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firedrake_geometry.h
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firedrake_geometry.h
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/* --- Computation of Jacobian matrices --- */
/* Compute Jacobian J for interval embedded in R^1 */
#define compute_jacobian_interval_1d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0];
/* Compute Jacobian J for interval embedded in R^2 */
#define compute_jacobian_interval_2d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[3][0] - coordinate_dofs[2][0];
/* Compute Jacobian J for quad embedded in R^2 */
#define compute_jacobian_quad_2d(J, coordinate_dofs) \
J[0] = 0.5*(coordinate_dofs[2][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[1] = 0.5*(coordinate_dofs[1][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0]); \
J[2] = 0.5*(coordinate_dofs[6][0] + coordinate_dofs[7][0] - coordinate_dofs[4][0] - coordinate_dofs[5][0]); \
J[3] = 0.5*(coordinate_dofs[5][0] + coordinate_dofs[7][0] - coordinate_dofs[4][0] - coordinate_dofs[6][0]);
/* Compute Jacobian J for quad embedded in R^3 */
#define compute_jacobian_quad_3d(J, coordinate_dofs) \
J[0] = 0.5*(coordinate_dofs[2][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[1] = 0.5*(coordinate_dofs[1][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0]); \
J[2] = 0.5*(coordinate_dofs[6][0] + coordinate_dofs[7][0] - coordinate_dofs[4][0] - coordinate_dofs[5][0]); \
J[3] = 0.5*(coordinate_dofs[5][0] + coordinate_dofs[7][0] - coordinate_dofs[4][0] - coordinate_dofs[6][0]); \
J[4] = 0.5*(coordinate_dofs[10][0] + coordinate_dofs[11][0] - coordinate_dofs[8][0] - coordinate_dofs[9][0]); \
J[5] = 0.5*(coordinate_dofs[9][0] + coordinate_dofs[11][0] - coordinate_dofs[8][0] - coordinate_dofs[10][0]);
/* Compute Jacobian J for interval embedded in R^3 */
#define compute_jacobian_interval_3d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[3][0] - coordinate_dofs[2][0]; \
J[2] = coordinate_dofs[5][0] - coordinate_dofs[4][0];
/* Compute Jacobian J for triangle embedded in R^2 */
#define compute_jacobian_triangle_2d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[2][0] - coordinate_dofs[0][0]; \
J[2] = coordinate_dofs[4][0] - coordinate_dofs[3][0]; \
J[3] = coordinate_dofs[5][0] - coordinate_dofs[3][0];
/* Compute Jacobian J for triangle embedded in R^3 */
#define compute_jacobian_triangle_3d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[2][0] - coordinate_dofs[0][0]; \
J[2] = coordinate_dofs[4][0] - coordinate_dofs[3][0]; \
J[3] = coordinate_dofs[5][0] - coordinate_dofs[3][0]; \
J[4] = coordinate_dofs[7][0] - coordinate_dofs[6][0]; \
J[5] = coordinate_dofs[8][0] - coordinate_dofs[6][0];
/* Compute Jacobian J for tetrahedron embedded in R^3 */
#define compute_jacobian_tetrahedron_3d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1] [0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[2] [0] - coordinate_dofs[0][0]; \
J[2] = coordinate_dofs[3] [0] - coordinate_dofs[0][0]; \
J[3] = coordinate_dofs[5] [0] - coordinate_dofs[4][0]; \
J[4] = coordinate_dofs[6] [0] - coordinate_dofs[4][0]; \
J[5] = coordinate_dofs[7] [0] - coordinate_dofs[4][0]; \
J[6] = coordinate_dofs[9] [0] - coordinate_dofs[8][0]; \
J[7] = coordinate_dofs[10][0] - coordinate_dofs[8][0]; \
J[8] = coordinate_dofs[11][0] - coordinate_dofs[8][0];
/* Compute Jacobian J for tensor product prism embedded in R^3 */
/* Explanation: the CG1 x CG1 basis functions are, in order,
(1-X-Y)(1-Z), (1-X-Y)Z, X(1-Z), XZ, Y(1-Z), YZ. Each row of the
Jacobian is the derivatives of these w.r.t. X, Y and Z in turn,
evaluated at the midpoint (1/3, 1/3, 1/2). This gives the
coefficients below.*/
#define compute_jacobian_prism_3d(J, coordinate_dofs) \
J[0] = 0.5*(coordinate_dofs[2][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[1] = 0.5*(coordinate_dofs[4][0] + coordinate_dofs[5][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[2] = (coordinate_dofs[1][0] + coordinate_dofs[3][0] + coordinate_dofs[5][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0] - coordinate_dofs[4][0])/3.0; \
J[3] = 0.5*(coordinate_dofs[8][0] + coordinate_dofs[9][0] - coordinate_dofs[6][0] - coordinate_dofs[7][0]); \
J[4] = 0.5*(coordinate_dofs[10][0] + coordinate_dofs[11][0] - coordinate_dofs[6][0] - coordinate_dofs[7][0]); \
J[5] = (coordinate_dofs[7][0] + coordinate_dofs[9][0] + coordinate_dofs[11][0] - coordinate_dofs[6][0] - coordinate_dofs[8][0] - coordinate_dofs[10][0])/3.0; \
J[6] = 0.5*(coordinate_dofs[14][0] + coordinate_dofs[15][0] - coordinate_dofs[12][0] - coordinate_dofs[13][0]); \
J[7] = 0.5*(coordinate_dofs[16][0] + coordinate_dofs[17][0] - coordinate_dofs[12][0] - coordinate_dofs[13][0]); \
J[8] = (coordinate_dofs[13][0] + coordinate_dofs[15][0] + coordinate_dofs[17][0] - coordinate_dofs[12][0] - coordinate_dofs[14][0] - coordinate_dofs[16][0])/3.0;
/* Compute Jacobian J for tensor product hexahedron embedded in R^3 */
/* Explanation: the CG1 x CG1 basis functions are, in order, (1-X)(1-Y)(1-Z),
(1-X)(1-Y)Z, (1-X)Y(1-Z), (1-X)YZ, X(1-Y)(1-Z), X(1-Y)Z, XY(1-Z), XYZ.
Each row of the Jacobian is the derivatives of these w.r.t. X, Y and Z in turn,
evaluated at the midpoint (1/2, 1/2, 1/2). This gives the coefficients below. */
#define compute_jacobian_hex_3d(J, coordinate_dofs) \
J[0] = 0.25*(coordinate_dofs[4][0] + coordinate_dofs[5][0] + coordinate_dofs[6][0] + coordinate_dofs[7][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0] - coordinate_dofs[2][0] - coordinate_dofs[3][0]); \
J[1] = 0.25*(coordinate_dofs[2][0] + coordinate_dofs[3][0] + coordinate_dofs[6][0] + coordinate_dofs[7][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0] - coordinate_dofs[4][0] - coordinate_dofs[5][0]); \
J[2] = 0.25*(coordinate_dofs[1][0] + coordinate_dofs[3][0] + coordinate_dofs[5][0] + coordinate_dofs[7][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0] - coordinate_dofs[4][0] - coordinate_dofs[6][0]); \
J[3] = 0.25*(coordinate_dofs[12][0] + coordinate_dofs[13][0] + coordinate_dofs[14][0] + coordinate_dofs[15][0] - coordinate_dofs[8][0] - coordinate_dofs [9][0] - coordinate_dofs[10][0] - coordinate_dofs[11][0]); \
J[4] = 0.25*(coordinate_dofs[10][0] + coordinate_dofs[11][0] + coordinate_dofs[14][0] + coordinate_dofs[15][0] - coordinate_dofs[8][0] - coordinate_dofs [9][0] - coordinate_dofs[12][0] - coordinate_dofs[13][0]); \
J[5] = 0.25*(coordinate_dofs [9][0] + coordinate_dofs[11][0] + coordinate_dofs[13][0] + coordinate_dofs[15][0] - coordinate_dofs[8][0] - coordinate_dofs[10][0] - coordinate_dofs[12][0] - coordinate_dofs[14][0]); \
J[6] = 0.25*(coordinate_dofs[20][0] + coordinate_dofs[21][0] + coordinate_dofs[22][0] + coordinate_dofs[23][0] - coordinate_dofs[16][0] - coordinate_dofs[17][0] - coordinate_dofs[18][0] - coordinate_dofs[19][0]); \
J[7] = 0.25*(coordinate_dofs[18][0] + coordinate_dofs[19][0] + coordinate_dofs[22][0] + coordinate_dofs[23][0] - coordinate_dofs[16][0] - coordinate_dofs[17][0] - coordinate_dofs[20][0] - coordinate_dofs[21][0]); \
J[8] = 0.25*(coordinate_dofs[17][0] + coordinate_dofs[19][0] + coordinate_dofs[21][0] + coordinate_dofs[23][0] - coordinate_dofs[16][0] - coordinate_dofs[18][0] - coordinate_dofs[20][0] - coordinate_dofs[22][0]);
/* Jacobians for interior facets of different sorts */
/* Compute Jacobian J for interval embedded in R^1 */
#define compute_jacobian_interval_int_1d compute_jacobian_interval_1d
/* Compute Jacobian J for interval embedded in R^2 */
#define compute_jacobian_interval_int_2d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[5][0] - coordinate_dofs[4][0];
/* Compute Jacobian J for quad embedded in R^2 */
#define compute_jacobian_quad_int_2d(J, coordinate_dofs) \
J[0] = 0.5*(coordinate_dofs[2][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[1] = 0.5*(coordinate_dofs[1][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0]); \
J[2] = 0.5*(coordinate_dofs[10][0] + coordinate_dofs[11][0] - coordinate_dofs[8][0] - coordinate_dofs[9][0]); \
J[3] = 0.5*(coordinate_dofs[9][0] + coordinate_dofs[11][0] - coordinate_dofs[8][0] - coordinate_dofs[10][0]);
/* Compute Jacobian J for quad embedded in R^3 */
#define compute_jacobian_quad_int_3d(J, coordinate_dofs) \
J[0] = 0.5*(coordinate_dofs[2][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[1] = 0.5*(coordinate_dofs[1][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0]); \
J[2] = 0.5*(coordinate_dofs[10][0] + coordinate_dofs[11][0] - coordinate_dofs[8][0] - coordinate_dofs[9][0]); \
J[3] = 0.5*(coordinate_dofs[9][0] + coordinate_dofs[11][0] - coordinate_dofs[8][0] - coordinate_dofs[10][0]); \
J[4] = 0.5*(coordinate_dofs[18][0] + coordinate_dofs[19][0] - coordinate_dofs[16][0] - coordinate_dofs[17][0]); \
J[5] = 0.5*(coordinate_dofs[17][0] + coordinate_dofs[19][0] - coordinate_dofs[16][0] - coordinate_dofs[18][0]);
/* Compute Jacobian J for interval embedded in R^3 */
#define compute_jacobian_interval_int_3d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[5][0] - coordinate_dofs[4][0]; \
J[2] = coordinate_dofs[9][0] - coordinate_dofs[8][0];
/* Compute Jacobian J for triangle embedded in R^2 */
#define compute_jacobian_triangle_int_2d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1][0] - coordinate_dofs[0][0]; \
J[1] = coordinate_dofs[2][0] - coordinate_dofs[0][0]; \
J[2] = coordinate_dofs[7][0] - coordinate_dofs[6][0]; \
J[3] = coordinate_dofs[8][0] - coordinate_dofs[6][0];
/* Compute Jacobian J for triangle embedded in R^3 */
#define compute_jacobian_triangle_int_3d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1] [0] - coordinate_dofs[0] [0]; \
J[1] = coordinate_dofs[2] [0] - coordinate_dofs[0] [0]; \
J[2] = coordinate_dofs[7] [0] - coordinate_dofs[6] [0]; \
J[3] = coordinate_dofs[8] [0] - coordinate_dofs[6] [0]; \
J[4] = coordinate_dofs[13][0] - coordinate_dofs[12][0]; \
J[5] = coordinate_dofs[14][0] - coordinate_dofs[12][0];
/* Compute Jacobian J for tetrahedron embedded in R^3 */
#define compute_jacobian_tetrahedron_int_3d(J, coordinate_dofs) \
J[0] = coordinate_dofs[1] [0] - coordinate_dofs[0] [0]; \
J[1] = coordinate_dofs[2] [0] - coordinate_dofs[0] [0]; \
J[2] = coordinate_dofs[3] [0] - coordinate_dofs[0] [0]; \
J[3] = coordinate_dofs[9] [0] - coordinate_dofs[8] [0]; \
J[4] = coordinate_dofs[10][0] - coordinate_dofs[8] [0]; \
J[5] = coordinate_dofs[11][0] - coordinate_dofs[8] [0]; \
J[6] = coordinate_dofs[17][0] - coordinate_dofs[16][0]; \
J[7] = coordinate_dofs[18][0] - coordinate_dofs[16][0]; \
J[8] = coordinate_dofs[19][0] - coordinate_dofs[16][0];
/* Compute Jacobian J for tensor product prism embedded in R^3 */
#define compute_jacobian_prism_int_3d(J, coordinate_dofs) \
J[0] = 0.5*(coordinate_dofs[2][0] + coordinate_dofs[3][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[1] = 0.5*(coordinate_dofs[4][0] + coordinate_dofs[5][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0]); \
J[2] = (coordinate_dofs[1][0] + coordinate_dofs[3][0] + coordinate_dofs[5][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0] - coordinate_dofs[4][0])/3.0; \
J[3] = 0.5*(coordinate_dofs[14][0] + coordinate_dofs[15][0] - coordinate_dofs[12][0] - coordinate_dofs[13][0]); \
J[4] = 0.5*(coordinate_dofs[16][0] + coordinate_dofs[17][0] - coordinate_dofs[12][0] - coordinate_dofs[13][0]); \
J[5] = (coordinate_dofs[13][0] + coordinate_dofs[15][0] + coordinate_dofs[17][0] - coordinate_dofs[12][0] - coordinate_dofs[14][0] - coordinate_dofs[16][0])/3.0; \
J[6] = 0.5*(coordinate_dofs[26][0] + coordinate_dofs[27][0] - coordinate_dofs[24][0] - coordinate_dofs[25][0]); \
J[7] = 0.5*(coordinate_dofs[28][0] + coordinate_dofs[29][0] - coordinate_dofs[24][0] - coordinate_dofs[25][0]); \
J[8] = (coordinate_dofs[25][0] + coordinate_dofs[27][0] + coordinate_dofs[29][0] - coordinate_dofs[24][0] - coordinate_dofs[26][0] - coordinate_dofs[28][0])/3.0;
/* Compute Jacobian J for tensor product hexahedron embedded in R^3 */
#define compute_jacobian_hex_int_3d(J, coordinate_dofs) \
J[0] = 0.25*(coordinate_dofs[4][0] + coordinate_dofs[5][0] + coordinate_dofs[6][0] + coordinate_dofs[7][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0] - coordinate_dofs[2][0] - coordinate_dofs[3][0]); \
J[1] = 0.25*(coordinate_dofs[2][0] + coordinate_dofs[3][0] + coordinate_dofs[6][0] + coordinate_dofs[7][0] - coordinate_dofs[0][0] - coordinate_dofs[1][0] - coordinate_dofs[4][0] - coordinate_dofs[5][0]); \
J[2] = 0.25*(coordinate_dofs[1][0] + coordinate_dofs[3][0] + coordinate_dofs[5][0] + coordinate_dofs[7][0] - coordinate_dofs[0][0] - coordinate_dofs[2][0] - coordinate_dofs[4][0] - coordinate_dofs[6][0]); \
J[3] = 0.25*(coordinate_dofs[20][0] + coordinate_dofs[21][0] + coordinate_dofs[22][0] + coordinate_dofs[23][0] - coordinate_dofs[16][0] - coordinate_dofs[17][0] - coordinate_dofs[18][0] - coordinate_dofs[19][0]); \
J[4] = 0.25*(coordinate_dofs[18][0] + coordinate_dofs[19][0] + coordinate_dofs[22][0] + coordinate_dofs[23][0] - coordinate_dofs[16][0] - coordinate_dofs[17][0] - coordinate_dofs[20][0] - coordinate_dofs[21][0]); \
J[5] = 0.25*(coordinate_dofs[17][0] + coordinate_dofs[19][0] + coordinate_dofs[21][0] + coordinate_dofs[23][0] - coordinate_dofs[16][0] - coordinate_dofs[18][0] - coordinate_dofs[20][0] - coordinate_dofs[22][0]); \
J[6] = 0.25*(coordinate_dofs[36][0] + coordinate_dofs[37][0] + coordinate_dofs[38][0] + coordinate_dofs[39][0] - coordinate_dofs[32][0] - coordinate_dofs[33][0] - coordinate_dofs[34][0] - coordinate_dofs[35][0]); \
J[7] = 0.25*(coordinate_dofs[34][0] + coordinate_dofs[35][0] + coordinate_dofs[38][0] + coordinate_dofs[39][0] - coordinate_dofs[32][0] - coordinate_dofs[33][0] - coordinate_dofs[36][0] - coordinate_dofs[37][0]); \
J[8] = 0.25*(coordinate_dofs[33][0] + coordinate_dofs[35][0] + coordinate_dofs[37][0] + coordinate_dofs[39][0] - coordinate_dofs[32][0] - coordinate_dofs[34][0] - coordinate_dofs[36][0] - coordinate_dofs[38][0]);
/* --- Computation of Jacobian inverses --- */
/* Compute Jacobian inverse K for interval embedded in R^1 */
#define compute_jacobian_inverse_interval_1d(K, det, J) \
det = J[0]; \
K[0] = 1.0 / det;
/* Compute Jacobian (pseudo)inverse K for interval embedded in R^2 */
#define compute_jacobian_inverse_interval_2d(K, det, J) \
do { const double det2 = J[0]*J[0] + J[1]*J[1]; \
det = sqrt(det2); \
K[0] = J[0] / det2; \
K[1] = J[1] / det2; } while (0)
/* Compute Jacobian (pseudo)inverse K for interval embedded in R^3 */
#define compute_jacobian_inverse_interval_3d(K, det, J) \
do { const double det2 = J[0]*J[0] + J[1]*J[1] + J[2]*J[2]; \
det = sqrt(det2); \
K[0] = J[0] / det2; \
K[1] = J[1] / det2; \
K[2] = J[2] / det2; } while (0)
/* Compute Jacobian inverse K for triangle embedded in R^2 */
#define compute_jacobian_inverse_triangle_2d(K, det, J) \
det = J[0]*J[3] - J[1]*J[2]; \
K[0] = J[3] / det; \
K[1] = -J[1] / det; \
K[2] = -J[2] / det; \
K[3] = J[0] / det;
/* Compute Jacobian (pseudo)inverse K for triangle embedded in R^3 */
#define compute_jacobian_inverse_triangle_3d(K, det, J) \
do { const double d_0 = J[2]*J[5] - J[4]*J[3]; \
const double d_1 = J[4]*J[1] - J[0]*J[5]; \
const double d_2 = J[0]*J[3] - J[2]*J[1]; \
const double c_0 = J[0]*J[0] + J[2]*J[2] + J[4]*J[4]; \
const double c_1 = J[1]*J[1] + J[3]*J[3] + J[5]*J[5]; \
const double c_2 = J[0]*J[1] + J[2]*J[3] + J[4]*J[5]; \
const double den = c_0*c_1 - c_2*c_2; \
const double det2 = d_0*d_0 + d_1*d_1 + d_2*d_2; \
det = sqrt(det2); \
K[0] = (J[0]*c_1 - J[1]*c_2) / den; \
K[1] = (J[2]*c_1 - J[3]*c_2) / den; \
K[2] = (J[4]*c_1 - J[5]*c_2) / den; \
K[3] = (J[1]*c_0 - J[0]*c_2) / den; \
K[4] = (J[3]*c_0 - J[2]*c_2) / den; \
K[5] = (J[5]*c_0 - J[4]*c_2) / den; } while (0)
/* Compute Jacobian (pseudo)inverse K for quad embedded in R^2 */
#define compute_jacobian_inverse_quad_2d compute_jacobian_inverse_triangle_2d
/* Compute Jacobian (pseudo)inverse K for quad embedded in R^3 */
#define compute_jacobian_inverse_quad_3d compute_jacobian_inverse_triangle_3d
/* Compute Jacobian inverse K for tetrahedron embedded in R^3 */
#define compute_jacobian_inverse_tetrahedron_3d(K, det, J) \
do { const double d_00 = J[4]*J[8] - J[5]*J[7]; \
const double d_01 = J[5]*J[6] - J[3]*J[8]; \
const double d_02 = J[3]*J[7] - J[4]*J[6]; \
const double d_10 = J[2]*J[7] - J[1]*J[8]; \
const double d_11 = J[0]*J[8] - J[2]*J[6]; \
const double d_12 = J[1]*J[6] - J[0]*J[7]; \
const double d_20 = J[1]*J[5] - J[2]*J[4]; \
const double d_21 = J[2]*J[3] - J[0]*J[5]; \
const double d_22 = J[0]*J[4] - J[1]*J[3]; \
det = J[0]*d_00 + J[3]*d_10 + J[6]*d_20; \
K[0] = d_00 / det; \
K[1] = d_10 / det; \
K[2] = d_20 / det; \
K[3] = d_01 / det; \
K[4] = d_11 / det; \
K[5] = d_21 / det; \
K[6] = d_02 / det; \
K[7] = d_12 / det; \
K[8] = d_22 / det; } while(0)
/* Compute Jacobian inverse K for tensor product prism embedded in R^3 - identical to tetrahedron */
#define compute_jacobian_inverse_prism_3d compute_jacobian_inverse_tetrahedron_3d
/* Compute Jacobian inverse K for tensor product hexahedron embedded in R^3 - identical to tetrahedron */
#define compute_jacobian_inverse_hex_3d compute_jacobian_inverse_tetrahedron_3d
/* --- Compute facet edge lengths --- */
#define compute_facet_edge_length_tetrahedron_3d(facet, coordinate_dofs) \
const unsigned int tetrahedron_facet_edge_vertices[4][3][2] = { \
{{2, 3}, {1, 3}, {1, 2}}, \
{{2, 3}, {0, 3}, {0, 2}}, \
{{1, 3}, {0, 3}, {0, 1}}, \
{{1, 2}, {0, 2}, {0, 1}}, \
}; \
double edge_lengths_sqr[3]; \
for (unsigned int edge = 0; edge < 3; ++edge) \
{ \
const unsigned int vertex0 = tetrahedron_facet_edge_vertices[facet][edge][0]; \
const unsigned int vertex1 = tetrahedron_facet_edge_vertices[facet][edge][1]; \
edge_lengths_sqr[edge] = (coordinate_dofs[vertex1 + 0][0] - coordinate_dofs[vertex0 + 0][0])*(coordinate_dofs[vertex1 + 0][0] - coordinate_dofs[vertex0 + 0][0]) \
+ (coordinate_dofs[vertex1 + 4][0] - coordinate_dofs[vertex0 + 4][0])*(coordinate_dofs[vertex1 + 4][0] - coordinate_dofs[vertex0 + 4][0]) \
+ (coordinate_dofs[vertex1 + 8][0] - coordinate_dofs[vertex0 + 8][0])*(coordinate_dofs[vertex1 + 8][0] - coordinate_dofs[vertex0 + 8][0]); \
}
/* Compute min edge length in facet of tetrahedron embedded in R^3 */
#define compute_min_facet_edge_length_tetrahedron_3d(min_edge_length, facet, coordinate_dofs) \
compute_facet_edge_length_tetrahedron_3d(facet, coordinate_dofs); \
min_edge_length = sqrt(fmin(fmin(edge_lengths_sqr[1], edge_lengths_sqr[1]), edge_lengths_sqr[2]));
/* Compute max edge length in facet of tetrahedron embedded in R^3 */
/*
* FIXME: we can't call compute_facet_edge_length_tetrahedron_3d again, so we
* rely on the fact that max is always computed after min
*/
#define compute_max_facet_edge_length_tetrahedron_3d(max_edge_length, facet, coordinate_dofs) \
max_edge_length = sqrt(fmax(fmax(edge_lengths_sqr[1], edge_lengths_sqr[1]), edge_lengths_sqr[2]));