xref: /petsc/src/dm/impls/plex/plexgeometry.c (revision 5167406814f7f49a97e0d17844aa49dba92c178e)
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 = NULL;
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 = DMGetCoordinateSection(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, 3, 2, 1,  5, 4, 7, 6,  3, 0, 4, 5,
89                               1, 2, 6, 7,  3, 5, 6, 2,  0, 1, 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 = DMGetCoordinateSection(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       = PetscMalloc1(numPoints, &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 6:
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 = PetscSqrtReal(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(PetscInt coordSize, PetscScalar coords[], PetscReal R[])
229 {
230   PetscReal      x1[3],  x2[3], n[3], norm;
231   PetscReal      x1p[3], x2p[3], xnp[3];
232   PetscReal      sqrtz, alpha;
233   const PetscInt dim = 3;
234   PetscInt       d, e, p;
235 
236   PetscFunctionBegin;
237   /* 0) Calculate normal vector */
238   for (d = 0; d < dim; ++d) {
239     x1[d] = PetscRealPart(coords[1*dim+d] - coords[0*dim+d]);
240     x2[d] = PetscRealPart(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 = PetscSqrtReal(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 = PetscSqrtReal(1.0 - n[2]*n[2]);
260   /* Check for n = z */
261   if (sqrtz < 1.0e-10) {
262     if (n[2] < 0.0) {
263       if (coordSize > 9) {
264         coords[2] = PetscRealPart(coords[3*dim+0] - coords[0*dim+0]);
265         coords[3] = PetscRealPart(coords[3*dim+0] - coords[0*dim+0]);
266         coords[4] = x2[0];
267         coords[5] = x2[1];
268         coords[6] = x1[0];
269         coords[7] = x1[1];
270       } else {
271         coords[2] = x2[0];
272         coords[3] = x2[1];
273         coords[4] = x1[0];
274         coords[5] = x1[1];
275       }
276       R[0] = 1.0; R[1] = 0.0; R[2] = 0.0;
277       R[3] = 0.0; R[4] = 1.0; R[5] = 0.0;
278       R[6] = 0.0; R[7] = 0.0; R[8] = -1.0;
279     } else {
280       for (p = 3; p < coordSize/3; ++p) {
281         coords[p*2+0] = PetscRealPart(coords[p*dim+0] - coords[0*dim+0]);
282         coords[p*2+1] = PetscRealPart(coords[p*dim+1] - coords[0*dim+1]);
283       }
284       coords[2] = x1[0];
285       coords[3] = x1[1];
286       coords[4] = x2[0];
287       coords[5] = x2[1];
288       R[0] = 1.0; R[1] = 0.0; R[2] = 0.0;
289       R[3] = 0.0; R[4] = 1.0; R[5] = 0.0;
290       R[6] = 0.0; R[7] = 0.0; R[8] = 1.0;
291     }
292     coords[0] = 0.0;
293     coords[1] = 0.0;
294     PetscFunctionReturn(0);
295   }
296   alpha = 1.0/sqrtz;
297   R[0] =  alpha*n[0]*n[2]; R[1] = alpha*n[1]*n[2]; R[2] = -sqrtz;
298   R[3] = -alpha*n[1];      R[4] = alpha*n[0];      R[5] = 0.0;
299   R[6] =  n[0];            R[7] = n[1];            R[8] = n[2];
300   for (d = 0; d < dim; ++d) {
301     x1p[d] = 0.0;
302     x2p[d] = 0.0;
303     for (e = 0; e < dim; ++e) {
304       x1p[d] += R[d*dim+e]*x1[e];
305       x2p[d] += R[d*dim+e]*x2[e];
306     }
307   }
308   if (PetscAbsReal(x1p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
309   if (PetscAbsReal(x2p[2]) > 1.0e-9) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Invalid rotation calculated");
310   /* 2) Project to (x, y) */
311   for (p = 3; p < coordSize/3; ++p) {
312     for (d = 0; d < dim; ++d) {
313       xnp[d] = 0.0;
314       for (e = 0; e < dim; ++e) {
315         xnp[d] += R[d*dim+e]*PetscRealPart(coords[p*dim+e] - coords[0*dim+e]);
316       }
317       if (d < dim-1) coords[p*2+d] = xnp[d];
318     }
319   }
320   coords[0] = 0.0;
321   coords[1] = 0.0;
322   coords[2] = x1p[0];
323   coords[3] = x1p[1];
324   coords[4] = x2p[0];
325   coords[5] = x2p[1];
326   /* Output R^T which rotates \hat z to the input normal */
327   for (d = 0; d < dim; ++d) {
328     for (e = d+1; e < dim; ++e) {
329       PetscReal tmp;
330 
331       tmp        = R[d*dim+e];
332       R[d*dim+e] = R[e*dim+d];
333       R[e*dim+d] = tmp;
334     }
335   }
336   PetscFunctionReturn(0);
337 }
338 
339 #undef __FUNCT__
340 #define __FUNCT__ "Invert2D_Internal"
341 PETSC_STATIC_INLINE void Invert2D_Internal(PetscReal invJ[], PetscReal J[], PetscReal detJ)
342 {
343   const PetscReal invDet = 1.0/detJ;
344 
345   invJ[0] =  invDet*J[3];
346   invJ[1] = -invDet*J[1];
347   invJ[2] = -invDet*J[2];
348   invJ[3] =  invDet*J[0];
349   PetscLogFlops(5.0);
350 }
351 
352 #undef __FUNCT__
353 #define __FUNCT__ "Invert3D_Internal"
354 PETSC_STATIC_INLINE void Invert3D_Internal(PetscReal invJ[], PetscReal J[], PetscReal detJ)
355 {
356   const PetscReal invDet = 1.0/detJ;
357 
358   invJ[0*3+0] = invDet*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]);
359   invJ[0*3+1] = invDet*(J[0*3+2]*J[2*3+1] - J[0*3+1]*J[2*3+2]);
360   invJ[0*3+2] = invDet*(J[0*3+1]*J[1*3+2] - J[0*3+2]*J[1*3+1]);
361   invJ[1*3+0] = invDet*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]);
362   invJ[1*3+1] = invDet*(J[0*3+0]*J[2*3+2] - J[0*3+2]*J[2*3+0]);
363   invJ[1*3+2] = invDet*(J[0*3+2]*J[1*3+0] - J[0*3+0]*J[1*3+2]);
364   invJ[2*3+0] = invDet*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]);
365   invJ[2*3+1] = invDet*(J[0*3+1]*J[2*3+0] - J[0*3+0]*J[2*3+1]);
366   invJ[2*3+2] = invDet*(J[0*3+0]*J[1*3+1] - J[0*3+1]*J[1*3+0]);
367   PetscLogFlops(37.0);
368 }
369 
370 #undef __FUNCT__
371 #define __FUNCT__ "Det2D_Internal"
372 PETSC_STATIC_INLINE void Det2D_Internal(PetscReal *detJ, PetscReal J[])
373 {
374   *detJ = J[0]*J[3] - J[1]*J[2];
375   PetscLogFlops(3.0);
376 }
377 
378 #undef __FUNCT__
379 #define __FUNCT__ "Det3D_Internal"
380 PETSC_STATIC_INLINE void Det3D_Internal(PetscReal *detJ, PetscReal J[])
381 {
382   *detJ = (J[0*3+0]*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]) +
383            J[0*3+1]*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]) +
384            J[0*3+2]*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]));
385   PetscLogFlops(12.0);
386 }
387 
388 #undef __FUNCT__
389 #define __FUNCT__ "Volume_Triangle_Internal"
390 PETSC_UNUSED
391 PETSC_STATIC_INLINE void Volume_Triangle_Internal(PetscReal *vol, PetscReal coords[])
392 {
393   /* Signed volume is 1/2 the determinant
394 
395    |  1  1  1 |
396    | x0 x1 x2 |
397    | y0 y1 y2 |
398 
399      but if x0,y0 is the origin, we have
400 
401    | x1 x2 |
402    | y1 y2 |
403   */
404   const PetscReal x1 = coords[2] - coords[0], y1 = coords[3] - coords[1];
405   const PetscReal x2 = coords[4] - coords[0], y2 = coords[5] - coords[1];
406   PetscReal       M[4], detM;
407   M[0] = x1; M[1] = x2;
408   M[2] = y1; M[3] = y2;
409   Det2D_Internal(&detM, M);
410   *vol = 0.5*detM;
411   PetscLogFlops(5.0);
412 }
413 
414 #undef __FUNCT__
415 #define __FUNCT__ "Volume_Triangle_Origin_Internal"
416 PETSC_STATIC_INLINE void Volume_Triangle_Origin_Internal(PetscReal *vol, PetscReal coords[])
417 {
418   Det2D_Internal(vol, coords);
419   *vol *= 0.5;
420 }
421 
422 #undef __FUNCT__
423 #define __FUNCT__ "Volume_Tetrahedron_Internal"
424 PETSC_UNUSED
425 PETSC_STATIC_INLINE void Volume_Tetrahedron_Internal(PetscReal *vol, PetscReal coords[])
426 {
427   /* Signed volume is 1/6th of the determinant
428 
429    |  1  1  1  1 |
430    | x0 x1 x2 x3 |
431    | y0 y1 y2 y3 |
432    | z0 z1 z2 z3 |
433 
434      but if x0,y0,z0 is the origin, we have
435 
436    | x1 x2 x3 |
437    | y1 y2 y3 |
438    | z1 z2 z3 |
439   */
440   const PetscReal x1 = coords[3] - coords[0], y1 = coords[4]  - coords[1], z1 = coords[5]  - coords[2];
441   const PetscReal x2 = coords[6] - coords[0], y2 = coords[7]  - coords[1], z2 = coords[8]  - coords[2];
442   const PetscReal x3 = coords[9] - coords[0], y3 = coords[10] - coords[1], z3 = coords[11] - coords[2];
443   PetscReal       M[9], detM;
444   M[0] = x1; M[1] = x2; M[2] = x3;
445   M[3] = y1; M[4] = y2; M[5] = y3;
446   M[6] = z1; M[7] = z2; M[8] = z3;
447   Det3D_Internal(&detM, M);
448   *vol = -0.16666666666666666666666*detM;
449   PetscLogFlops(10.0);
450 }
451 
452 #undef __FUNCT__
453 #define __FUNCT__ "Volume_Tetrahedron_Origin_Internal"
454 PETSC_STATIC_INLINE void Volume_Tetrahedron_Origin_Internal(PetscReal *vol, PetscReal coords[])
455 {
456   Det3D_Internal(vol, coords);
457   *vol *= -0.16666666666666666666666;
458 }
459 
460 #undef __FUNCT__
461 #define __FUNCT__ "DMPlexComputeLineGeometry_Internal"
462 static PetscErrorCode DMPlexComputeLineGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
463 {
464   PetscSection   coordSection;
465   Vec            coordinates;
466   PetscScalar   *coords = NULL;
467   PetscInt       numCoords, d;
468   PetscErrorCode ierr;
469 
470   PetscFunctionBegin;
471   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
472   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
473   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
474   *detJ = 0.0;
475   if (numCoords == 4) {
476     const PetscInt dim = 2;
477     PetscReal      R[4], J0;
478 
479     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
480     ierr = DMPlexComputeProjection2Dto1D_Internal(coords, R);CHKERRQ(ierr);
481     if (J)    {
482       J0   = 0.5*PetscRealPart(coords[1]);
483       J[0] = R[0]*J0; J[1] = R[1];
484       J[2] = R[2]*J0; J[3] = R[3];
485       Det2D_Internal(detJ, J);
486     }
487     if (invJ) {Invert2D_Internal(invJ, J, *detJ);}
488   } else if (numCoords == 2) {
489     const PetscInt dim = 1;
490 
491     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
492     if (J)    {
493       J[0]  = 0.5*(PetscRealPart(coords[1]) - PetscRealPart(coords[0]));
494       *detJ = J[0];
495       PetscLogFlops(2.0);
496     }
497     if (invJ) {invJ[0] = 1.0/J[0]; PetscLogFlops(1.0);}
498   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this segment is %d != 2", numCoords);
499   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
500   PetscFunctionReturn(0);
501 }
502 
503 #undef __FUNCT__
504 #define __FUNCT__ "DMPlexComputeTriangleGeometry_Internal"
505 static PetscErrorCode DMPlexComputeTriangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
506 {
507   PetscSection   coordSection;
508   Vec            coordinates;
509   PetscScalar   *coords = NULL;
510   PetscInt       numCoords, d, f, g;
511   PetscErrorCode ierr;
512 
513   PetscFunctionBegin;
514   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
515   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
516   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
517   *detJ = 0.0;
518   if (numCoords == 9) {
519     const PetscInt dim = 3;
520     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
521 
522     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
523     ierr = DMPlexComputeProjection3Dto2D_Internal(numCoords, coords, R);CHKERRQ(ierr);
524     if (J)    {
525       const PetscInt pdim = 2;
526 
527       for (d = 0; d < pdim; d++) {
528         for (f = 0; f < pdim; f++) {
529           J0[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
530         }
531       }
532       PetscLogFlops(8.0);
533       Det3D_Internal(detJ, J0);
534       for (d = 0; d < dim; d++) {
535         for (f = 0; f < dim; f++) {
536           J[d*dim+f] = 0.0;
537           for (g = 0; g < dim; g++) {
538             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
539           }
540         }
541       }
542       PetscLogFlops(18.0);
543     }
544     if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
545   } else if (numCoords == 6) {
546     const PetscInt dim = 2;
547 
548     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
549     if (J)    {
550       for (d = 0; d < dim; d++) {
551         for (f = 0; f < dim; f++) {
552           J[d*dim+f] = 0.5*(PetscRealPart(coords[(f+1)*dim+d]) - PetscRealPart(coords[0*dim+d]));
553         }
554       }
555       PetscLogFlops(8.0);
556       Det2D_Internal(detJ, J);
557     }
558     if (invJ) {Invert2D_Internal(invJ, J, *detJ);}
559   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this triangle is %d != 6", numCoords);
560   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
561   PetscFunctionReturn(0);
562 }
563 
564 #undef __FUNCT__
565 #define __FUNCT__ "DMPlexComputeRectangleGeometry_Internal"
566 static PetscErrorCode DMPlexComputeRectangleGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
567 {
568   PetscSection   coordSection;
569   Vec            coordinates;
570   PetscScalar   *coords = NULL;
571   PetscInt       numCoords, d, f, g;
572   PetscErrorCode ierr;
573 
574   PetscFunctionBegin;
575   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
576   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
577   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
578   *detJ = 0.0;
579   if (numCoords == 12) {
580     const PetscInt dim = 3;
581     PetscReal      R[9], J0[9] = {1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0};
582 
583     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
584     ierr = DMPlexComputeProjection3Dto2D_Internal(numCoords, coords, R);CHKERRQ(ierr);
585     if (J)    {
586       const PetscInt pdim = 2;
587 
588       for (d = 0; d < pdim; d++) {
589         J0[d*dim+0] = 0.5*(PetscRealPart(coords[1*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
590         J0[d*dim+1] = 0.5*(PetscRealPart(coords[3*pdim+d]) - PetscRealPart(coords[0*pdim+d]));
591       }
592       PetscLogFlops(8.0);
593       Det3D_Internal(detJ, J0);
594       for (d = 0; d < dim; d++) {
595         for (f = 0; f < dim; f++) {
596           J[d*dim+f] = 0.0;
597           for (g = 0; g < dim; g++) {
598             J[d*dim+f] += R[d*dim+g]*J0[g*dim+f];
599           }
600         }
601       }
602       PetscLogFlops(18.0);
603     }
604     if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
605   } else if (numCoords == 8) {
606     const PetscInt dim = 2;
607 
608     if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
609     if (J)    {
610       for (d = 0; d < dim; d++) {
611         J[d*dim+0] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
612         J[d*dim+1] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
613       }
614       PetscLogFlops(8.0);
615       Det2D_Internal(detJ, J);
616     }
617     if (invJ) {Invert2D_Internal(invJ, J, *detJ);}
618   } else SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "The number of coordinates for this quadrilateral is %d != 6", numCoords);
619   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, &numCoords, &coords);CHKERRQ(ierr);
620   PetscFunctionReturn(0);
621 }
622 
623 #undef __FUNCT__
624 #define __FUNCT__ "DMPlexComputeTetrahedronGeometry_Internal"
625 static PetscErrorCode DMPlexComputeTetrahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
626 {
627   PetscSection   coordSection;
628   Vec            coordinates;
629   PetscScalar   *coords = NULL;
630   const PetscInt dim = 3;
631   PetscInt       d;
632   PetscErrorCode ierr;
633 
634   PetscFunctionBegin;
635   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
636   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
637   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
638   *detJ = 0.0;
639   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
640   if (J)    {
641     for (d = 0; d < dim; d++) {
642       /* I orient with outward face normals */
643       J[d*dim+0] = 0.5*(PetscRealPart(coords[2*dim+d]) - PetscRealPart(coords[0*dim+d]));
644       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
645       J[d*dim+2] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
646     }
647     PetscLogFlops(18.0);
648     Det3D_Internal(detJ, J);
649   }
650   if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
651   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
652   PetscFunctionReturn(0);
653 }
654 
655 #undef __FUNCT__
656 #define __FUNCT__ "DMPlexComputeHexahedronGeometry_Internal"
657 static PetscErrorCode DMPlexComputeHexahedronGeometry_Internal(DM dm, PetscInt e, PetscReal v0[], PetscReal J[], PetscReal invJ[], PetscReal *detJ)
658 {
659   PetscSection   coordSection;
660   Vec            coordinates;
661   PetscScalar   *coords = NULL;
662   const PetscInt dim = 3;
663   PetscInt       d;
664   PetscErrorCode ierr;
665 
666   PetscFunctionBegin;
667   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
668   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
669   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
670   *detJ = 0.0;
671   if (v0)   {for (d = 0; d < dim; d++) v0[d] = PetscRealPart(coords[d]);}
672   if (J)    {
673     for (d = 0; d < dim; d++) {
674       J[d*dim+0] = 0.5*(PetscRealPart(coords[3*dim+d]) - PetscRealPart(coords[0*dim+d]));
675       J[d*dim+1] = 0.5*(PetscRealPart(coords[1*dim+d]) - PetscRealPart(coords[0*dim+d]));
676       J[d*dim+2] = 0.5*(PetscRealPart(coords[4*dim+d]) - PetscRealPart(coords[0*dim+d]));
677     }
678     PetscLogFlops(18.0);
679     Det3D_Internal(detJ, J);
680   }
681   if (invJ) {Invert3D_Internal(invJ, J, *detJ);}
682   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, e, NULL, &coords);CHKERRQ(ierr);
683   PetscFunctionReturn(0);
684 }
685 
686 #undef __FUNCT__
687 #define __FUNCT__ "DMPlexComputeCellGeometry"
688 /*@C
689   DMPlexComputeCellGeometry - Compute the Jacobian, inverse Jacobian, and Jacobian determinant for a given cell
690 
691   Collective on DM
692 
693   Input Arguments:
694 + dm   - the DM
695 - cell - the cell
696 
697   Output Arguments:
698 + v0   - the translation part of this affine transform
699 . J    - the Jacobian of the transform from the reference element
700 . invJ - the inverse of the Jacobian
701 - detJ - the Jacobian determinant
702 
703   Level: advanced
704 
705   Fortran Notes:
706   Since it returns arrays, this routine is only available in Fortran 90, and you must
707   include petsc.h90 in your code.
708 
709 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
710 @*/
711 PetscErrorCode DMPlexComputeCellGeometry(DM dm, PetscInt cell, PetscReal *v0, PetscReal *J, PetscReal *invJ, PetscReal *detJ)
712 {
713   PetscInt       depth, dim, coneSize;
714   PetscErrorCode ierr;
715 
716   PetscFunctionBegin;
717   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
718   ierr = DMPlexGetConeSize(dm, cell, &coneSize);CHKERRQ(ierr);
719   if (depth == 1) {
720     ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
721     switch (dim) {
722     case 1:
723       ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
724       break;
725     case 2:
726       switch (coneSize) {
727       case 3:
728         ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
729         break;
730       case 4:
731         ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
732         break;
733       default:
734         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
735       }
736       break;
737     case 3:
738       switch (coneSize) {
739       case 4:
740         ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
741         break;
742       case 8:
743         ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
744         break;
745       default:
746         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
747       }
748       break;
749     default:
750       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
751     }
752   } else {
753     /* We need to keep a pointer to the depth label */
754     ierr = DMPlexGetLabelValue(dm, "depth", cell, &dim);CHKERRQ(ierr);
755     /* Cone size is now the number of faces */
756     switch (dim) {
757     case 1:
758       ierr = DMPlexComputeLineGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
759       break;
760     case 2:
761       switch (coneSize) {
762       case 3:
763         ierr = DMPlexComputeTriangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
764         break;
765       case 4:
766         ierr = DMPlexComputeRectangleGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
767         break;
768       default:
769         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
770       }
771       break;
772     case 3:
773       switch (coneSize) {
774       case 4:
775         ierr = DMPlexComputeTetrahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
776         break;
777       case 6:
778         ierr = DMPlexComputeHexahedronGeometry_Internal(dm, cell, v0, J, invJ, detJ);CHKERRQ(ierr);
779         break;
780       default:
781         SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported number of vertices %D in cell %D for element geometry computation", coneSize, cell);
782       }
783       break;
784     default:
785       SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
786     }
787   }
788   PetscFunctionReturn(0);
789 }
790 
791 #undef __FUNCT__
792 #define __FUNCT__ "DMPlexComputeGeometryFVM_1D_Internal"
793 static PetscErrorCode DMPlexComputeGeometryFVM_1D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
794 {
795   PetscSection   coordSection;
796   Vec            coordinates;
797   PetscScalar   *coords = NULL;
798   PetscInt       coordSize;
799   PetscErrorCode ierr;
800 
801   PetscFunctionBegin;
802   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
803   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
804   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
805   if (dim != 2) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "We only support 2D edges right now");
806   if (centroid) {
807     centroid[0] = 0.5*PetscRealPart(coords[0] + coords[dim+0]);
808     centroid[1] = 0.5*PetscRealPart(coords[1] + coords[dim+1]);
809   }
810   if (normal) {
811     PetscReal norm;
812 
813     normal[0] = -PetscRealPart(coords[1] - coords[dim+1]);
814     normal[1] =  PetscRealPart(coords[0] - coords[dim+0]);
815     norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1]);
816     normal[0] /= norm;
817     normal[1] /= norm;
818   }
819   if (vol) {
820     *vol = PetscSqrtReal(PetscSqr(PetscRealPart(coords[0] - coords[dim+0])) + PetscSqr(PetscRealPart(coords[1] - coords[dim+1])));
821   }
822   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
823   PetscFunctionReturn(0);
824 }
825 
826 #undef __FUNCT__
827 #define __FUNCT__ "DMPlexComputeGeometryFVM_2D_Internal"
828 /* Centroid_i = (\sum_n A_n Cn_i ) / A */
829 static PetscErrorCode DMPlexComputeGeometryFVM_2D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
830 {
831   PetscSection   coordSection;
832   Vec            coordinates;
833   PetscScalar   *coords = NULL;
834   PetscReal      vsum = 0.0, csum[3] = {0.0, 0.0, 0.0}, vtmp, ctmp[4], v0[3], R[9];
835   PetscInt       tdim = 2, coordSize, numCorners, p, d, e;
836   PetscErrorCode ierr;
837 
838   PetscFunctionBegin;
839   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
840   ierr = DMPlexGetConeSize(dm, cell, &numCorners);CHKERRQ(ierr);
841   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
842   ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
843   dim  = coordSize/numCorners;
844   if (normal) {
845     if (dim > 2) {
846       const PetscReal x0 = PetscRealPart(coords[dim+0] - coords[0]), x1 = PetscRealPart(coords[dim*2+0] - coords[0]);
847       const PetscReal y0 = PetscRealPart(coords[dim+1] - coords[1]), y1 = PetscRealPart(coords[dim*2+1] - coords[1]);
848       const PetscReal z0 = PetscRealPart(coords[dim+2] - coords[2]), z1 = PetscRealPart(coords[dim*2+2] - coords[2]);
849       PetscReal       norm;
850 
851       v0[0]     = PetscRealPart(coords[0]);
852       v0[1]     = PetscRealPart(coords[1]);
853       v0[2]     = PetscRealPart(coords[2]);
854       normal[0] = y0*z1 - z0*y1;
855       normal[1] = z0*x1 - x0*z1;
856       normal[2] = x0*y1 - y0*x1;
857       norm = PetscSqrtReal(normal[0]*normal[0] + normal[1]*normal[1] + normal[2]*normal[2]);
858       normal[0] /= norm;
859       normal[1] /= norm;
860       normal[2] /= norm;
861     } else {
862       for (d = 0; d < dim; ++d) normal[d] = 0.0;
863     }
864   }
865   if (dim == 3) {ierr = DMPlexComputeProjection3Dto2D_Internal(coordSize, coords, R);CHKERRQ(ierr);}
866   for (p = 0; p < numCorners; ++p) {
867     /* Need to do this copy to get types right */
868     for (d = 0; d < tdim; ++d) {
869       ctmp[d]      = PetscRealPart(coords[p*tdim+d]);
870       ctmp[tdim+d] = PetscRealPart(coords[((p+1)%numCorners)*tdim+d]);
871     }
872     Volume_Triangle_Origin_Internal(&vtmp, ctmp);
873     vsum += vtmp;
874     for (d = 0; d < tdim; ++d) {
875       csum[d] += (ctmp[d] + ctmp[tdim+d])*vtmp;
876     }
877   }
878   for (d = 0; d < tdim; ++d) {
879     csum[d] /= (tdim+1)*vsum;
880   }
881   ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, cell, &coordSize, &coords);CHKERRQ(ierr);
882   if (vol) *vol = PetscAbsReal(vsum);
883   if (centroid) {
884     if (dim > 2) {
885       for (d = 0; d < dim; ++d) {
886         centroid[d] = v0[d];
887         for (e = 0; e < dim; ++e) {
888           centroid[d] += R[d*dim+e]*csum[e];
889         }
890       }
891     } else for (d = 0; d < dim; ++d) centroid[d] = csum[d];
892   }
893   PetscFunctionReturn(0);
894 }
895 
896 #undef __FUNCT__
897 #define __FUNCT__ "DMPlexComputeGeometryFVM_3D_Internal"
898 /* Centroid_i = (\sum_n V_n Cn_i ) / V */
899 static PetscErrorCode DMPlexComputeGeometryFVM_3D_Internal(DM dm, PetscInt dim, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
900 {
901   PetscSection    coordSection;
902   Vec             coordinates;
903   PetscScalar    *coords = NULL;
904   PetscReal       vsum = 0.0, vtmp, coordsTmp[3*3];
905   const PetscInt *faces, *facesO;
906   PetscInt        numFaces, f, coordSize, numCorners, p, d;
907   PetscErrorCode  ierr;
908 
909   PetscFunctionBegin;
910   ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
911   ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
912 
913   if (centroid) for (d = 0; d < dim; ++d) centroid[d] = 0.0;
914   ierr = DMPlexGetConeSize(dm, cell, &numFaces);CHKERRQ(ierr);
915   ierr = DMPlexGetCone(dm, cell, &faces);CHKERRQ(ierr);
916   ierr = DMPlexGetConeOrientation(dm, cell, &facesO);CHKERRQ(ierr);
917   for (f = 0; f < numFaces; ++f) {
918     ierr = DMPlexVecGetClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
919     numCorners = coordSize/dim;
920     switch (numCorners) {
921     case 3:
922       for (d = 0; d < dim; ++d) {
923         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
924         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
925         coordsTmp[2*dim+d] = PetscRealPart(coords[2*dim+d]);
926       }
927       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
928       if (facesO[f] < 0) vtmp = -vtmp;
929       vsum += vtmp;
930       if (centroid) {           /* Centroid of OABC = (a+b+c)/4 */
931         for (d = 0; d < dim; ++d) {
932           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
933         }
934       }
935       break;
936     case 4:
937       /* DO FOR PYRAMID */
938       /* First tet */
939       for (d = 0; d < dim; ++d) {
940         coordsTmp[0*dim+d] = PetscRealPart(coords[0*dim+d]);
941         coordsTmp[1*dim+d] = PetscRealPart(coords[1*dim+d]);
942         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
943       }
944       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
945       if (facesO[f] < 0) vtmp = -vtmp;
946       vsum += vtmp;
947       if (centroid) {
948         for (d = 0; d < dim; ++d) {
949           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
950         }
951       }
952       /* Second tet */
953       for (d = 0; d < dim; ++d) {
954         coordsTmp[0*dim+d] = PetscRealPart(coords[1*dim+d]);
955         coordsTmp[1*dim+d] = PetscRealPart(coords[2*dim+d]);
956         coordsTmp[2*dim+d] = PetscRealPart(coords[3*dim+d]);
957       }
958       Volume_Tetrahedron_Origin_Internal(&vtmp, coordsTmp);
959       if (facesO[f] < 0) vtmp = -vtmp;
960       vsum += vtmp;
961       if (centroid) {
962         for (d = 0; d < dim; ++d) {
963           for (p = 0; p < 3; ++p) centroid[d] += coordsTmp[p*dim+d]*vtmp;
964         }
965       }
966       break;
967     default:
968       SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot handle faces with %d vertices", numCorners);
969     }
970     ierr = DMPlexVecRestoreClosure(dm, coordSection, coordinates, faces[f], &coordSize, &coords);CHKERRQ(ierr);
971   }
972   if (vol)     *vol = PetscAbsReal(vsum);
973   if (normal)   for (d = 0; d < dim; ++d) normal[d]    = 0.0;
974   if (centroid) for (d = 0; d < dim; ++d) centroid[d] /= (vsum*4);
975   PetscFunctionReturn(0);
976 }
977 
978 #undef __FUNCT__
979 #define __FUNCT__ "DMPlexComputeCellGeometryFVM"
980 /*@C
981   DMPlexComputeCellGeometryFVM - Compute the volume for a given cell
982 
983   Collective on DM
984 
985   Input Arguments:
986 + dm   - the DM
987 - cell - the cell
988 
989   Output Arguments:
990 + volume   - the cell volume
991 . centroid - the cell centroid
992 - normal - the cell normal, if appropriate
993 
994   Level: advanced
995 
996   Fortran Notes:
997   Since it returns arrays, this routine is only available in Fortran 90, and you must
998   include petsc.h90 in your code.
999 
1000 .seealso: DMGetCoordinateSection(), DMGetCoordinateVec()
1001 @*/
1002 PetscErrorCode DMPlexComputeCellGeometryFVM(DM dm, PetscInt cell, PetscReal *vol, PetscReal centroid[], PetscReal normal[])
1003 {
1004   PetscInt       depth, dim;
1005   PetscErrorCode ierr;
1006 
1007   PetscFunctionBegin;
1008   ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
1009   ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
1010   if (depth != dim) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Mesh must be interpolated");
1011   /* We need to keep a pointer to the depth label */
1012   ierr = DMPlexGetLabelValue(dm, "depth", cell, &depth);CHKERRQ(ierr);
1013   /* Cone size is now the number of faces */
1014   switch (depth) {
1015   case 1:
1016     ierr = DMPlexComputeGeometryFVM_1D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1017     break;
1018   case 2:
1019     ierr = DMPlexComputeGeometryFVM_2D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1020     break;
1021   case 3:
1022     ierr = DMPlexComputeGeometryFVM_3D_Internal(dm, dim, cell, vol, centroid, normal);CHKERRQ(ierr);
1023     break;
1024   default:
1025     SETERRQ1(PetscObjectComm((PetscObject)dm), PETSC_ERR_SUP, "Unsupported dimension %D for element geometry computation", dim);
1026   }
1027   PetscFunctionReturn(0);
1028 }
1029