xref: /petsc/src/dm/impls/plex/plexgeometry.c (revision 7f07f36205ec0f0e57548d51590c4939e5dc2e0e)
1 #include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
2 
3 #undef __FUNCT__
4 #define __FUNCT__ "DMPlexLocatePoint_Simplex_2D_Internal"
5 static PetscErrorCode DMPlexLocatePoint_Simplex_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
6 {
7   const PetscInt embedDim = 2;
8   PetscReal      x        = PetscRealPart(point[0]);
9   PetscReal      y        = PetscRealPart(point[1]);
10   PetscReal      v0[2], J[4], invJ[4], detJ;
11   PetscReal      xi, eta;
12   PetscErrorCode ierr;
13 
14   PetscFunctionBegin;
15   ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
16   xi  = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]);
17   eta = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]);
18 
19   if ((xi >= 0.0) && (eta >= 0.0) && (xi + eta <= 2.0)) *cell = c;
20   else *cell = -1;
21   PetscFunctionReturn(0);
22 }
23 
24 #undef __FUNCT__
25 #define __FUNCT__ "DMPlexLocatePoint_General_2D_Internal"
26 static PetscErrorCode DMPlexLocatePoint_General_2D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
27 {
28   PetscSection       coordSection;
29   Vec             coordsLocal;
30   PetscScalar    *coords;
31   const PetscInt  faces[8]  = {0, 1, 1, 2, 2, 3, 3, 0};
32   PetscReal       x         = PetscRealPart(point[0]);
33   PetscReal       y         = PetscRealPart(point[1]);
34   PetscInt        crossings = 0, f;
35   PetscErrorCode  ierr;
36 
37   PetscFunctionBegin;
38   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
39   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
40   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
41   for (f = 0; f < 4; ++f) {
42     PetscReal x_i   = PetscRealPart(coords[faces[2*f+0]*2+0]);
43     PetscReal y_i   = PetscRealPart(coords[faces[2*f+0]*2+1]);
44     PetscReal x_j   = PetscRealPart(coords[faces[2*f+1]*2+0]);
45     PetscReal y_j   = PetscRealPart(coords[faces[2*f+1]*2+1]);
46     PetscReal slope = (y_j - y_i) / (x_j - x_i);
47     PetscBool cond1 = (x_i <= x) && (x < x_j) ? PETSC_TRUE : PETSC_FALSE;
48     PetscBool cond2 = (x_j <= x) && (x < x_i) ? PETSC_TRUE : PETSC_FALSE;
49     PetscBool above = (y < slope * (x - x_i) + y_i) ? PETSC_TRUE : PETSC_FALSE;
50     if ((cond1 || cond2)  && above) ++crossings;
51   }
52   if (crossings % 2) *cell = c;
53   else *cell = -1;
54   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
55   PetscFunctionReturn(0);
56 }
57 
58 #undef __FUNCT__
59 #define __FUNCT__ "DMPlexLocatePoint_Simplex_3D_Internal"
60 static PetscErrorCode DMPlexLocatePoint_Simplex_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
61 {
62   const PetscInt embedDim = 3;
63   PetscReal      v0[3], J[9], invJ[9], detJ;
64   PetscReal      x = PetscRealPart(point[0]);
65   PetscReal      y = PetscRealPart(point[1]);
66   PetscReal      z = PetscRealPart(point[2]);
67   PetscReal      xi, eta, zeta;
68   PetscErrorCode ierr;
69 
70   PetscFunctionBegin;
71   ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
72   xi   = invJ[0*embedDim+0]*(x - v0[0]) + invJ[0*embedDim+1]*(y - v0[1]) + invJ[0*embedDim+2]*(z - v0[2]);
73   eta  = invJ[1*embedDim+0]*(x - v0[0]) + invJ[1*embedDim+1]*(y - v0[1]) + invJ[1*embedDim+2]*(z - v0[2]);
74   zeta = invJ[2*embedDim+0]*(x - v0[0]) + invJ[2*embedDim+1]*(y - v0[1]) + invJ[2*embedDim+2]*(z - v0[2]);
75 
76   if ((xi >= 0.0) && (eta >= 0.0) && (zeta >= 0.0) && (xi + eta + zeta <= 2.0)) *cell = c;
77   else *cell = -1;
78   PetscFunctionReturn(0);
79 }
80 
81 #undef __FUNCT__
82 #define __FUNCT__ "DMPlexLocatePoint_General_3D_Internal"
83 static PetscErrorCode DMPlexLocatePoint_General_3D_Internal(DM dm, const PetscScalar point[], PetscInt c, PetscInt *cell)
84 {
85   PetscSection       coordSection;
86   Vec            coordsLocal;
87   PetscScalar   *coords;
88   const PetscInt faces[24] = {0, 1, 2, 3,  5, 4, 7, 6,  1, 0, 4, 5,
89                               3, 2, 6, 7,  1, 5, 6, 2,  0, 3, 7, 4};
90   PetscBool      found = PETSC_TRUE;
91   PetscInt       f;
92   PetscErrorCode ierr;
93 
94   PetscFunctionBegin;
95   ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
96   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
97   ierr = DMPlexVecGetClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
98   for (f = 0; f < 6; ++f) {
99     /* Check the point is under plane */
100     /*   Get face normal */
101     PetscReal v_i[3];
102     PetscReal v_j[3];
103     PetscReal normal[3];
104     PetscReal pp[3];
105     PetscReal dot;
106 
107     v_i[0]    = PetscRealPart(coords[faces[f*4+3]*3+0]-coords[faces[f*4+0]*3+0]);
108     v_i[1]    = PetscRealPart(coords[faces[f*4+3]*3+1]-coords[faces[f*4+0]*3+1]);
109     v_i[2]    = PetscRealPart(coords[faces[f*4+3]*3+2]-coords[faces[f*4+0]*3+2]);
110     v_j[0]    = PetscRealPart(coords[faces[f*4+1]*3+0]-coords[faces[f*4+0]*3+0]);
111     v_j[1]    = PetscRealPart(coords[faces[f*4+1]*3+1]-coords[faces[f*4+0]*3+1]);
112     v_j[2]    = PetscRealPart(coords[faces[f*4+1]*3+2]-coords[faces[f*4+0]*3+2]);
113     normal[0] = v_i[1]*v_j[2] - v_i[2]*v_j[1];
114     normal[1] = v_i[2]*v_j[0] - v_i[0]*v_j[2];
115     normal[2] = v_i[0]*v_j[1] - v_i[1]*v_j[0];
116     pp[0]     = PetscRealPart(coords[faces[f*4+0]*3+0] - point[0]);
117     pp[1]     = PetscRealPart(coords[faces[f*4+0]*3+1] - point[1]);
118     pp[2]     = PetscRealPart(coords[faces[f*4+0]*3+2] - point[2]);
119     dot       = normal[0]*pp[0] + normal[1]*pp[1] + normal[2]*pp[2];
120 
121     /* Check that projected point is in face (2D location problem) */
122     if (dot < 0.0) {
123       found = PETSC_FALSE;
124       break;
125     }
126   }
127   if (found) *cell = c;
128   else *cell = -1;
129   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordsLocal, c, NULL, &coords);CHKERRQ(ierr);
130   PetscFunctionReturn(0);
131 }
132 
133 #undef __FUNCT__
134 #define __FUNCT__ "DMLocatePoints_Plex"
135 /*
136  Need to implement using the guess
137 */
138 PetscErrorCode DMLocatePoints_Plex(DM dm, Vec v, IS *cellIS)
139 {
140   PetscInt       cell = -1 /*, guess = -1*/;
141   PetscInt       bs, numPoints, p;
142   PetscInt       dim, cStart, cEnd, cMax, c, coneSize;
143   PetscInt      *cells;
144   PetscScalar   *a;
145   PetscErrorCode ierr;
146 
147   PetscFunctionBegin;
148   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
149   ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
150   ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
151   if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
152   ierr = VecGetLocalSize(v, &numPoints);CHKERRQ(ierr);
153   ierr = VecGetBlockSize(v, &bs);CHKERRQ(ierr);
154   ierr = VecGetArray(v, &a);CHKERRQ(ierr);
155   if (bs != dim) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Block size for point vector %d must be the mesh coordinate dimension %d", bs, dim);
156   numPoints /= bs;
157   ierr       = PetscMalloc(numPoints * sizeof(PetscInt), &cells);CHKERRQ(ierr);
158   for (p = 0; p < numPoints; ++p) {
159     const PetscScalar *point = &a[p*bs];
160 
161     switch (dim) {
162     case 2:
163       for (c = cStart; c < cEnd; ++c) {
164         ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
165         switch (coneSize) {
166         case 3:
167           ierr = DMPlexLocatePoint_Simplex_2D_Internal(dm, point, c, &cell);CHKERRQ(ierr);
168           break;
169         case 4:
170           ierr = DMPlexLocatePoint_General_2D_Internal(dm, point, c, &cell);CHKERRQ(ierr);
171           break;
172         default:
173           SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %d", coneSize);
174         }
175         if (cell >= 0) break;
176       }
177       break;
178     case 3:
179       for (c = cStart; c < cEnd; ++c) {
180         ierr = DMPlexGetConeSize(dm, c, &coneSize);CHKERRQ(ierr);
181         switch (coneSize) {
182         case 4:
183           ierr = DMPlexLocatePoint_Simplex_3D_Internal(dm, point, c, &cell);CHKERRQ(ierr);
184           break;
185         case 8:
186           ierr = DMPlexLocatePoint_General_3D_Internal(dm, point, c, &cell);CHKERRQ(ierr);
187           break;
188         default:
189           SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for cell with cone size %d", coneSize);
190         }
191         if (cell >= 0) break;
192       }
193       break;
194     default:
195       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "No point location for mesh dimension %d", dim);
196     }
197     cells[p] = cell;
198   }
199   ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
200   ierr = ISCreateGeneral(PETSC_COMM_SELF, numPoints, cells, PETSC_OWN_POINTER, cellIS);CHKERRQ(ierr);
201   PetscFunctionReturn(0);
202 }
203 
204 #undef __FUNCT__
205 #define __FUNCT__ "DMPlexComputeProjection2Dto1D_Internal"
206 /*
207   DMPlexComputeProjection2Dto1D_Internal - Rewrite coordinates to be the 1D projection of the 2D
208 */
209 static PetscErrorCode DMPlexComputeProjection2Dto1D_Internal(PetscScalar coords[], PetscReal R[])
210 {
211   const PetscReal x = PetscRealPart(coords[2] - coords[0]);
212   const PetscReal y = PetscRealPart(coords[3] - coords[1]);
213   const PetscReal r = sqrt(x*x + y*y), c = x/r, s = y/r;
214 
215   PetscFunctionBegin;
216   R[0] =  c; R[1] = s;
217   R[2] = -s; R[3] = c;
218   coords[0] = 0.0;
219   coords[1] = r;
220   PetscFunctionReturn(0);
221 }
222 
223 #undef __FUNCT__
224 #define __FUNCT__ "DMPlexComputeProjection3Dto2D_Internal"
225 /*
226   DMPlexComputeProjection3Dto2D_Internal - Rewrite coordinates to be the 2D projection of the 3D
227 */
228 static PetscErrorCode DMPlexComputeProjection3Dto2D_Internal(PetscScalar coords[], PetscReal R[])
229 {
230   PetscScalar    x1[3],  x2[3], n[3], norm;
231   PetscScalar    x1p[3], x2p[3];
232   PetscReal      sqrtz, alpha;
233   const PetscInt dim = 3;
234   PetscInt       d, e;
235 
236   PetscFunctionBegin;
237   /* 0) Calculate normal vector */
238   for (d = 0; d < dim; ++d) {
239     x1[d] = coords[1*dim+d] - coords[0*dim+d];
240     x2[d] = coords[2*dim+d] - coords[0*dim+d];
241   }
242   n[0] = x1[1]*x2[2] - x1[2]*x2[1];
243   n[1] = x1[2]*x2[0] - x1[0]*x2[2];
244   n[2] = x1[0]*x2[1] - x1[1]*x2[0];
245   norm = sqrt(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
246   n[0] /= norm;
247   n[1] /= norm;
248   n[2] /= norm;
249   /* 1) Take the normal vector and rotate until it is \hat z
250 
251     Let the normal vector be <nx, ny, nz> and alpha = 1/sqrt(1 - nz^2), then
252 
253     R = /  alpha nx nz  alpha ny nz -1/alpha \
254         | -alpha ny     alpha nx        0    |
255         \     nx            ny         nz    /
256 
257     will rotate the normal vector to \hat z
258   */
259   sqrtz = sqrt(1.0 - PetscAbsScalar(n[2]*n[2]));
260   /* Check for n = z */
261   if (sqrtz < 1.0e-10) {
262     coords[0] = 0.0;
263     coords[1] = 0.0;
264     if (PetscRealPart(n[2]) < 0.0) {
265       coords[2] = x2[0];
266       coords[3] = x2[1];
267       coords[4] = x1[0];
268       coords[5] = x1[1];
269     } else {
270       coords[2] = x1[0];
271       coords[3] = x1[1];
272       coords[4] = x2[0];
273       coords[5] = x2[1];
274     }
275     PetscFunctionReturn(0);
276   }
277   alpha = 1.0/sqrtz;
278   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
279   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
280   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
281   for (d = 0; d < dim; ++d) {
282     x1p[d] = 0.0;
283     x2p[d] = 0.0;
284     for (e = 0; e < dim; ++e) {
285       x1p[d] += R[d*dim+e]*x1[e];
286       x2p[d] += R[d*dim+e]*x2[e];
287     }
288   }
289   if (PetscAbsScalar(x1p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
290   if (PetscAbsScalar(x2p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
291   /* 2) Project to (x, y) */
292   coords[0] = 0.0;
293   coords[1] = 0.0;
294   coords[2] = x1p[0];
295   coords[3] = x1p[1];
296   coords[4] = x2p[0];
297   coords[5] = x2p[1];
298   /* Output R^T which rotates \hat z to the input normal */
299   for (d = 0; d < dim; ++d) {
300     for (e = d+1; e < dim; ++e) {
301       PetscReal tmp;
302 
303       tmp        = R[d*dim+e];
304       R[d*dim+e] = R[e*dim+d];
305       R[e*dim+d] = tmp;
306     }
307   }
308   PetscFunctionReturn(0);
309 }
310 
311 #undef __FUNCT__
312 #define __FUNCT__ "Invert2D_Internal"
313 PETSC_STATIC_INLINE void Invert2D_Internal(PetscReal invJ[], PetscReal J[], PetscReal detJ)
314 {
315   const PetscReal invDet = 1.0/detJ;
316 
317   invJ[0] =  invDet*J[3];
318   invJ[1] = -invDet*J[1];
319   invJ[2] = -invDet*J[2];
320   invJ[3] =  invDet*J[0];
321   PetscLogFlops(5.0);
322 }
323 
324 #undef __FUNCT__
325 #define __FUNCT__ "Invert3D_Internal"
326 PETSC_STATIC_INLINE void Invert3D_Internal(PetscReal invJ[], PetscReal J[], PetscReal detJ)
327 {
328   const PetscReal invDet = 1.0/detJ;
329 
330   invJ[0*3+0] = invDet*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]);
331   invJ[0*3+1] = invDet*(J[0*3+2]*J[2*3+1] - J[0*3+1]*J[2*3+2]);
332   invJ[0*3+2] = invDet*(J[0*3+1]*J[1*3+2] - J[0*3+2]*J[1*3+1]);
333   invJ[1*3+0] = invDet*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]);
334   invJ[1*3+1] = invDet*(J[0*3+0]*J[2*3+2] - J[0*3+2]*J[2*3+0]);
335   invJ[1*3+2] = invDet*(J[0*3+2]*J[1*3+0] - J[0*3+0]*J[1*3+2]);
336   invJ[2*3+0] = invDet*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]);
337   invJ[2*3+1] = invDet*(J[0*3+1]*J[2*3+0] - J[0*3+0]*J[2*3+1]);
338   invJ[2*3+2] = invDet*(J[0*3+0]*J[1*3+1] - J[0*3+1]*J[1*3+0]);
339   PetscLogFlops(37.0);
340 }
341 
342 #undef __FUNCT__
343 #define __FUNCT__ "Det2D_Internal"
344 PETSC_STATIC_INLINE void Det2D_Internal(PetscReal *detJ, PetscReal J[])
345 {
346   *detJ = J[0]*J[3] - J[1]*J[2];
347   PetscLogFlops(3.0);
348 }
349 
350 #undef __FUNCT__
351 #define __FUNCT__ "Det3D_Internal"
352 PETSC_STATIC_INLINE void Det3D_Internal(PetscReal *detJ, PetscReal J[])
353 {
354   *detJ = (J[0*3+0]*(J[1*3+2]*J[2*3+1] - J[1*3+1]*J[2*3+2]) +
355            J[0*3+1]*(J[1*3+0]*J[2*3+2] - J[1*3+2]*J[2*3+0]) +
356            J[0*3+2]*(J[1*3+1]*J[2*3+0] - J[1*3+0]*J[2*3+1]));
357   PetscLogFlops(12.0);
358 }
359 
360 #undef __FUNCT__
361 #define __FUNCT__ "DMPlexComputeLineGeometry_Internal"
362 static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
363 {
364   PetscSection   coordSection;
365   Vec            coordinates;
366   PetscScalar   *coords;
367   PetscInt       numCoords, d;
368   PetscErrorCode ierr;
369 
370   PetscFunctionBegin;
371   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
372   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
373   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
374   *detJ = 0.0;
375   if (numCoords == 4) {
376     const PetscInt dim = 2;
377     PetscReal      R[4], J0;
378 
379     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
380     ierr = DMPlexComputeProjection2Dto1D_Internal(coords, R);CHKERRQ(ierr);
381     if (J)    {
382       J0   = 0.5*PetscRealPart(coords[1]);
383       J[0] = R[0]*J0; J[1] = R[1];
384       J[2] = R[2]*J0; J[3] = R[3];
385       Det2D_Internal(detJ, J);
386     }
387     if (invJ) {Invert2D_Internal(invJ, J, *detJ);}
388   } else if (numCoords == 2) {
389     const PetscInt dim = 1;
390 
391     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
392     if (J)    {
393       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
394       *detJ = J[0];
395       PetscLogFlops(2.0);
396     }
397     if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
398   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %d != 2", numCoords);
399   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
400   PetscFunctionReturn(0);
401 }
402 
403 #undef __FUNCT__
404 #define __FUNCT__ "DMPlexComputeTriangleGeometry_Internal"
405 static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
406 {
407   PetscSection   coordSection;
408   Vec            coordinates;
409   PetscScalar   *coords;
410   PetscInt       numCoords, d, f, g;
411   PetscErrorCode ierr;
412 
413   PetscFunctionBegin;
414   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
415   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
416   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
417   *detJ = 0.0;
418   if (numCoords == 9) {
419     const PetscInt dim = 3;
420     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
421 
422     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
423     ierr = DMPlexComputeProjection3Dto2D_Internal(coords, R);CHKERRQ(ierr);
424     if (J)    {
425       for (d = 0; d < dim-1; d++) {
426         for (f = 0; f < dim-1; f++) {
427           J0[d*(dim+1)+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
428         }
429       }
430       PetscLogFlops(8.0);
431       for (d = 0; d < dim; d++) {
432         for (f = 0; f < dim; f++) {
433           J[d*dim+f] = 0.0;
434           for (g = 0; g < dim; g++) {
435             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
436           }
437         }
438       }
439       PetscLogFlops(18.0);
440       Det3D_Internal(detJ, J);
441     }
442     if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
443   } else if (numCoords == 6) {
444     const PetscInt dim = 2;
445 
446     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
447     if (J)    {
448       for (d = 0; d < dim; d++) {
449         for (f = 0; f < dim; f++) {
450           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
451         }
452       }
453       PetscLogFlops(8.0);
454       Det2D_Internal(detJ, J);
455     }
456     if (invJ) {Invert2D_Internal(invJ, J, *detJ);}
457   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %d != 6", numCoords);
458   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
459   PetscFunctionReturn(0);
460 }
461 
462 #undef __FUNCT__
463 #define __FUNCT__ "DMPlexComputeRectangleGeometry_Internal"
464 static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
465 {
466   PetscSection   coordSection;
467   Vec            coordinates;
468   PetscScalar   *coords;
469   const PetscInt dim = 2;
470   PetscInt       d, f;
471   PetscErrorCode ierr;
472 
473   PetscFunctionBegin;
474   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
475   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
476   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
477   *detJ = 0.0;
478   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
479   if (J)    {
480     for (d = 0; d < dim; d++) {
481       for (f = 0; f < dim; f++) {
482         J[d*dim+f] = 0.5*(PetscRealPart(coords[(f*2+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
483       }
484     }
485     PetscLogFlops(8.0);
486     Det2D_Internal(detJ, J);
487   }
488   if (invJ) {Invert2D_Internal(invJ, J, *detJ);}
489   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
490   PetscFunctionReturn(0);
491 }
492 
493 #undef __FUNCT__
494 #define __FUNCT__ "DMPlexComputeTetrahedronGeometry_Internal"
495 static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
496 {
497   PetscSection   coordSection;
498   Vec            coordinates;
499   PetscScalar   *coords;
500   const PetscInt dim = 3;
501   PetscInt       d, f;
502   PetscErrorCode ierr;
503 
504   PetscFunctionBegin;
505   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
506   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
507   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
508   *detJ = 0.0;
509   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
510   if (J)    {
511     for (d = 0; d < dim; d++) {
512       for (f = 0; f < dim; f++) {
513         J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
514       }
515     }
516     PetscLogFlops(18.0);
517     Det3D_Internal(detJ, J);
518   }
519   if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
520   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
521   PetscFunctionReturn(0);
522 }
523 
524 #undef __FUNCT__
525 #define __FUNCT__ "DMPlexComputeHexahedronGeometry_Internal"
526 static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
527 {
528   PetscSection   coordSection;
529   Vec            coordinates;
530   PetscScalar   *coords;
531   const PetscInt dim = 3;
532   PetscInt       d;
533   PetscErrorCode ierr;
534 
535   PetscFunctionBegin;
536   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
537   ierr = DMPlexGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
538   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
539   *detJ = 0.0;
540   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
541   if (J)    {
542     for (d = 0; d < dim; d++) {
543       J[d*dim+0] = 0.5*(PetscRealPart(coords[(0+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
544       J[d*dim+1] = 0.5*(PetscRealPart(coords[(1+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
545       J[d*dim+2] = 0.5*(PetscRealPart(coords[(3+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
546     }
547     PetscLogFlops(18.0);
548     Det3D_Internal(detJ, J);
549   }
550   if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
551   *detJ *= -8.0;
552   ierr   = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
553   PetscFunctionReturn(0);
554 }
555 
556 #undef __FUNCT__
557 #define __FUNCT__ "DMPlexComputeCellGeometry"
558 /*@C
559   DMPlexComputeCellGeometry - Compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
560 
561   Collective on DM
562 
563   Input Arguments:
564 + dm   - the DM
565 - cell - the cell
566 
567   Output Arguments:
568 + v0   - the translation part of this affine transform
569 . J    - the Jacobian of the transform from the reference element
570 . invJ - the inverse of the Jacobian
571 - detJ - the Jacobian determinant
572 
573   Level: advanced
574 
575   Fortran Notes:
576   Since it returns arrays, this routine is only available in Fortran 90, and you must
577   include petsc.h90 in your code.
578 
579 .seealso: DMPlexGetCoordinateSection(), DMPlexGetCoordinateVec()
580 @*/
581 PetscErrorCode DMPlexComputeCellGeometry(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
582 {
583   PetscInt       depth, dim, coneSize;
584   PetscErrorCode ierr;
585 
586   PetscFunctionBegin;
587   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
588   ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
589   if (depth == 1) {
590     ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
591     switch (dim) {
592     case 1:
593       ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
594       break;
595     case 2:
596       switch (coneSize) {
597       case 3:
598         ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
599         break;
600       case 4:
601         ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
602         break;
603       default:
604         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
605       }
606       break;
607     case 3:
608       switch (coneSize) {
609       case 4:
610         ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
611         break;
612       case 8:
613         ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
614         break;
615       default:
616         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
617       }
618       break;
619     default:
620       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
621     }
622   } else {
623     /* We need to keep a pointer to the depth label */
624     ierr = DMPlexGetLabelValue(dm, "depth", cell, &dim);CHKERRQ(ierr);
625     /* Cone size is now the number of faces */
626     switch (dim) {
627     case 1:
628       ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
629       break;
630     case 2:
631       switch (coneSize) {
632       case 3:
633         ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
634         break;
635       case 4:
636         ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
637         break;
638       default:
639         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
640       }
641       break;
642     case 3:
643       switch (coneSize) {
644       case 4:
645         ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
646         break;
647       case 6:
648         ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
649         break;
650       default:
651         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
652       }
653       break;
654     default:
655       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
656     }
657   }
658   PetscFunctionReturn(0);
659 }
660