 3, 0, 4, 0, 5, 0, 1, 0, 0, 0,
469:                                  4, 0, 5, 0, 0, 0, 1, 0, 3, 0, 2, 0,
470:                                  5, 0, 4, 0, 1, 0, 0, 0, 3, 0, 2, 0,
471:                                  3, 0, 2, 0, 4, 0, 5, 0, 0, 0, 1, 0,
472:                                  3, 0, 2, 0, 5, 0, 4, 0, 1, 0, 0, 0,
473:                                  4, 0, 5, 0, 1, 0, 0, 0, 2, 0, 3, 0,
474:                                  2, 0, 3, 0, 5, 0, 4, 0, 0, 0, 1, 0,
475:                                  5, 0, 4, 0, 0, 0, 1, 0, 2, 0, 3, 0,
476:                                  4, 0, 5, 0, 3, 0, 2, 0, 1, 0, 0, 0,
477:                                  5, 0, 4, 0, 3, 0, 2, 0, 0, 0, 1, 0,
478:                                  3, 0, 2, 0, 1, 0, 0, 0, 4, 0, 5, 0,
479:                                  2, 0, 3, 0, 0, 0, 1, 0, 4, 0, 5, 0,
480:                                  1, 0, 0, 0, 4, 0, 5, 0, 3, 0, 2, 0,
481:                                  1, 0, 0, 0, 5, 0, 4, 0, 2, 0, 3, 0,
482:                                  5, 0, 4, 0, 2, 0, 3, 0, 1, 0, 0, 0,
483:                                  1, 0, 0, 0, 2, 0, 3, 0, 4, 0, 5, 0,
484:                                  4, 0, 5, 0, 2, 0, 3, 0, 0, 0, 1, 0,
485:                                  3, 0, 2, 0, 0, 0, 1, 0, 5, 0, 4, 0,
486:                                  1, 0, 0, 0, 3, 0, 2, 0, 5, 0, 4, 0,
487:                                  2, 0, 3, 0, 1, 0, 0, 0, 5, 0, 4, 0,
488:                                  0, 0, 1, 0, 4, 0, 5, 0, 2, 0, 3, 0,
489:                                  0, 0, 1, 0, 3, 0, 2, 0, 4, 0, 5, 0,
490:                                  0, 0, 1, 0, 5, 0, 4, 0, 3, 0, 2, 0,
491:                                  0, 0, 1, 0, 2, 0, 3, 0, 5, 0, 4, 0,
492:                                  0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0,
493:                                  0, 0, 1, 0, 5, 0, 4, 0, 2, 0, 3, 0,
494:                                  0, 0, 1, 0, 3, 0, 2, 0, 5, 0, 4, 0,
495:                                  0, 0, 1, 0, 4, 0, 5, 0, 3, 0, 2, 0,
496:                                  2, 0, 3, 0, 1, 0, 0, 0, 4, 0, 5, 0,
497:                                  1, 0, 0, 0, 3, 0, 2, 0, 4, 0, 5, 0,
498:                                  3, 0, 2, 0, 0, 0, 1, 0, 4, 0, 5, 0,
499:                                  4, 0, 5, 0, 2, 0, 3, 0, 1, 0, 0, 0,
500:                                  1, 0, 0, 0, 2, 0, 3, 0, 5, 0, 4, 0,
501:                                  5, 0, 4, 0, 2, 0, 3, 0, 0, 0, 1, 0,
502:                                  1, 0, 0, 0, 5, 0, 4, 0, 3, 0, 2, 0,
503:                                  1, 0, 0, 0, 4, 0, 5, 0, 2, 0, 3, 0,
504:                                  2, 0, 3, 0, 0, 0, 1, 0, 5, 0, 4, 0,
505:                                  3, 0, 2, 0, 1, 0, 0, 0, 5, 0, 4, 0,
506:                                  5, 0, 4, 0, 3, 0, 2, 0, 1, 0, 0, 0,
507:                                  4, 0, 5, 0, 3, 0, 2, 0, 0, 0, 1, 0,
508:                                  5, 0, 4, 0, 0, 0, 1, 0, 3, 0, 2, 0,
509:                                  2, 0, 3, 0, 5, 0, 4, 0, 1, 0, 0, 0,
510:                                  4, 0, 5, 0, 1, 0, 0, 0, 3, 0, 2, 0,
511:                                  3, 0, 2, 0, 5, 0, 4, 0, 0, 0, 1, 0,
512:                                  3, 0, 2, 0, 4, 0, 5, 0, 1, 0, 0, 0,
513:                                  5, 0, 4, 0, 1, 0, 0, 0, 2, 0, 3, 0,
514:                                  4, 0, 5, 0, 0, 0, 1, 0, 2, 0, 3, 0,
515:                                  2, 0, 3, 0, 4, 0, 5, 0, 0, 0, 1, 0};
516:   static PetscInt hex_quad[]   = {7, -2, 4, -2, 5, -2, 6, -2, 8, -3, 11, -3, 10, -3, 9, -3, 3, 1, 2, 1, 1, 1, 0, 1,
517:                                  8, -2, 9, -2, 10, -2, 11, -2, 3, -4, 0, -4, 1, -4, 2, -4, 7, 0, 4, 0, 5, 0, 6, 0,
518:                                  9, 1, 8, 1, 11, 1, 10, 1, 0, 3, 3, 3, 2, 3, 1, 3, 5, 2, 6, 2, 7, 2, 4, 2,
519:                                  6, 3, 5, 3, 4, 3, 7, 3, 10, -1, 9, -1, 8, -1, 11, -1, 2, -4, 3, -4, 0, -4, 1, -4,
520:                                  4, 1, 7, 1, 6, 1, 5, 1, 11, 2, 8, 2, 9, 2, 10, 2, 1, 3, 0, 3, 3, 3, 2, 3,
521:                                  10, -4, 11, -4, 8, -4, 9, -4, 2, 1, 1, 1, 0, 1, 3, 1, 6, -1, 5, -1, 4, -1, 7, -1,
522:                                  5, -4, 6, -4, 7, -4, 4, -4, 9, 0, 10, 0, 11, 0, 8, 0, 0, -2, 1, -2, 2, -2, 3, -2,
523:                                  11, 3, 10, 3, 9, 3, 8, 3, 1, -2, 2, -2, 3, -2, 0, -2, 4, -3, 7, -3, 6, -3, 5, -3,
524:                                  11, -1, 8, -1, 9, -1, 10, -1, 7, 3, 4, 3, 5, 3, 6, 3, 2, 2, 1, 2, 0, 2, 3, 2,
525:                                  10, 2, 9, 2, 8, 2, 11, 2, 5, 1, 6, 1, 7, 1, 4, 1, 1, -1, 2, -1, 3, -1, 0, -1,
526:                                  5, 2, 4, 2, 7, 2, 6, 2, 1, 2, 0, 2, 3, 2, 2, 2, 10, -4, 9, -4, 8, -4, 11, -4,
527:                                  4, -3, 5, -3, 6, -3, 7, -3, 0, -3, 1, -3, 2, -3, 3, -3, 8, -2, 11, -2, 10, -2, 9, -2,
528:                                  3, 1, 0, 1, 1, 1, 2, 1, 9, -4, 8, -4, 11, -4, 10, -4, 6, 3, 7, 3, 4, 3, 5, 3,
529:                                  1, 3, 2, 3, 3, 3, 0, 3, 10, 1, 11, 1, 8, 1, 9, 1, 5, -4, 4, -4, 7, -4, 6, -4,
530:                                  8, 0, 11, 0, 10, 0, 9, 0, 4, -4, 7, -4, 6, -4, 5, -4, 0, 0, 3, 0, 2, 0, 1, 0,
531:                                  0, 0, 1, 0, 2, 0, 3, 0, 5, -1, 4, -1, 7, -1, 6, -1, 9, -3, 8, -3, 11, -3, 10, -3,
532:                                  9, -3, 10, -3, 11, -3, 8, -3, 6, -2, 5, -2, 4, -2, 7, -2, 3, -3, 0, -3, 1, -3, 2, -3,
533:                                  7, 0, 6, 0, 5, 0, 4, 0, 2, -1, 3, -1, 0, -1, 1, -1, 11, 3, 8, 3, 9, 3, 10, 3,
534:                                  2, 2, 3, 2, 0, 2, 1, 2, 6, 2, 7, 2, 4, 2, 5, 2, 10, 2, 11, 2, 8, 2, 9, 2,
535:                                  6, -1, 7, -1, 4, -1, 5, -1, 3, 0, 2, 0, 1, 0, 0, 0, 9, 1, 10, 1, 11, 1, 8, 1,
536:                                  2, -4, 1, -4, 0, -4, 3, -4, 11, -2, 10, -2, 9, -2, 8, -2, 7, -2, 6, -2, 5, -2, 4, -2,
537:                                  1, -1, 0, -1, 3, -1, 2, -1, 4, 0, 5, 0, 6, 0, 7, 0, 11, -1, 10, -1, 9, -1, 8, -1,
538:                                  0, -2, 3, -2, 2, -2, 1, -2, 8, 3, 9, 3, 10, 3, 11, 3, 4, 1, 5, 1, 6, 1, 7, 1,
539:                                  3, -3, 2, -3, 1, -3, 0, -3, 7, -3, 6, -3, 5, -3, 4, -3, 8, 0, 9, 0, 10, 0, 11, 0,
540:                                  0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0,
541:                                  1, 3, 2, 3, 3, 3, 0, 3, 11, -2, 10, -2, 9, -2, 8, -2, 4, 1, 5, 1, 6, 1, 7, 1,
542:                                  2, 2, 3, 2, 0, 2, 1, 2, 7, -3, 6, -3, 5, -3, 4, -3, 11, -1, 10, -1, 9, -1, 8, -1,
543:                                  3, 1, 0, 1, 1, 1, 2, 1, 8, 3, 9, 3, 10, 3, 11, 3, 7, -2, 6, -2, 5, -2, 4, -2,
544:                                  5, 2, 4, 2, 7, 2, 6, 2, 0, -3, 1, -3, 2, -3, 3, -3, 9, 1, 10, 1, 11, 1, 8, 1,
545:                                  1, -1, 0, -1, 3, -1, 2, -1, 5, -1, 4, -1, 7, -1, 6, -1, 10, 2, 11, 2, 8, 2, 9, 2,
546:                                  4, -3, 5, -3, 6, -3, 7, -3, 1, 2, 0, 2, 3, 2, 2, 2, 11, 3, 8, 3, 9, 3, 10, 3,
547:                                  8, 0, 11, 0, 10, 0, 9, 0, 7, 3, 4, 3, 5, 3, 6, 3, 3, -3, 0, -3, 1, -3, 2, -3,
548:                                  3, -3, 2, -3, 1, -3, 0, -3, 6, 2, 7, 2, 4, 2, 5, 2, 9, -3, 8, -3, 11, -3, 10, -3,
549:                                  9, -3, 10, -3, 11, -3, 8, -3, 5, 1, 6, 1, 7, 1, 4, 1, 0, 0, 3, 0, 2, 0, 1, 0,
550:                                  0, -2, 3, -2, 2, -2, 1, -2, 9, -4, 8, -4, 11, -4, 10, -4, 5, -4, 4, -4, 7, -4, 6, -4,
551:                                  2, -4, 1, -4, 0, -4, 3, -4, 10, 1, 11, 1, 8, 1, 9, 1, 6, 3, 7, 3, 4, 3, 5, 3,
552:                                  7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1, 0, 0, 0, 8, -2, 11, -2, 10, -2, 9, -2,
553:                                  6, -1, 7, -1, 4, -1, 5, -1, 2, -1, 3, -1, 0, -1, 1, -1, 10, -4, 9, -4, 8, -4, 11, -4,
554:                                  11, -1, 8, -1, 9, -1, 10, -1, 4, -4, 7, -4, 6, -4, 5, -4, 1, -1, 2, -1, 3, -1, 0, -1,
555:                                  10, 2, 9, 2, 8, 2, 11, 2, 6, -2, 5, -2, 4, -2, 7, -2, 2, 2, 1, 2, 0, 2, 3, 2,
556:                                  8, -2, 9, -2, 10, -2, 11, -2, 0, 3, 3, 3, 2, 3, 1, 3, 4, -3, 7, -3, 6, -3, 5, -3,
557:                                  4, 1, 7, 1, 6, 1, 5, 1, 8, -3, 11, -3, 10, -3, 9, -3, 0, -2, 1, -2, 2, -2, 3, -2,
558:                                  9, 1, 8, 1, 11, 1, 10, 1, 3, -4, 0, -4, 1, -4, 2, -4, 6, -1, 5, -1, 4, -1, 7, -1,
559:                                  5, -4, 6, -4, 7, -4, 4, -4, 10, -1, 9, -1, 8, -1, 11, -1, 1, 3, 0, 3, 3, 3, 2, 3,
560:                                  7, -2, 4, -2, 5, -2, 6, -2, 11, 2, 8, 2, 9, 2, 10, 2, 2, -4, 3, -4, 0, -4, 1, -4,
561:                                  10, -4, 11, -4, 8, -4, 9, -4, 1, -2, 2, -2, 3, -2, 0, -2, 5, 2, 6, 2, 7, 2, 4, 2,
562:                                  11, 3, 10, 3, 9, 3, 8, 3, 2, 1, 1, 1, 0, 1, 3, 1, 7, 0, 4, 0, 5, 0, 6, 0,
563:                                  6, 3, 5, 3, 4, 3, 7, 3, 9, 0, 10, 0, 11, 0, 8, 0, 3, 1, 2, 1, 1, 1, 0, 1};
564:   static PetscInt hex_hex[]   = {3, -24, 0, -24, 4, -24, 5, -24, 2, -24, 6, -24, 7, -24, 1, -24,
565:                                  3, -23, 5, -23, 6, -23, 2, -23, 0, -23, 1, -23, 7, -23, 4, -23,
566:                                  4, -22, 0, -22, 1, -22, 7, -22, 5, -22, 6, -22, 2, -22, 3, -22,
567:                                  6, -21, 7, -21, 1, -21, 2, -21, 5, -21, 3, -21, 0, -21, 4, -21,
568:                                  1, -20, 2, -20, 6, -20, 7, -20, 0, -20, 4, -20, 5, -20, 3, -20,
569:                                  6, -19, 2, -19, 3, -19, 5, -19, 7, -19, 4, -19, 0, -19, 1, -19,
570:                                  4, -18, 5, -18, 3, -18, 0, -18, 7, -18, 1, -18, 2, -18, 6, -18,
571:                                  1, -17, 7, -17, 4, -17, 0, -17, 2, -17, 3, -17, 5, -17, 6, -17,
572:                                  2, -16, 3, -16, 5, -16, 6, -16, 1, -16, 7, -16, 4, -16, 0, -16,
573:                                  7, -15, 4, -15, 0, -15, 1, -15, 6, -15, 2, -15, 3, -15, 5, -15,
574:                                  7, -14, 1, -14, 2, -14, 6, -14, 4, -14, 5, -14, 3, -14, 0, -14,
575:                                  0, -13, 4, -13, 5, -13, 3, -13, 1, -13, 2, -13, 6, -13, 7, -13,
576:                                  5, -12, 4, -12, 7, -12, 6, -12, 3, -12, 2, -12, 1, -12, 0, -12,
577:                                  7, -11, 6, -11, 5, -11, 4, -11, 1, -11, 0, -11, 3, -11, 2, -11,
578:                                  0, -10, 1, -10, 7, -10, 4, -10, 3, -10, 5, -10, 6, -10, 2, -10,
579:                                  4, -9, 7, -9, 6, -9, 5, -9, 0, -9, 3, -9, 2, -9, 1, -9,
580:                                  5, -8, 6, -8, 2, -8, 3, -8, 4, -8, 0, -8, 1, -8, 7, -8,
581:                                  2, -7, 6, -7, 7, -7, 1, -7, 3, -7, 0, -7, 4, -7, 5, -7,
582:                                  6, -6, 5, -6, 4, -6, 7, -6, 2, -6, 1, -6, 0, -6, 3, -6,
583:                                  5, -5, 3, -5, 0, -5, 4, -5, 6, -5, 7, -5, 1, -5, 2, -5,
584:                                  2, -4, 1, -4, 0, -4, 3, -4, 6, -4, 5, -4, 4, -4, 7, -4,
585:                                  1, -3, 0, -3, 3, -3, 2, -3, 7, -3, 6, -3, 5, -3, 4, -3,
586:                                  0, -2, 3, -2, 2, -2, 1, -2, 4, -2, 7, -2, 6, -2, 5, -2,
587:                                  3, -1, 2, -1, 1, -1, 0, -1, 5, -1, 4, -1, 7, -1, 6, -1,
588:                                  0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0,
589:                                  1, 1, 2, 1, 3, 1, 0, 1, 7, 1, 4, 1, 5, 1, 6, 1,
590:                                  2, 2, 3, 2, 0, 2, 1, 2, 6, 2, 7, 2, 4, 2, 5, 2,
591:                                  3, 3, 0, 3, 1, 3, 2, 3, 5, 3, 6, 3, 7, 3, 4, 3,
592:                                  4, 4, 0, 4, 3, 4, 5, 4, 7, 4, 6, 4, 2, 4, 1, 4,
593:                                  7, 5, 4, 5, 5, 5, 6, 5, 1, 5, 2, 5, 3, 5, 0, 5,
594:                                  1, 6, 7, 6, 6, 6, 2, 6, 0, 6, 3, 6, 5, 6, 4, 6,
595:                                  3, 7, 2, 7, 6, 7, 5, 7, 0, 7, 4, 7, 7, 7, 1, 7,
596:                                  5, 8, 6, 8, 7, 8, 4, 8, 3, 8, 0, 8, 1, 8, 2, 8,
597:                                  4, 9, 7, 9, 1, 9, 0, 9, 5, 9, 3, 9, 2, 9, 6, 9,
598:                                  4, 10, 5, 10, 6, 10, 7, 10, 0, 10, 1, 10, 2, 10, 3, 10,
599:                                  6, 11, 7, 11, 4, 11, 5, 11, 2, 11, 3, 11, 0, 11, 1, 11,
600:                                  3, 12, 5, 12, 4, 12, 0, 12, 2, 12, 1, 12, 7, 12, 6, 12,
601:                                  6, 13, 2, 13, 1, 13, 7, 13, 5, 13, 4, 13, 0, 13, 3, 13,
602:                                  1, 14, 0, 14, 4, 14, 7, 14, 2, 14, 6, 14, 5, 14, 3, 14,
603:                                  6, 15, 5, 15, 3, 15, 2, 15, 7, 15, 1, 15, 0, 15, 4, 15,
604:                                  0, 16, 4, 16, 7, 16, 1, 16, 3, 16, 2, 16, 6, 16, 5, 16,
605:                                  0, 17, 3, 17, 5, 17, 4, 17, 1, 17, 7, 17, 6, 17, 2, 17,
606:                                  5, 18, 3, 18, 2, 18, 6, 18, 4, 18, 7, 18, 1, 18, 0, 18,
607:                                  7, 19, 6, 19, 2, 19, 1, 19, 4, 19, 0, 19, 3, 19, 5, 19,
608:                                  2, 20, 1, 20, 7, 20, 6, 20, 3, 20, 5, 20, 4, 20, 0, 20,
609:                                  7, 21, 1, 21, 0, 21, 4, 21, 6, 21, 5, 21, 3, 21, 2, 21,
610:                                  2, 22, 6, 22, 5, 22, 3, 22, 1, 22, 0, 22, 4, 22, 7, 22,
611:                                  5, 23, 4, 23, 0, 23, 3, 23, 6, 23, 2, 23, 1, 23, 7, 23};
612:   static PetscInt trip_seg[]   = {1,  0, 2,  0, 0,  0,
613:                                   2,  0, 0,  0, 1,  0,
614:                                   0,  0, 1,  0, 2,  0,
615:                                   0, -1, 2, -1, 1, -1,
616:                                   1, -1, 0, -1, 2, -1,
617:                                   2, -1, 1, -1, 0, -1,
618:                                   0,  0, 1,  0, 2,  0,
619:                                   2,  0, 0,  0, 1,  0,
620:                                   1,  0, 2,  0, 0,  0,
621:                                   2, -1, 1, -1, 0, -1,
622:                                   1, -1, 0, -1, 2, -1,
623:                                   0, -1, 2, -1, 1, -1};
624:   static PetscInt trip_tri[]   = {1, 1, 2, 1, 0, 1, 3, 1,
625:                                   2, 2, 0, 2, 1, 2, 3, 2,
626:                                   0, 0, 1, 0, 2, 0, 3, 0,
627:                                   2, -1, 1, -1, 0, -1, 3, -3,
628:                                   0, -2, 2, -2, 1, -2, 3, -1,
629:                                   1, -3, 0, -3, 2, -3, 3, -2,
630:                                   0, 0, 1, 0, 2, 0, 3, 0,
631:                                   2, 2, 0, 2, 1, 2, 3, 2,
632:                                   1, 1, 2, 1, 0, 1, 3, 1,
633:                                   1, -3, 0, -3, 2, -3, 3, -2,
634:                                   0, -2, 2, -2, 1, -2, 3, -1,
635:                                   2, -1, 1, -1, 0, -1, 3, -3};
636:   static PetscInt trip_quad[]  = {4, -1, 5, -1, 3, -1, 1, -1, 2, -1, 0, -1,
637:                                   5, -1, 3, -1, 4, -1, 2, -1, 0, -1, 1, -1,
638:                                   3, -1, 4, -1, 5, -1, 0, -1, 1, -1, 2, -1,
639:                                   0, -3, 2, -3, 1, -3, 3, -3, 5, -3, 4, -3,
640:                                   1, -3, 0, -3, 2, -3, 4, -3, 3, -3, 5, -3,
641:                                   2, -3, 1, -3, 0, -3, 5, -3, 4, -3, 3, -3,
642:                                   0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0,
643:                                   2, 0, 0, 0, 1, 0, 5, 0, 3, 0, 4, 0,
644:                                   1, 0, 2, 0, 0, 0, 4, 0, 5, 0, 3, 0,
645:                                   5, 2, 4, 2, 3, 2, 2, 2, 1, 2, 0, 2,
646:                                   4, 2, 3, 2, 5, 2, 1, 2, 0, 2, 2, 2,
647:                                   3, 2, 5, 2, 4, 2, 0, 2, 2, 2, 1, 2};
648:   static PetscInt trip_trip[]  = {5, -6, 6, -6, 4, -6, 7, -6, 1, -6, 2, -6, 0, -6, 3, -6,
649:                                   6, -5, 4, -5, 5, -5, 7, -5, 2, -5, 0, -5, 1, -5, 3, -5,
650:                                   4, -4, 5, -4, 6, -4, 7, -4, 0, -4, 1, -4, 2, -4, 3, -4,
651:                                   2, -3, 1, -3, 0, -3, 3, -1, 6, -3, 5, -3, 4, -3, 7, -1,
652:                                   0, -2, 2, -2, 1, -2, 3, -3, 4, -2, 6, -2, 5, -2, 7, -3,
653:                                   1, -1, 0, -1, 2, -1, 3, -2, 5, -1, 4, -1, 6, -1, 7, -2,
654:                                   0, 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0,
655:                                   2, 1, 0, 1, 1, 1, 3, 1, 6, 1, 4, 1, 5, 1, 7, 1,
656:                                   1, 2, 2, 2, 0, 2, 3, 2, 5, 2, 6, 2, 4, 2, 7, 2,
657:                                   5, 3, 4, 3, 6, 3, 7, 4, 1, 3, 0, 3, 2, 3, 3, 4,
658:                                   4, 4, 6, 4, 5, 4, 7, 5, 0, 4, 2, 4, 1, 4, 3, 5,
659:                                   6, 5, 5, 5, 4, 5, 7, 3, 2, 5, 1, 5, 0, 5, 3, 3};
660:   static PetscInt ttri_tseg[]  = {2, -2, 1, -2, 0, -2,
661:                                   1, -2, 0, -2, 2, -2,
662:                                   0, -2, 2, -2, 1, -2,
663:                                   2, -1, 1, -1, 0, -1,
664:                                   1, -1, 0, -1, 2, -1,
665:                                   0, -1, 2, -1, 1, -1,
666:                                   0, 0, 1, 0, 2, 0,
667:                                   1, 0, 2, 0, 0, 0,
668:                                   2, 0, 0, 0, 1, 0,
669:                                   0, 1, 1, 1, 2, 1,
670:                                   1, 1, 2, 1, 0, 1,
671:                                   2, 1, 0, 1, 1, 1};
672:   static PetscInt ttri_ttri[]  = {1, -6, 0, -6, 2, -6, 3, -5,
673:                                   0, -5, 2, -5, 1, -5, 3, -4,
674:                                   2, -4, 1, -4, 0, -4, 3, -6,
675:                                   1, -3, 0, -3, 2, -3, 3, -2,
676:                                   0, -2, 2, -2, 1, -2, 3, -1,
677:                                   2, -1, 1, -1, 0, -1, 3, -3,
678:                                   0, 0, 1, 0, 2, 0, 3, 0,
679:                                   1, 1, 2, 1, 0, 1, 3, 1,
680:                                   2, 2, 0, 2, 1, 2, 3, 2,
681:                                   0, 3, 1, 3, 2, 3, 3, 3,
682:                                   1, 4, 2, 4, 0, 4, 3, 4,
683:                                   2, 5, 0, 5, 1, 5, 3, 5};
684:   static PetscInt tquad_tvert[]  = {0, -1,
685:                                     0, -1,
686:                                     0, -1,
687:                                     0, -1,
688:                                     0,  0,
689:                                     0,  0,
690:                                     0,  0,
691:                                     0,  0,
692:                                     0,  0,
693:                                     0,  0,
694:                                     0,  0,
695:                                     0,  0,
696:                                     0, -1,
697:                                     0, -1,
698:                                     0, -1,
699:                                     0, -1};
700:   static PetscInt tquad_tseg[]   = {1, 1, 0, 1, 3, 1, 2, 1,
701:                                     0, 1, 3, 1, 2, 1, 1, 1,
702:                                     3, 1, 2, 1, 1, 1, 0, 1,
703:                                     2, 1, 1, 1, 0, 1, 3, 1,
704:                                     1, 0, 0, 0, 3, 0, 2, 0,
705:                                     0, 0, 3, 0, 2, 0, 1, 0,
706:                                     3, 0, 2, 0, 1, 0, 0, 0,
707:                                     2, 0, 1, 0, 0, 0, 3, 0,
708:                                     0, 0, 1, 0, 2, 0, 3, 0,
709:                                     1, 0, 2, 0, 3, 0, 0, 0,
710:                                     2, 0, 3, 0, 0, 0, 1, 0,
711:                                     3, 0, 0, 0, 1, 0, 2, 0,
712:                                     0, 1, 1, 1, 2, 1, 3, 1,
713:                                     1, 1, 2, 1, 3, 1, 0, 1,
714:                                     2, 1, 3, 1, 0, 1, 1, 1,
715:                                     3, 1, 0, 1, 1, 1, 2, 1};
716:   static PetscInt tquad_tquad[]  = {2, -8, 1, -8, 0, -8, 3, -8,
717:                                     1, -7, 0, -7, 3, -7, 2, -7,
718:                                     0, -6, 3, -6, 2, -6, 1, -6,
719:                                     3, -5, 2, -5, 1, -5, 0, -5,
720:                                     2, -4, 1, -4, 0, -4, 3, -4,
721:                                     1, -3, 0, -3, 3, -3, 2, -3,
722:                                     0, -2, 3, -2, 2, -2, 1, -2,
723:                                     3, -1, 2, -1, 1, -1, 0, -1,
724:                                     0, 0, 1, 0, 2, 0, 3, 0,
725:                                     1, 1, 2, 1, 3, 1, 0, 1,
726:                                     2, 2, 3, 2, 0, 2, 1, 2,
727:                                     3, 3, 0, 3, 1, 3, 2, 3,
728:                                     0, 4, 1, 4, 2, 4, 3, 4,
729:                                     1, 5, 2, 5, 3, 5, 0, 5,
730:                                     2, 6, 3, 6, 0, 6, 1, 6,
731:                                     3, 7, 0, 7, 1, 7, 2, 7};

734:   *rnew = r; *onew = o;
735:   if (!so) return 0;
736:   switch (sct) {
737:     case DM_POLYTOPE_POINT: break;
738:     case DM_POLYTOPE_POINT_PRISM_TENSOR:
739:     *onew = so < 0 ? -(o+1) : o;
740:     break;
741:     case DM_POLYTOPE_SEGMENT:
742:     switch (tct) {
743:       case DM_POLYTOPE_POINT: break;
744:       case DM_POLYTOPE_SEGMENT:
745:         *rnew = seg_seg[(so+1)*4 + r*2];
746:         *onew = DMPolytopeTypeComposeOrientation(tct, o, seg_seg[(so+1)*4 + r*2 + 1]);
747:         break;
748:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
749:     }
750:     break;
751:     case DM_POLYTOPE_TRIANGLE:
752:     switch (tct) {
753:       case DM_POLYTOPE_SEGMENT:
754:         *rnew = tri_seg[(so+3)*6 + r*2];
755:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tri_seg[(so+3)*6 + r*2 + 1]);
756:         break;
757:       case DM_POLYTOPE_TRIANGLE:
758:         *rnew = tri_tri[(so+3)*8 + r*2];
759:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tri_tri[(so+3)*8 + r*2 + 1]);
760:         break;
761:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
762:     }
763:     break;
764:     case DM_POLYTOPE_QUADRILATERAL:
765:     switch (tct) {
766:       case DM_POLYTOPE_POINT: break;
767:       case DM_POLYTOPE_SEGMENT:
768:         *rnew = quad_seg[(so+4)*8 + r*2];
769:         *onew = DMPolytopeTypeComposeOrientation(tct, o, quad_seg[(so+4)*8 + r*2 + 1]);
770:         break;
771:       case DM_POLYTOPE_QUADRILATERAL:
772:         *rnew = quad_quad[(so+4)*8 + r*2];
773:         *onew = DMPolytopeTypeComposeOrientation(tct, o, quad_quad[(so+4)*8 + r*2 + 1]);
774:         break;
775:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
776:     }
777:     break;
778:     case DM_POLYTOPE_SEG_PRISM_TENSOR:
779:     switch (tct) {
780:       case DM_POLYTOPE_POINT_PRISM_TENSOR:
781:         *rnew = tseg_seg[(so+2)*2 + r*2];
782:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tseg_seg[(so+2)*2 + r*2 + 1]);
783:         break;
784:       case DM_POLYTOPE_SEG_PRISM_TENSOR:
785:         *rnew = tseg_tseg[(so+2)*4 + r*2];
786:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tseg_tseg[(so+2)*4 + r*2 + 1]);
787:         break;
788:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
789:     }
790:     break;
791:     case DM_POLYTOPE_TETRAHEDRON:
792:     switch (tct) {
793:       case DM_POLYTOPE_SEGMENT:
794:         *rnew = tet_seg[(so+12)*2 + r*2];
795:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tet_seg[(so+12)*2 + r*2 + 1]);
796:         break;
797:       case DM_POLYTOPE_TRIANGLE:
798:         *rnew = tet_tri[(so+12)*16 + r*2];
799:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tet_tri[(so+12)*16 + r*2 + 1]);
800:         break;
801:       case DM_POLYTOPE_TETRAHEDRON:
802:         *rnew = tet_tet[(so+12)*16 + r*2];
803:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tet_tet[(so+12)*16 + r*2 + 1]);
804:         break;
805:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
806:     }
807:     break;
808:     case DM_POLYTOPE_HEXAHEDRON:
809:     switch (tct) {
810:       case DM_POLYTOPE_POINT: break;
811:       case DM_POLYTOPE_SEGMENT:
812:         *rnew = hex_seg[(so+24)*12 + r*2];
813:         *onew = DMPolytopeTypeComposeOrientation(tct, o, hex_seg[(so+24)*12 + r*2 + 1]);
814:         break;
815:       case DM_POLYTOPE_QUADRILATERAL:
816:         *rnew = hex_quad[(so+24)*24 + r*2];
817:         *onew = DMPolytopeTypeComposeOrientation(tct, o, hex_quad[(so+24)*24 + r*2 + 1]);
818:         break;
819:       case DM_POLYTOPE_HEXAHEDRON:
820:         *rnew = hex_hex[(so+24)*16 + r*2];
821:         *onew = DMPolytopeTypeComposeOrientation(tct, o, hex_hex[(so+24)*16 + r*2 + 1]);
822:         break;
823:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
824:     }
825:     break;
826:     case DM_POLYTOPE_TRI_PRISM:
827:     switch (tct) {
828:       case DM_POLYTOPE_SEGMENT:
829:         *rnew = trip_seg[(so+6)*6 + r*2];
830:         *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_seg[(so+6)*6 + r*2 + 1]);
831:         break;
832:       case DM_POLYTOPE_TRIANGLE:
833:         *rnew = trip_tri[(so+6)*8 + r*2];
834:         *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_tri[(so+6)*8 + r*2 + 1]);
835:         break;
836:       case DM_POLYTOPE_QUADRILATERAL:
837:         *rnew = trip_quad[(so+6)*12 + r*2];
838:         *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_quad[(so+6)*12 + r*2 + 1]);
839:         break;
840:       case DM_POLYTOPE_TRI_PRISM:
841:         *rnew = trip_trip[(so+6)*16 + r*2];
842:         *onew = DMPolytopeTypeComposeOrientation(tct, o, trip_trip[(so+6)*16 + r*2 + 1]);
843:         break;
844:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
845:     }
846:     break;
847:     case DM_POLYTOPE_TRI_PRISM_TENSOR:
848:     switch (tct) {
849:       case DM_POLYTOPE_SEG_PRISM_TENSOR:
850:         *rnew = ttri_tseg[(so+6)*6 + r*2];
851:         *onew = DMPolytopeTypeComposeOrientation(tct, o, ttri_tseg[(so+6)*6 + r*2 + 1]);
852:         break;
853:       case DM_POLYTOPE_TRI_PRISM_TENSOR:
854:         *rnew = ttri_ttri[(so+6)*8 + r*2];
855:         *onew = DMPolytopeTypeComposeOrientation(tct, o, ttri_ttri[(so+6)*8 + r*2 + 1]);
856:         break;
857:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
858:     }
859:     break;
860:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:
861:     switch (tct) {
862:       case DM_POLYTOPE_POINT_PRISM_TENSOR:
863:         *rnew = tquad_tvert[(so+8)*2 + r*2];
864:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tquad_tvert[(so+8)*2 + r*2 + 1]);
865:         break;
866:       case DM_POLYTOPE_SEG_PRISM_TENSOR:
867:         *rnew = tquad_tseg[(so+8)*8 + r*2];
868:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tquad_tseg[(so+8)*8 + r*2 + 1]);
869:         break;
870:       case DM_POLYTOPE_QUAD_PRISM_TENSOR:
871:         *rnew = tquad_tquad[(so+8)*8 + r*2];
872:         *onew = DMPolytopeTypeComposeOrientation(tct, o, tquad_tquad[(so+8)*8 + r*2 + 1]);
873:         break;
874:       default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cell type %s is not produced by %s", DMPolytopeTypes[tct], DMPolytopeTypes[sct]);
875:     }
876:     break;
877:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Unsupported cell type %s", DMPolytopeTypes[sct]);
878:   }
879:   return 0;
880: }

882: PetscErrorCode DMPlexTransformCellRefine_Regular(DMPlexTransform tr, DMPolytopeType source, PetscInt p, PetscInt *rt, PetscInt *Nt, DMPolytopeType *target[], PetscInt *size[], PetscInt *cone[], PetscInt *ornt[])
883: {
884:   /* All vertices remain in the refined mesh */
885:   static DMPolytopeType vertexT[] = {DM_POLYTOPE_POINT};
886:   static PetscInt       vertexS[] = {1};
887:   static PetscInt       vertexC[] = {0};
888:   static PetscInt       vertexO[] = {0};
889:   /* Split all edges with a new vertex, making two new 2 edges
890:      0--0--0--1--1
891:   */
892:   static DMPolytopeType segT[]    = {DM_POLYTOPE_POINT, DM_POLYTOPE_SEGMENT};
893:   static PetscInt       segS[]    = {1, 2};
894:   static PetscInt       segC[]    = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 0, 0,  DM_POLYTOPE_POINT, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0};
895:   static PetscInt       segO[]    = {                         0,                       0,                        0,                          0};
896:   /* Do not split tensor edges */
897:   static DMPolytopeType tvertT[]  = {DM_POLYTOPE_POINT_PRISM_TENSOR};
898:   static PetscInt       tvertS[]  = {1};
899:   static PetscInt       tvertC[]  = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0};
900:   static PetscInt       tvertO[]  = {                         0,                          0};
901:   /* Add 3 edges inside every triangle, making 4 new triangles.
902:    2
903:    |\
904:    | \
905:    |  \
906:    0   1
907:    | C  \
908:    |     \
909:    |      \
910:    2---1---1
911:    |\  D  / \
912:    1 2   0   0
913:    |A \ /  B  \
914:    0-0-0---1---1
915:   */
916:   static DMPolytopeType triT[]    = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE};
917:   static PetscInt       triS[]    = {3, 4};
918:   static PetscInt       triC[]    = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0,
919:                                      DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 1, 2, 0,
920:                                      DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 1, 0, 0,
921:                                      DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 1, 2, 1,
922:                                      DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0,    0,
923:                                      DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 2, 0,
924:                                      DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 0,    2};
925:   static PetscInt       triO[]    = {0, 0,
926:                                      0, 0,
927:                                      0, 0,
928:                                      0, -1,  0,
929:                                      0,  0, -1,
930:                                     -1,  0,  0,
931:                                      0,  0,  0};
932:   /* Add a vertex in the center of each quadrilateral, and 4 edges inside, making 4 new quads.
933:      3----1----2----0----2
934:      |         |         |
935:      0    D    2    C    1
936:      |         |         |
937:      3----3----0----1----1
938:      |         |         |
939:      1    A    0    B    0
940:      |         |         |
941:      0----0----0----1----1
942:   */
943:   static DMPolytopeType quadT[]   = {DM_POLYTOPE_POINT, DM_POLYTOPE_SEGMENT, DM_POLYTOPE_QUADRILATERAL};
944:   static PetscInt       quadS[]   = {1, 4, 4};
945:   static PetscInt       quadC[]   = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 0, 0,
946:                                      DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 0, 0,
947:                                      DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 0, 0,
948:                                      DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 0, 0,
949:                                      DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 0,    3, DM_POLYTOPE_SEGMENT, 1, 3, 1,
950:                                      DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 0,    0,
951:                                      DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0,    2,
952:                                      DM_POLYTOPE_SEGMENT, 0,    3, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 3, 0};
953:   static PetscInt       quadO[]   = {0, 0,
954:                                      0, 0,
955:                                      0, 0,
956:                                      0, 0,
957:                                      0,  0, -1,  0,
958:                                      0,  0,  0, -1,
959:                                     -1,  0,  0,  0,
960:                                      0, -1,  0,  0};
961:   /* Add 1 edge inside every tensor quad, making 2 new tensor quads
962:      2----2----1----3----3
963:      |         |         |
964:      |         |         |
965:      |         |         |
966:      4    A    6    B    5
967:      |         |         |
968:      |         |         |
969:      |         |         |
970:      0----0----0----1----1
971:   */
972:   static DMPolytopeType tsegT[]  = {DM_POLYTOPE_POINT_PRISM_TENSOR, DM_POLYTOPE_SEG_PRISM_TENSOR};
973:   static PetscInt       tsegS[]  = {1, 2};
974:   static PetscInt       tsegC[]  = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0,
975:                                     DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0,   0,
976:                                     DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_POINT_PRISM_TENSOR, 0,    0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0};
977:   static PetscInt       tsegO[]  = {0, 0,
978:                                     0, 0, 0, 0,
979:                                     0, 0, 0, 0};
980:   /* Add 1 edge and 8 triangles inside every cell, making 8 new tets
981:      The vertices of our reference tet are [(-1, -1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, 1)], which we call [v0, v1, v2, v3]. The first
982:      three edges are [v0, v1], [v1, v2], [v2, v0] called e0, e1, and e2, and then three edges to the top point [v0, v3], [v1, v3], [v2, v3]
983:      called e3, e4, and e5. The faces of a tet, given in DMPlexGetRawFaces_Internal() are
984:        [v0, v1, v2], [v0, v3, v1], [v0, v2, v3], [v2, v1, v3]
985:      The first four tets just cut off the corners, using the replica notation for new vertices,
986:        [v0,      (e0, 0), (e2, 0), (e3, 0)]
987:        [(e0, 0), v1,      (e1, 0), (e4, 0)]
988:        [(e2, 0), (e1, 0), v2,      (e5, 0)]
989:        [(e3, 0), (e4, 0), (e5, 0), v3     ]
990:      The next four tets match a vertex to the newly created faces from cutting off those first tets.
991:        [(e2, 0), (e3, 0), (e0, 0), (e5, 0)]
992:        [(e4, 0), (e1, 0), (e0, 0), (e5, 0)]
993:        [(e5, 0), (e0, 0), (e2, 0), (e1, 0)]
994:        [(e5, 0), (e0, 0), (e4, 0), (e3, 0)]
995:      We can see that a new edge is introduced in the cell [(e0, 0), (e5, 0)] which we call (-1, 0). The first four faces created are
996:        [(e2, 0), (e0, 0), (e3, 0)]
997:        [(e0, 0), (e1, 0), (e4, 0)]
998:        [(e2, 0), (e5, 0), (e1, 0)]
999:        [(e3, 0), (e4, 0), (e5, 0)]
1000:      The next four, from the second group of tets, are
1001:        [(e2, 0), (e0, 0), (e5, 0)]
1002:        [(e4, 0), (e0, 0), (e5, 0)]
1003:        [(e0, 0), (e1, 0), (e5, 0)]
1004:        [(e5, 0), (e3, 0), (e0, 0)]
1005:      I could write a program to generate these orientations by comparing the faces from GetRawFaces() with my existing table.
1006:    */
1007:   static DMPolytopeType tetT[]    = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE, DM_POLYTOPE_TETRAHEDRON};
1008:   static PetscInt       tetS[]    = {1, 8, 8};
1009:   static PetscInt       tetC[]    = {DM_POLYTOPE_POINT, 2, 0, 0, 0, DM_POLYTOPE_POINT, 2, 2, 1, 0,
1010:                                      DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 1, 2, 2,
1011:                                      DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 1, 1, 1,
1012:                                      DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 1, 0, 1,
1013:                                      DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 2, 1,
1014:                                      DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 1, 2, 0,
1015:                                      DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 1, 3, 1,
1016:                                      DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 0,    0,
1017:                                      DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 0,    0,
1018:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_TRIANGLE, 1, 2, 0, DM_POLYTOPE_TRIANGLE, 0,    0,
1019:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_TRIANGLE, 0,    1, DM_POLYTOPE_TRIANGLE, 1, 3, 1,
1020:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 0,    2, DM_POLYTOPE_TRIANGLE, 1, 2, 1, DM_POLYTOPE_TRIANGLE, 1, 3, 0,
1021:                                      DM_POLYTOPE_TRIANGLE, 0,    3, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_TRIANGLE, 1, 2, 2, DM_POLYTOPE_TRIANGLE, 1, 3, 2,
1022:                                      DM_POLYTOPE_TRIANGLE, 0,    0, DM_POLYTOPE_TRIANGLE, 1, 2, 3, DM_POLYTOPE_TRIANGLE, 0,    4, DM_POLYTOPE_TRIANGLE, 0,    7,
1023:                                      DM_POLYTOPE_TRIANGLE, 0,    1, DM_POLYTOPE_TRIANGLE, 1, 3, 3, DM_POLYTOPE_TRIANGLE, 0,    5, DM_POLYTOPE_TRIANGLE, 0,    6,
1024:                                      DM_POLYTOPE_TRIANGLE, 0,    4, DM_POLYTOPE_TRIANGLE, 0,    6, DM_POLYTOPE_TRIANGLE, 0,    2, DM_POLYTOPE_TRIANGLE, 1, 0, 3,
1025:                                      DM_POLYTOPE_TRIANGLE, 0,    5, DM_POLYTOPE_TRIANGLE, 0,    7, DM_POLYTOPE_TRIANGLE, 0,    3, DM_POLYTOPE_TRIANGLE, 1, 1, 3};
1026:   static PetscInt       tetO[]    = {0, 0,
1027:                                      0,  0,  0,
1028:                                      0,  0,  0,
1029:                                      0,  0,  0,
1030:                                      0,  0,  0,
1031:                                      0,  0, -1,
1032:                                      0,  0, -1,
1033:                                      0, -1, -1,
1034:                                      0, -1,  0,
1035:                                      0,  0,  0,  0,
1036:                                      0,  0,  0,  0,
1037:                                      0,  0,  0,  0,
1038:                                      0,  0,  0,  0,
1039:                                     -2,  0,  0, -1,
1040:                                     -1,  1,  0,  0,
1041:                                     -1, -1, -3,  2,
1042:                                     -1,  0, -1,  1};
1043:   /* Add a vertex in the center of each cell, add 6 edges and 12 quads inside every cell, making 8 new hexes
1044:      The vertices of our reference hex are (-1, -1, -1), (-1, 1, -1), (1, 1, -1), (1, -1, -1), (-1, -1, 1), (1, -1, 1), (1, 1, 1), (-1, 1, 1) which we call [v0, v1, v2, v3, v4, v5, v6, v7]. The fours edges around the bottom [v0, v1], [v1, v2], [v2, v3], [v3, v0] are [e0, e1, e2, e3], and likewise around the top [v4, v5], [v5, v6], [v6, v7], [v7, v4] are [e4, e5, e6, e7]. Finally [v0, v4], [v1, v7], [v2, v6], [v3, v5] are [e9, e10, e11, e8]. The faces of a hex, given in DMPlexGetRawFaces_Internal(), oriented with outward normals, are
1045:        [v0, v1, v2, v3] f0 bottom
1046:        [v4, v5, v6, v7] f1 top
1047:        [v0, v3, v5, v4] f2 front
1048:        [v2, v1, v7, v6] f3 back
1049:        [v3, v2, v6, v5] f4 right
1050:        [v0, v4, v7, v1] f5 left
1051:      The eight hexes are divided into four on the bottom, and four on the top,
1052:        [v0,      (e0, 0),  (f0, 0),  (e3, 0),  (e9, 0), (f2, 0),  (c0, 0),  (f5, 0)]
1053:        [(e0, 0), v1,       (e1, 0),  (f0, 0),  (f5, 0), (c0, 0),  (f3, 0),  (e10, 0)]
1054:        [(f0, 0), (e1, 0),  v2,       (e2, 0),  (c0, 0), (f4, 0),  (e11, 0), (f3, 0)]
1055:        [(e3, 0), (f0, 0),  (e2, 0),  v3,       (f2, 0), (e8, 0),  (f4, 0),  (c0, 0)]
1056:        [(e9, 0), (f5, 0),  (c0, 0),  (f2, 0),  v4,      (e4, 0),  (f1, 0),  (e7, 0)]
1057:        [(f2, 0), (c0, 0),  (f4, 0),  (e8, 0),  (e4, 0), v5,       (e5, 0),  (f1, 0)]
1058:        [(c0, 0), (f3, 0),  (e11, 0), (f4, 0),  (f1, 0), (e5, 0),  v6,       (e6, 0)]
1059:        [(f5, 0), (e10, 0), (f3, 0),  (c0, 0),  (e7, 0), (f1, 0),  (e6, 0),  v7]
1060:      The 6 internal edges will go from the faces to the central vertex. The 12 internal faces can be divided into groups of 4 by the plane on which they sit. First the faces on the x-y plane are,
1061:        [(e9, 0), (f2, 0),  (c0, 0),  (f5, 0)]
1062:        [(f5, 0), (c0, 0),  (f3, 0),  (e10, 0)]
1063:        [(c0, 0), (f4, 0),  (e11, 0), (f3, 0)]
1064:        [(f2, 0), (e8, 0),  (f4, 0),  (c0, 0)]
1065:      and on the x-z plane,
1066:        [(f0, 0), (e0, 0), (f5, 0), (c0, 0)]
1067:        [(c0, 0), (f5, 0), (e7, 0), (f1, 0)]
1068:        [(f4, 0), (c0, 0), (f1, 0), (e5, 0)]
1069:        [(e2, 0), (f0, 0), (c0, 0), (f4, 0)]
1070:      and on the y-z plane,
1071:        [(e3, 0), (f2, 0), (c0, 0), (f0, 0)]
1072:        [(f2, 0), (e4, 0), (f1, 0), (c0, 0)]
1073:        [(c0, 0), (f1, 0), (e6, 0), (f3, 0)]
1074:        [(f0, 0), (c0, 0), (f3, 0), (e1, 0)]
1075:   */
1076:   static DMPolytopeType hexT[]    = {DM_POLYTOPE_POINT, DM_POLYTOPE_SEGMENT, DM_POLYTOPE_QUADRILATERAL, DM_POLYTOPE_HEXAHEDRON};
1077:   static PetscInt       hexS[]    = {1, 6, 12, 8};
1078:   static PetscInt       hexC[]    = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 0, 0,
1079:                                      DM_POLYTOPE_POINT, 1, 1, 0, DM_POLYTOPE_POINT, 0, 0,
1080:                                      DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 0, 0,
1081:                                      DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 0, 0,
1082:                                      DM_POLYTOPE_POINT, 1, 4, 0, DM_POLYTOPE_POINT, 0, 0,
1083:                                      DM_POLYTOPE_POINT, 1, 5, 0, DM_POLYTOPE_POINT, 0, 0,
1084:                                      DM_POLYTOPE_SEGMENT, 1, 2, 3, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 0,    5, DM_POLYTOPE_SEGMENT, 1, 5, 0,
1085:                                      DM_POLYTOPE_SEGMENT, 0,    5, DM_POLYTOPE_SEGMENT, 0,    3, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 5, 2,
1086:                                      DM_POLYTOPE_SEGMENT, 0,    4, DM_POLYTOPE_SEGMENT, 1, 4, 1, DM_POLYTOPE_SEGMENT, 1, 3, 3, DM_POLYTOPE_SEGMENT, 0,    3,
1087:                                      DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 4, 3, DM_POLYTOPE_SEGMENT, 0,    4, DM_POLYTOPE_SEGMENT, 0,    2,
1088:                                      DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 5, 3, DM_POLYTOPE_SEGMENT, 0,    5, DM_POLYTOPE_SEGMENT, 0,    0,
1089:                                      DM_POLYTOPE_SEGMENT, 0,    5, DM_POLYTOPE_SEGMENT, 1, 5, 1, DM_POLYTOPE_SEGMENT, 1, 1, 3, DM_POLYTOPE_SEGMENT, 0,    1,
1090:                                      DM_POLYTOPE_SEGMENT, 0,    4, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 4, 2,
1091:                                      DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 0,    4, DM_POLYTOPE_SEGMENT, 1, 4, 0,
1092:                                      DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 1, 0, 3,
1093:                                      DM_POLYTOPE_SEGMENT, 1, 2, 2, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 0,    2,
1094:                                      DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 0,    3,
1095:                                      DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 0,    3, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 1, 0, 1,
1096:                                      DM_POLYTOPE_QUADRILATERAL, 1, 0, 0, DM_POLYTOPE_QUADRILATERAL, 0,    0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 0, DM_POLYTOPE_QUADRILATERAL, 0,    4, DM_POLYTOPE_QUADRILATERAL, 0,    8, DM_POLYTOPE_QUADRILATERAL, 1, 5, 0,
1097:                                      DM_POLYTOPE_QUADRILATERAL, 1, 0, 1, DM_POLYTOPE_QUADRILATERAL, 0,    1, DM_POLYTOPE_QUADRILATERAL, 0,    4, DM_POLYTOPE_QUADRILATERAL, 1, 3, 1, DM_POLYTOPE_QUADRILATERAL, 0,   11, DM_POLYTOPE_QUADRILATERAL, 1, 5, 3,
1098:                                      DM_POLYTOPE_QUADRILATERAL, 1, 0, 2, DM_POLYTOPE_QUADRILATERAL, 0,    2, DM_POLYTOPE_QUADRILATERAL, 0,    7, DM_POLYTOPE_QUADRILATERAL, 1, 3, 0, DM_POLYTOPE_QUADRILATERAL, 1, 4, 1, DM_POLYTOPE_QUADRILATERAL, 0,   11,
1099:                                      DM_POLYTOPE_QUADRILATERAL, 1, 0, 3, DM_POLYTOPE_QUADRILATERAL, 0,    3, DM_POLYTOPE_QUADRILATERAL, 1, 2, 1, DM_POLYTOPE_QUADRILATERAL, 0,    7, DM_POLYTOPE_QUADRILATERAL, 1, 4, 0, DM_POLYTOPE_QUADRILATERAL, 0,    8,
1100:                                      DM_POLYTOPE_QUADRILATERAL, 0,    0, DM_POLYTOPE_QUADRILATERAL, 1, 1, 0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 3, DM_POLYTOPE_QUADRILATERAL, 0,    5, DM_POLYTOPE_QUADRILATERAL, 0,    9, DM_POLYTOPE_QUADRILATERAL, 1, 5, 1,
1101:                                      DM_POLYTOPE_QUADRILATERAL, 0,    3, DM_POLYTOPE_QUADRILATERAL, 1, 1, 1, DM_POLYTOPE_QUADRILATERAL, 1, 2, 2, DM_POLYTOPE_QUADRILATERAL, 0,    6, DM_POLYTOPE_QUADRILATERAL, 1, 4, 3, DM_POLYTOPE_QUADRILATERAL, 0,    9,
1102:                                      DM_POLYTOPE_QUADRILATERAL, 0,    2, DM_POLYTOPE_QUADRILATERAL, 1, 1, 2, DM_POLYTOPE_QUADRILATERAL, 0,    6, DM_POLYTOPE_QUADRILATERAL, 1, 3, 3, DM_POLYTOPE_QUADRILATERAL, 1, 4, 2, DM_POLYTOPE_QUADRILATERAL, 0,   10,
1103:                                      DM_POLYTOPE_QUADRILATERAL, 0,    1, DM_POLYTOPE_QUADRILATERAL, 1, 1, 3, DM_POLYTOPE_QUADRILATERAL, 0,    5, DM_POLYTOPE_QUADRILATERAL, 1, 3, 2, DM_POLYTOPE_QUADRILATERAL, 0,   10, DM_POLYTOPE_QUADRILATERAL, 1, 5, 2};
1104:   static PetscInt       hexO[]    = {0, 0,
1105:                                      0, 0,
1106:                                      0, 0,
1107:                                      0, 0,
1108:                                      0, 0,
1109:                                      0, 0,
1110:                                      0,  0, -1, -1,
1111:                                      0, -1, -1,  0,
1112:                                     -1, -1,  0,  0,
1113:                                     -1,  0,  0, -1,
1114:                                     -1,  0,  0, -1,
1115:                                     -1, -1,  0,  0,
1116:                                      0, -1, -1,  0,
1117:                                      0,  0, -1, -1,
1118:                                      0,  0, -1, -1,
1119:                                     -1,  0,  0, -1,
1120:                                     -1, -1,  0,  0,
1121:                                      0, -1, -1,  0,
1122:                                      0, 0,  0, 0, -2, 0,
1123:                                      0, 0, -3, 0, -2, 0,
1124:                                      0, 0, -3, 0,  0, 0,
1125:                                      0, 0,  0, 0,  0, 0,
1126:                                     -2, 0,  0, 0, -2, 0,
1127:                                     -2, 0,  0, 0,  0, 0,
1128:                                     -2, 0, -3, 0,  0, 0,
1129:                                     -2, 0, -3, 0, -2, 0};
1130:   /* Add 3 quads inside every triangular prism, making 4 new prisms. */
1131:   static DMPolytopeType tripT[]   = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE, DM_POLYTOPE_QUADRILATERAL, DM_POLYTOPE_TRI_PRISM};
1132:   static PetscInt       tripS[]   = {3, 4, 6, 8};
1133:   static PetscInt       tripC[]   = {DM_POLYTOPE_POINT, 1, 2, 0, DM_POLYTOPE_POINT, 1, 3, 0,
1134:                                      DM_POLYTOPE_POINT, 1, 3, 0, DM_POLYTOPE_POINT, 1, 4, 0,
1135:                                      DM_POLYTOPE_POINT, 1, 4, 0, DM_POLYTOPE_POINT, 1, 2, 0,
1136:                                      DM_POLYTOPE_SEGMENT, 1, 2, 3, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 1, 4, 1,
1137:                                      DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 3, 3, DM_POLYTOPE_SEGMENT, 0,    0,
1138:                                      DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 4, 3,
1139:                                      DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 0,    2,
1140:                                      DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 1, 2, 0,
1141:                                      DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 4, 0, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 3, 0,
1142:                                      DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 1, 4, 0,
1143:                                      DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 1, 3, 2, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 1, 2, 2,
1144:                                      DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 4, 2, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 3, 2,
1145:                                      DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 1, 2, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_SEGMENT, 1, 4, 2,
1146:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 0,    0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 0, DM_POLYTOPE_QUADRILATERAL, 0,    2, DM_POLYTOPE_QUADRILATERAL, 1, 4, 1,
1147:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 0,    1, DM_POLYTOPE_QUADRILATERAL, 1, 2, 1, DM_POLYTOPE_QUADRILATERAL, 1, 3, 0, DM_POLYTOPE_QUADRILATERAL, 0,    0,
1148:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 0,    2, DM_POLYTOPE_QUADRILATERAL, 0,    1, DM_POLYTOPE_QUADRILATERAL, 1, 3, 1, DM_POLYTOPE_QUADRILATERAL, 1, 4, 0,
1149:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 3, DM_POLYTOPE_TRIANGLE, 0,    3, DM_POLYTOPE_QUADRILATERAL, 0,    0, DM_POLYTOPE_QUADRILATERAL, 0,    1, DM_POLYTOPE_QUADRILATERAL, 0,    2,
1150:                                      DM_POLYTOPE_TRIANGLE, 0,    0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_QUADRILATERAL, 1, 2, 3, DM_POLYTOPE_QUADRILATERAL, 0,    5, DM_POLYTOPE_QUADRILATERAL, 1, 4, 2,
1151:                                      DM_POLYTOPE_TRIANGLE, 0,    1, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_QUADRILATERAL, 1, 2, 2, DM_POLYTOPE_QUADRILATERAL, 1, 3, 3, DM_POLYTOPE_QUADRILATERAL, 0,    3,
1152:                                      DM_POLYTOPE_TRIANGLE, 0,    2, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_QUADRILATERAL, 0,    4, DM_POLYTOPE_QUADRILATERAL, 1, 3, 2, DM_POLYTOPE_QUADRILATERAL, 1, 4, 3,
1153:                                      DM_POLYTOPE_TRIANGLE, 0,    3, DM_POLYTOPE_TRIANGLE, 1, 1, 3, DM_POLYTOPE_QUADRILATERAL, 0,    3, DM_POLYTOPE_QUADRILATERAL, 0,    4, DM_POLYTOPE_QUADRILATERAL, 0,    5};
1154:   static PetscInt       tripO[]   = {0, 0,
1155:                                      0, 0,
1156:                                      0, 0,
1157:                                      0, -1, -1,
1158:                                     -1,  0, -1,
1159:                                     -1, -1,  0,
1160:                                      0,  0,  0,
1161:                                     -1,  0, -1, -1,
1162:                                     -1,  0, -1, -1,
1163:                                     -1,  0, -1, -1,
1164:                                      0, -1, -1,  0,
1165:                                      0, -1, -1,  0,
1166:                                      0, -1, -1,  0,
1167:                                      0,  0,  0, -3,  0,
1168:                                      0,  0,  0,  0, -3,
1169:                                      0,  0, -3,  0,  0,
1170:                                      2,  0,  0,  0,  0,
1171:                                     -2,  0,  0, -3,  0,
1172:                                     -2,  0,  0,  0, -3,
1173:                                     -2,  0, -3,  0,  0,
1174:                                     -2,  0,  0,  0,  0};
1175:   /* Add 3 tensor quads inside every tensor triangular prism, making 4 new prisms.
1176:       2
1177:       |\
1178:       | \
1179:       |  \
1180:       0---1

1182:       2

1184:       0   1

1186:       2
1187:       |\
1188:       | \
1189:       |  \
1190:       0---1
1191:   */
1192:   static DMPolytopeType ttriT[]   = {DM_POLYTOPE_SEG_PRISM_TENSOR, DM_POLYTOPE_TRI_PRISM_TENSOR};
1193:   static PetscInt       ttriS[]   = {3, 4};
1194:   static PetscInt       ttriC[]   = {DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0,
1195:                                      DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 4, 0,
1196:                                      DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0,
1197:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    2, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 1,
1198:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    0,
1199:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 0,
1200:                                      DM_POLYTOPE_TRIANGLE, 1, 0, 3, DM_POLYTOPE_TRIANGLE, 1, 1, 3, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,     1, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    2};
1201:   static PetscInt       ttriO[]   = {0, 0, 0, 0,
1202:                                      0, 0, 0, 0,
1203:                                      0, 0, 0, 0,
1204:                                      0, 0,  0, -1,  0,
1205:                                      0, 0,  0,  0, -1,
1206:                                      0, 0, -1,  0,  0,
1207:                                      0, 0,  0,  0,  0};
1208:   /* Add 1 edge and 4 tensor quads inside every tensor quad prism, making 4 new prisms. */
1209:   static DMPolytopeType tquadT[]   = {DM_POLYTOPE_POINT_PRISM_TENSOR, DM_POLYTOPE_SEG_PRISM_TENSOR, DM_POLYTOPE_QUAD_PRISM_TENSOR};
1210:   static PetscInt       tquadS[]   = {1, 4, 4};
1211:   static PetscInt       tquadC[]   = {DM_POLYTOPE_POINT, 1, 0, 0, DM_POLYTOPE_POINT, 1, 1, 0,
1212:                                       DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0,
1213:                                       DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0,
1214:                                       DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 1, 2, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0,
1215:                                       DM_POLYTOPE_SEGMENT, 1, 0, 3, DM_POLYTOPE_SEGMENT, 1, 1, 3, DM_POLYTOPE_POINT_PRISM_TENSOR, 1, 5, 0, DM_POLYTOPE_POINT_PRISM_TENSOR, 0, 0,
1216:                                       DM_POLYTOPE_QUADRILATERAL, 1, 0, 0, DM_POLYTOPE_QUADRILATERAL, 1, 1, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    3, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 5, 1,
1217:                                       DM_POLYTOPE_QUADRILATERAL, 1, 0, 1, DM_POLYTOPE_QUADRILATERAL, 1, 1, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 2, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    1, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    0,
1218:                                       DM_POLYTOPE_QUADRILATERAL, 1, 0, 2, DM_POLYTOPE_QUADRILATERAL, 1, 1, 2, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 3, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 0, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    2,
1219:                                       DM_POLYTOPE_QUADRILATERAL, 1, 0, 3, DM_POLYTOPE_QUADRILATERAL, 1, 1, 3, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    3, DM_POLYTOPE_SEG_PRISM_TENSOR, 0,    2, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 4, 1, DM_POLYTOPE_SEG_PRISM_TENSOR, 1, 5, 0};
1220:   static PetscInt       tquadO[]   = {0, 0,
1221:                                       0, 0, 0, 0,
1222:                                       0, 0, 0, 0,
1223:                                       0, 0, 0, 0,
1224:                                       0, 0, 0, 0,
1225:                                       0, 0,  0,  0, -1,  0,
1226:                                       0, 0,  0,  0,  0, -1,
1227:                                       0, 0, -1,  0,  0,  0,
1228:                                       0, 0,  0, -1,  0,  0};
1229:   /* Add 4 edges, 12 triangles, 1 quad, 4 tetrahedra, and 6 pyramids inside every pyramid. */
1230:   static DMPolytopeType tpyrT[] = {DM_POLYTOPE_SEGMENT, DM_POLYTOPE_TRIANGLE, DM_POLYTOPE_QUADRILATERAL, DM_POLYTOPE_TETRAHEDRON, DM_POLYTOPE_PYRAMID};
1231:   static PetscInt       tpyrS[] = {4, 12, 1, 4, 6};
1232:   static PetscInt       tpyrC[] = {DM_POLYTOPE_POINT, 2, 1, 1, 0, DM_POLYTOPE_POINT, 1, 0, 0,
1233:                                    DM_POLYTOPE_POINT, 2, 2, 1, 0, DM_POLYTOPE_POINT, 1, 0, 0,
1234:                                    DM_POLYTOPE_POINT, 2, 3, 1, 0, DM_POLYTOPE_POINT, 1, 0, 0,
1235:                                    DM_POLYTOPE_POINT, 2, 4, 1, 0, DM_POLYTOPE_POINT, 1, 0, 0,
1236:                                    /* These four triangle face out of the bottom pyramid */
1237:                                    DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 0, 3, DM_POLYTOPE_SEGMENT, 0, 0,
1238:                                    DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 0, 0, DM_POLYTOPE_SEGMENT, 0, 1,
1239:                                    DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 0, 1, DM_POLYTOPE_SEGMENT, 0, 2,
1240:                                    DM_POLYTOPE_SEGMENT, 1, 4, 1, DM_POLYTOPE_SEGMENT, 0, 2, DM_POLYTOPE_SEGMENT, 0, 3,
1241:                                    /* These eight triangles face out of the corner pyramids */
1242:                                    DM_POLYTOPE_SEGMENT, 1, 0, 3, DM_POLYTOPE_SEGMENT, 0,    3, DM_POLYTOPE_SEGMENT, 1, 1, 2,
1243:                                    DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 0,    0, DM_POLYTOPE_SEGMENT, 1, 2, 2,
1244:                                    DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 0,    1, DM_POLYTOPE_SEGMENT, 1, 3, 2,
1245:                                    DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 0,    2, DM_POLYTOPE_SEGMENT, 1, 4, 2,
1246:                                    DM_POLYTOPE_SEGMENT, 1, 0, 3, DM_POLYTOPE_SEGMENT, 1, 1, 0, DM_POLYTOPE_SEGMENT, 0,    0,
1247:                                    DM_POLYTOPE_SEGMENT, 1, 0, 2, DM_POLYTOPE_SEGMENT, 1, 2, 0, DM_POLYTOPE_SEGMENT, 0,    1,
1248:                                    DM_POLYTOPE_SEGMENT, 1, 0, 1, DM_POLYTOPE_SEGMENT, 1, 3, 0, DM_POLYTOPE_SEGMENT, 0,    2,
1249:                                    DM_POLYTOPE_SEGMENT, 1, 0, 0, DM_POLYTOPE_SEGMENT, 1, 4, 0, DM_POLYTOPE_SEGMENT, 0,    3,
1250:                                    /* This quad faces out of the bottom pyramid */
1251:                                    DM_POLYTOPE_SEGMENT, 1, 1, 1, DM_POLYTOPE_SEGMENT, 1, 2, 1, DM_POLYTOPE_SEGMENT, 1, 3, 1, DM_POLYTOPE_SEGMENT, 1, 4, 1,
1252:                                    /* The bottom face of each tet is on the triangular face */
1253:                                    DM_POLYTOPE_TRIANGLE, 1, 1, 3, DM_POLYTOPE_TRIANGLE, 0,  8, DM_POLYTOPE_TRIANGLE, 0, 4, DM_POLYTOPE_TRIANGLE, 0, 0,
1254:                                    DM_POLYTOPE_TRIANGLE, 1, 2, 3, DM_POLYTOPE_TRIANGLE, 0,  9, DM_POLYTOPE_TRIANGLE, 0, 5, DM_POLYTOPE_TRIANGLE, 0, 1,
1255:                                    DM_POLYTOPE_TRIANGLE, 1, 3, 3, DM_POLYTOPE_TRIANGLE, 0, 10, DM_POLYTOPE_TRIANGLE, 0, 6, DM_POLYTOPE_TRIANGLE, 0, 2,
1256:                                    DM_POLYTOPE_TRIANGLE, 1, 4, 3, DM_POLYTOPE_TRIANGLE, 0, 11, DM_POLYTOPE_TRIANGLE, 0, 7, DM_POLYTOPE_TRIANGLE, 0, 3,
1257:                                    /* The front face of all pyramids is toward the front */
1258:                                    DM_POLYTOPE_QUADRILATERAL, 1, 0, 0, DM_POLYTOPE_TRIANGLE, 1, 1, 0, DM_POLYTOPE_TRIANGLE, 0,    4, DM_POLYTOPE_TRIANGLE, 0,   11, DM_POLYTOPE_TRIANGLE, 1, 4, 1,
1259:                                    DM_POLYTOPE_QUADRILATERAL, 1, 0, 3, DM_POLYTOPE_TRIANGLE, 1, 1, 1, DM_POLYTOPE_TRIANGLE, 1, 2, 0, DM_POLYTOPE_TRIANGLE, 0,    5, DM_POLYTOPE_TRIANGLE, 0,    8,
1260:                                    DM_POLYTOPE_QUADRILATERAL, 1, 0, 2, DM_POLYTOPE_TRIANGLE, 0,    9, DM_POLYTOPE_TRIANGLE, 1, 2, 1, DM_POLYTOPE_TRIANGLE, 1, 3, 0, DM_POLYTOPE_TRIANGLE, 0,    6,
1261:                                    DM_POLYTOPE_QUADRILATERAL, 1, 0, 1, DM_POLYTOPE_TRIANGLE, 0,    7, DM_POLYTOPE_TRIANGLE, 0,   10, DM_POLYTOPE_TRIANGLE, 1, 3, 1, DM_POLYTOPE_TRIANGLE, 1, 4, 0,
1262:                                    DM_POLYTOPE_QUADRILATERAL, 0,    0, DM_POLYTOPE_TRIANGLE, 1, 1, 2, DM_POLYTOPE_TRIANGLE, 1, 2, 2, DM_POLYTOPE_TRIANGLE, 1, 3, 2, DM_POLYTOPE_TRIANGLE, 1, 4, 2,
1263:                                    DM_POLYTOPE_QUADRILATERAL, 0,    0, DM_POLYTOPE_TRIANGLE, 0,    0, DM_POLYTOPE_TRIANGLE, 0,    3, DM_POLYTOPE_TRIANGLE, 0,    2, DM_POLYTOPE_TRIANGLE, 0,    1,
1264:                                    };
1265:   static PetscInt       tpyrO[] = {0, 0,
1266:                                    0, 0,
1267:                                    0, 0,
1268:                                    0, 0,
1269:                                    0,  0, -1,
1270:                                    0,  0, -1,
1271:                                    0,  0, -1,
1272:                                    0,  0, -1,
1273:                                    0, -1,  0,
1274:                                    0, -1,  0,
1275:                                    0, -1,  0,
1276:                                    0, -1,  0,
1277:                                   -1,  0,  0,
1278:                                   -1,  0,  0,
1279:                                   -1,  0,  0,
1280:                                   -1,  0,  0,
1281:                                   -1, -1, -1, -1,
1282:                                    0, -3, -2, -3,
1283:                                    0, -3, -2, -3,
1284:                                    0, -3, -2, -3,
1285:                                    0, -3, -2, -3,
1286:                                    0, 0, 0, 0, 0,
1287:                                    0, 0, 0, 0, 0,
1288:                                    0, 0, 0, 0, 0,
1289:                                    0, 0, 0, 0, 0,
1290:                                   -2, 0, 0, 0, 0,
1291:                                    1, 0, 0, 0, 0};

1293:   if (rt) *rt = 0;
1294:   switch (source) {
1295:     case DM_POLYTOPE_POINT:              *Nt = 1; *target = vertexT; *size = vertexS; *cone = vertexC; *ornt = vertexO; break;
1296:     case DM_POLYTOPE_SEGMENT:            *Nt = 2; *target = segT;    *size = segS;    *cone = segC;    *ornt = segO;    break;
1297:     case DM_POLYTOPE_POINT_PRISM_TENSOR: *Nt = 1; *target = tvertT;  *size = tvertS;  *cone = tvertC;  *ornt = tvertO;  break;
1298:     case DM_POLYTOPE_TRIANGLE:           *Nt = 2; *target = triT;    *size = triS;    *cone = triC;    *ornt = triO;    break;
1299:     case DM_POLYTOPE_QUADRILATERAL:      *Nt = 3; *target = quadT;   *size = quadS;   *cone = quadC;   *ornt = quadO;   break;
1300:     case DM_POLYTOPE_SEG_PRISM_TENSOR:   *Nt = 2; *target = tsegT;   *size = tsegS;   *cone = tsegC;   *ornt = tsegO;   break;
1301:     case DM_POLYTOPE_TETRAHEDRON:        *Nt = 3; *target = tetT;    *size = tetS;    *cone = tetC;    *ornt = tetO;    break;
1302:     case DM_POLYTOPE_HEXAHEDRON:         *Nt = 4; *target = hexT;    *size = hexS;    *cone = hexC;    *ornt = hexO;    break;
1303:     case DM_POLYTOPE_TRI_PRISM:          *Nt = 4; *target = tripT;   *size = tripS;   *cone = tripC;   *ornt = tripO;   break;
1304:     case DM_POLYTOPE_TRI_PRISM_TENSOR:   *Nt = 2; *target = ttriT;   *size = ttriS;   *cone = ttriC;   *ornt = ttriO;   break;
1305:     case DM_POLYTOPE_QUAD_PRISM_TENSOR:  *Nt = 3; *target = tquadT;  *size = tquadS;  *cone = tquadC;  *ornt = tquadO;  break;
1306:     case DM_POLYTOPE_PYRAMID:            *Nt = 5; *target = tpyrT;   *size = tpyrS;   *cone = tpyrC;   *ornt = tpyrO;   break;
1307:     default: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "No refinement strategy for %s", DMPolytopeTypes[source]);
1308:   }
1309:   return 0;
1310: }

1312: static PetscErrorCode DMPlexTransformInitialize_Regular(DMPlexTransform tr)
1313: {
1314:   tr->ops->view    = DMPlexTransformView_Regular;
1315:   tr->ops->setup   = DMPlexTransformSetUp_Regular;
1316:   tr->ops->destroy = DMPlexTransformDestroy_Regular;
1317:   tr->ops->celltransform = DMPlexTransformCellRefine_Regular;
1318:   tr->ops->getsubcellorientation = DMPlexTransformGetSubcellOrientation_Regular;
1319:   tr->ops->mapcoordinates = DMPlexTransformMapCoordinatesBarycenter_Internal;
1320:   return 0;
1321: }

1323: PETSC_EXTERN PetscErrorCode DMPlexTransformCreate_Regular(DMPlexTransform tr)
1324: {
1325:   DMPlexRefine_Regular *f;

1328:   PetscNewLog(tr, &f);
1329:   tr->data = f;

1331:   DMPlexTransformInitialize_Regular(tr);
1332:   return 0;
1333: }