/usr/include/ufc_geometry.h is in ufc 2.3.0-1.
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// This code is released into the public domain.
//
// The FEniCS Project (http://www.fenicsproject.org/) 2013.
#ifndef __UFC_GEOMETRY_H
#define __UFC_GEOMETRY_H
#include <cmath>
/// A note regarding data structures. All matrices are represented as
/// row-major flattened raw C++ arrays. Benchmarks indicate that when
/// optimization (-O1 and up) is used, the following conditions hold:
///
/// 1. std::vector is just as fast as raw C++ arrays for indexing.
///
/// 2. Flattened arrays are twice as fast as nested arrays, both for
/// std:vector and raw C++ arrays.
///
/// 3. Defining an array by 'std::vector<double> x(n)', where n is a
/// literal, leads to dynamic allocation and results in significant
/// slowdowns compared to the definition 'double x[n]'.
///
/// The conclusion is that we should use flattened raw C++ arrays in
/// the interfaces for these utility functions, since some of the
/// arrays passed to these functions (in particular Jacobians) are
/// created inside the generated functions (tabulate_tensor). Note
/// that an std::vector x may also be passed as raw pointer by &x[0].
// TODO: Should signatures of compute_<foo>_<cell>_<n>d match for each foo?
// On one hand the snippets use different quantities, on the other
// some consistency is nice to simplify the code generation.
// Currently only the arguments that are actually used are included.
// TODO: Split this header into smaller files ufc_geometry_<cell>.h or ufc_geometry_<cell>_<n>d.h?
/// --- Local reference cell entity relations by UFC conventions ---
static const unsigned int interval_facet_vertices[2][2] = {{0}, {1}};
static const unsigned int triangle_facet_vertices[3][2] = {{1, 2}, {0, 2}, {0, 1}};
static const unsigned int tetrahedron_facet_vertices[4][3] = {{1, 2, 3}, {0, 2, 3}, {0, 1, 3}, {0, 1, 2}};
static 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}},
};
///--- Computation of Jacobian matrices ---
/// Compute Jacobian J for interval embedded in R^1
inline void compute_jacobian_interval_1d(double J[1],
const double vertex_coordinates[2])
{
J[0] = vertex_coordinates[1] - vertex_coordinates[0];
}
/// Compute Jacobian J for interval embedded in R^2
inline void compute_jacobian_interval_2d(double J[2],
const double vertex_coordinates[4])
{
J[0] = vertex_coordinates[2] - vertex_coordinates[0];
J[1] = vertex_coordinates[3] - vertex_coordinates[1];
}
/// Compute Jacobian J for interval embedded in R^3
inline void compute_jacobian_interval_3d(double J[3],
const double vertex_coordinates[6])
{
J[0] = vertex_coordinates[3] - vertex_coordinates[0];
J[1] = vertex_coordinates[4] - vertex_coordinates[1];
J[2] = vertex_coordinates[5] - vertex_coordinates[2];
}
/// Compute Jacobian J for triangle embedded in R^2
inline void compute_jacobian_triangle_2d(double J[4],
const double vertex_coordinates[6])
{
J[0] = vertex_coordinates[2] - vertex_coordinates[0];
J[1] = vertex_coordinates[4] - vertex_coordinates[0];
J[2] = vertex_coordinates[3] - vertex_coordinates[1];
J[3] = vertex_coordinates[5] - vertex_coordinates[1];
}
/// Compute Jacobian J for triangle embedded in R^3
inline void compute_jacobian_triangle_3d(double J[6],
const double vertex_coordinates[9])
{
J[0] = vertex_coordinates[3] - vertex_coordinates[0];
J[1] = vertex_coordinates[6] - vertex_coordinates[0];
J[2] = vertex_coordinates[4] - vertex_coordinates[1];
J[3] = vertex_coordinates[7] - vertex_coordinates[1];
J[4] = vertex_coordinates[5] - vertex_coordinates[2];
J[5] = vertex_coordinates[8] - vertex_coordinates[2];
}
/// Compute Jacobian J for tetrahedron embedded in R^3
inline void compute_jacobian_tetrahedron_3d(double J[9],
const double vertex_coordinates[12])
{
J[0] = vertex_coordinates[3] - vertex_coordinates[0];
J[1] = vertex_coordinates[6] - vertex_coordinates[0];
J[2] = vertex_coordinates[9] - vertex_coordinates[0];
J[3] = vertex_coordinates[4] - vertex_coordinates[1];
J[4] = vertex_coordinates[7] - vertex_coordinates[1];
J[5] = vertex_coordinates[10] - vertex_coordinates[1];
J[6] = vertex_coordinates[5] - vertex_coordinates[2];
J[7] = vertex_coordinates[8] - vertex_coordinates[2];
J[8] = vertex_coordinates[11] - vertex_coordinates[2];
}
//--- Computation of Jacobian inverses --- // TODO: Remove this when ffc is updated to use the NEW ones below
/// Compute Jacobian inverse K for interval embedded in R^1
inline void compute_jacobian_inverse_interval_1d(double* K,
double& det,
const double* J)
{
det = J[0];
K[0] = 1.0 / det;
}
/// Compute Jacobian (pseudo)inverse K for interval embedded in R^2
inline void compute_jacobian_inverse_interval_2d(double* K,
double& det,
const double* J)
{
const double det2 = J[0]*J[0] + J[1]*J[1];
det = std::sqrt(det2);
K[0] = J[0] / det2;
K[1] = J[1] / det2;
}
/// Compute Jacobian (pseudo)inverse K for interval embedded in R^3
inline void compute_jacobian_inverse_interval_3d(double* K,
double& det,
const double* J)
{
// TODO: Move computation of det to a separate function, det is often needed when K is not
const double det2 = J[0]*J[0] + J[1]*J[1] + J[2]*J[2];
det = std::sqrt(det2);
K[0] = J[0] / det2;
K[1] = J[1] / det2;
K[2] = J[2] / det2;
}
/// Compute Jacobian inverse K for triangle embedded in R^2
inline void compute_jacobian_inverse_triangle_2d(double* K,
double& det,
const double* 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
inline void compute_jacobian_inverse_triangle_3d(double* K,
double& det,
const double* J)
{
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 = std::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;
}
/// Compute Jacobian inverse K for tetrahedron embedded in R^3
inline void compute_jacobian_inverse_tetrahedron_3d(double* K,
double& det,
const double* J)
{
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;
}
//--- NEW Computation of Jacobian (sub)determinants ---
/// Compute Jacobian determinant for interval embedded in R^1
inline void compute_jacobian_determinants_interval_1d(double & det,
const double J[1])
{
det = J[0];
}
/// Compute Jacobian (pseudo)determinants for interval embedded in R^2
inline void compute_jacobian_determinants_interval_2d(double & det2,
double & det,
const double J[2])
{
det2 = J[0]*J[0] + J[1]*J[1];
det = std::sqrt(det2);
}
/// Compute Jacobian (pseudo)determinants for interval embedded in R^3
inline void compute_jacobian_determinants_interval_3d(double & det2,
double & det,
const double J[3])
{
det2 = J[0]*J[0] + J[1]*J[1] + J[2]*J[2];
det = std::sqrt(det2);
}
/// Compute Jacobian determinant for triangle embedded in R^2
inline void compute_jacobian_determinants_triangle_2d(double & det,
const double J[4])
{
det = J[0]*J[3] - J[1]*J[2];
}
/// Compute Jacobian (pseudo)determinants for triangle embedded in R^3
inline void compute_jacobian_determinants_triangle_3d(double & den,
double & det2,
double & det,
double c[3],
const double J[6])
{
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];
c[0] = J[0]*J[0] + J[2]*J[2] + J[4]*J[4];
c[1] = J[1]*J[1] + J[3]*J[3] + J[5]*J[5];
c[2] = J[0]*J[1] + J[2]*J[3] + J[4]*J[5];
den = c[0]*c[1] - c[2]*c[2];
det2 = d_0*d_0 + d_1*d_1 + d_2*d_2;
det = std::sqrt(det2);
}
/// Compute Jacobian determinants for tetrahedron embedded in R^3
inline void compute_jacobian_determinants_tetrahedron_3d(double & det,
double d[9],
const double J[9])
{
d[0*3 + 0] = J[4]*J[8] - J[5]*J[7];
d[0*3 + 1] = J[5]*J[6] - J[3]*J[8];
d[0*3 + 2] = J[3]*J[7] - J[4]*J[6];
d[1*3 + 0] = J[2]*J[7] - J[1]*J[8];
d[1*3 + 1] = J[0]*J[8] - J[2]*J[6];
d[1*3 + 2] = J[1]*J[6] - J[0]*J[7];
d[2*3 + 0] = J[1]*J[5] - J[2]*J[4];
d[2*3 + 1] = J[2]*J[3] - J[0]*J[5];
d[2*3 + 2] = J[0]*J[4] - J[1]*J[3];
det = J[0]*d[0*3 + 0] + J[3]*d[1*3 + 0] + J[6]*d[2*3 + 0];
}
//--- NEW Computation of Jacobian inverses ---
/// Compute Jacobian inverse K for interval embedded in R^1
inline void new_compute_jacobian_inverse_interval_1d(double K[1],
double det)
{
K[0] = 1.0 / det;
}
/// Compute Jacobian (pseudo)inverse K for interval embedded in R^2
inline void new_compute_jacobian_inverse_interval_2d(double K[2],
double det2,
const double J[2])
{
K[0] = J[0] / det2;
K[1] = J[1] / det2;
}
/// Compute Jacobian (pseudo)inverse K for interval embedded in R^3
inline void new_compute_jacobian_inverse_interval_3d(double K[3],
double det2,
const double J[3])
{
K[0] = J[0] / det2;
K[1] = J[1] / det2;
K[2] = J[2] / det2;
}
/// Compute Jacobian inverse K for triangle embedded in R^2
inline void new_compute_jacobian_inverse_triangle_2d(double K[4],
double det,
const double J[4])
{
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
inline void new_compute_jacobian_inverse_triangle_3d(double K[6],
double den,
const double c[3],
const double J[6])
{
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;
}
/// Compute Jacobian inverse K for tetrahedron embedded in R^3
inline void new_compute_jacobian_inverse_tetrahedron_3d(double K[9],
double det,
const double d[9])
{
K[0] = d[0*3 + 0] / det;
K[1] = d[1*3 + 0] / det;
K[2] = d[2*3 + 0] / det;
K[3] = d[0*3 + 1] / det;
K[4] = d[1*3 + 1] / det;
K[5] = d[2*3 + 1] / det;
K[6] = d[0*3 + 2] / det;
K[7] = d[1*3 + 2] / det;
K[8] = d[2*3 + 2] / det;
}
// --- Computation of edge, face, facet scaling factors
/// Compute edge scaling factors for triangle embedded in R^2
inline void compute_edge_scaling_factors_triangle_2d(double dx[2],
const double vertex_coordinates[6],
std::size_t facet)
{
// Get vertices on edge
const unsigned int v0 = triangle_facet_vertices[facet][0];
const unsigned int v1 = triangle_facet_vertices[facet][1];
// Compute scale factor (length of edge scaled by length of reference interval)
dx[0] = vertex_coordinates[2*v1 + 0] - vertex_coordinates[2*v0 + 0];
dx[1] = vertex_coordinates[2*v1 + 1] - vertex_coordinates[2*v0 + 1];
}
/// Compute facet scaling factor for triangle embedded in R^2
inline void compute_facet_scaling_factor_triangle_2d(double & det,
const double dx[2])
{
det = std::sqrt(dx[0]*dx[0] + dx[1]*dx[1]);
}
/// Compute edge scaling factors for triangle embedded in R^3
inline void compute_edge_scaling_factors_triangle_3d(double dx[3],
const double vertex_coordinates[9],
std::size_t facet)
{
// Get vertices on edge
const unsigned int v0 = triangle_facet_vertices[facet][0];
const unsigned int v1 = triangle_facet_vertices[facet][1];
// Compute scale factor (length of edge scaled by length of reference interval)
dx[0] = vertex_coordinates[3*v1 + 0] - vertex_coordinates[3*v0 + 0];
dx[1] = vertex_coordinates[3*v1 + 1] - vertex_coordinates[3*v0 + 1];
dx[2] = vertex_coordinates[3*v1 + 2] - vertex_coordinates[3*v0 + 2];
}
/// Compute facet scaling factor for triangle embedded in R^3
inline void compute_facet_scaling_factor_triangle_3d(double & det,
const double dx[3])
{
det = std::sqrt(dx[0]*dx[0] + dx[1]*dx[1] + dx[2]*dx[2]);
}
/// Compute face scaling factors for tetrahedron embedded in R^3
inline void compute_face_scaling_factors_tetrahedron_3d(double a[3],
const double vertex_coordinates[12],
std::size_t facet)
{
// Get vertices on face
const unsigned int v0 = tetrahedron_facet_vertices[facet][0];
const unsigned int v1 = tetrahedron_facet_vertices[facet][1];
const unsigned int v2 = tetrahedron_facet_vertices[facet][2];
// Compute scale factor (area of face scaled by area of reference triangle)
a[0] = (vertex_coordinates[3*v0 + 1]*vertex_coordinates[3*v1 + 2] +
vertex_coordinates[3*v0 + 2]*vertex_coordinates[3*v2 + 1] +
vertex_coordinates[3*v1 + 1]*vertex_coordinates[3*v2 + 2]) -
(vertex_coordinates[3*v2 + 1]*vertex_coordinates[3*v1 + 2] +
vertex_coordinates[3*v2 + 2]*vertex_coordinates[3*v0 + 1] +
vertex_coordinates[3*v1 + 1]*vertex_coordinates[3*v0 + 2]);
a[1] = (vertex_coordinates[3*v0 + 2]*vertex_coordinates[3*v1 + 0] +
vertex_coordinates[3*v0 + 0]*vertex_coordinates[3*v2 + 2] +
vertex_coordinates[3*v1 + 2]*vertex_coordinates[3*v2 + 0]) -
(vertex_coordinates[3*v2 + 2]*vertex_coordinates[3*v1 + 0] +
vertex_coordinates[3*v2 + 0]*vertex_coordinates[3*v0 + 2] +
vertex_coordinates[3*v1 + 2]*vertex_coordinates[3*v0 + 0]);
a[2] = (vertex_coordinates[3*v0 + 0]*vertex_coordinates[3*v1 + 1] +
vertex_coordinates[3*v0 + 1]*vertex_coordinates[3*v2 + 0] +
vertex_coordinates[3*v1 + 0]*vertex_coordinates[3*v2 + 1]) -
(vertex_coordinates[3*v2 + 0]*vertex_coordinates[3*v1 + 1] +
vertex_coordinates[3*v2 + 1]*vertex_coordinates[3*v0 + 0] +
vertex_coordinates[3*v1 + 0]*vertex_coordinates[3*v0 + 1]);
}
/// Compute facet scaling factor for tetrahedron embedded in R^3
inline void compute_facet_scaling_factor_tetrahedron_3d(double & det,
const double a[3])
{
det = std::sqrt(a[0]*a[0] + a[1]*a[1] + a[2]*a[2]);
}
///--- Compute facet normal directions ---
/// Compute facet direction for interval embedded in R^1
inline void compute_facet_normal_direction_interval_1d(bool & direction,
const double vertex_coordinates[2],
std::size_t facet)
{
direction = facet == 0
? vertex_coordinates[0] > vertex_coordinates[1]
: vertex_coordinates[1] > vertex_coordinates[0];
}
/// Compute facet direction for triangle embedded in R^2
inline void compute_facet_normal_direction_triangle_2d(bool & direction,
const double vertex_coordinates[6],
const double dx[2],
std::size_t facet)
{
const unsigned int v0 = triangle_facet_vertices[facet][0];
direction = dx[1]*(vertex_coordinates[2*facet ] - vertex_coordinates[2*v0 ])
- dx[0]*(vertex_coordinates[2*facet + 1] - vertex_coordinates[2*v0 + 1])
< 0;
}
/// Compute facet direction for tetrahedron embedded in R^3
inline void compute_facet_normal_direction_tetrahedron_3d(bool & direction,
const double vertex_coordinates[9],
const double a[3],
std::size_t facet)
{
const unsigned int v0 = tetrahedron_facet_vertices[facet][0];
direction = a[0]*(vertex_coordinates[3*facet ] - vertex_coordinates[3*v0 ])
+ a[1]*(vertex_coordinates[3*facet + 1] - vertex_coordinates[3*v0 + 1])
+ a[2]*(vertex_coordinates[3*facet + 2] - vertex_coordinates[3*v0 + 2])
< 0;
}
///--- Compute facet normal vectors ---
/// Compute facet normal for interval embedded in R^1
inline void compute_facet_normal_interval_1d(double n[1],
bool direction)
{
// Facet normals are 1.0 or -1.0: (-1.0) <-- X------X --> (1.0)
n[0] = direction ? 1.0 : -1.0;
}
/// Compute facet normal for interval embedded in R^2
inline void compute_facet_normal_interval_2d(double n[2],
const double vertex_coordinates[4],
std::size_t facet)
{
if (facet == 0)
{
n[0] = vertex_coordinates[0] - vertex_coordinates[2];
n[1] = vertex_coordinates[1] - vertex_coordinates[3];
}
else
{
n[0] = vertex_coordinates[2] - vertex_coordinates[0];
n[1] = vertex_coordinates[3] - vertex_coordinates[1];
}
const double n_length = std::sqrt(n[0]*n[0] + n[1]*n[1]);
n[0] /= n_length;
n[1] /= n_length;
}
/// Compute facet normal for interval embedded in R^3
inline void compute_facet_normal_interval_3d(double n[3],
const double vertex_coordinates[6],
std::size_t facet)
{
if (facet == 0)
{
n[0] = vertex_coordinates[0] - vertex_coordinates[3];
n[1] = vertex_coordinates[1] - vertex_coordinates[4];
n[1] = vertex_coordinates[2] - vertex_coordinates[5];
}
else
{
n[0] = vertex_coordinates[3] - vertex_coordinates[0];
n[1] = vertex_coordinates[4] - vertex_coordinates[1];
n[1] = vertex_coordinates[5] - vertex_coordinates[2];
}
const double n_length = std::sqrt(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
n[0] /= n_length;
n[1] /= n_length;
n[2] /= n_length;
}
/// Compute facet normal for triangle embedded in R^2
inline void compute_facet_normal_triangle_2d(double n[2],
const double dx[2],
const double det,
bool direction)
{
// Compute facet normals from the facet scale factor constants
n[0] = direction ? dx[1] / det : -dx[1] / det;
n[1] = direction ? -dx[0] / det : dx[0] / det;
}
/// Compute facet normal for triangle embedded in R^3
inline void compute_facet_normal_triangle_3d(double n[3],
const double vertex_coordinates[6],
std::size_t facet)
{
// Compute facet normal for triangles in 3D
const unsigned int vertex0 = facet;
// Get coordinates corresponding the vertex opposite this
const unsigned int vertex1 = triangle_facet_vertices[facet][0];
const unsigned int vertex2 = triangle_facet_vertices[facet][1];
// Define vectors n = (p2 - p0) and t = normalized (p2 - p1)
n[0] = vertex_coordinates[3*vertex2 + 0] - vertex_coordinates[3*vertex0 + 0];
n[1] = vertex_coordinates[3*vertex2 + 1] - vertex_coordinates[3*vertex0 + 1];
n[2] = vertex_coordinates[3*vertex2 + 2] - vertex_coordinates[3*vertex0 + 2];
double t0 = vertex_coordinates[3*vertex2 + 0] - vertex_coordinates[3*vertex1 + 0];
double t1 = vertex_coordinates[3*vertex2 + 1] - vertex_coordinates[3*vertex1 + 1];
double t2 = vertex_coordinates[3*vertex2 + 2] - vertex_coordinates[3*vertex1 + 2];
const double t_length = std::sqrt(t0*t0 + t1*t1 + t2*t2);
t0 /= t_length;
t1 /= t_length;
t2 /= t_length;
// Subtract, the projection of (p2 - p0) onto (p2 - p1), from (p2 - p0)
const double ndott = t0*n[0] + t1*n[1] + t2*n[2];
n[0] -= ndott*t0;
n[1] -= ndott*t1;
n[2] -= ndott*t2;
const double n_length = std::sqrt(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
// Normalize
n[0] /= n_length;
n[1] /= n_length;
n[2] /= n_length;
}
/// Compute facet normal for tetrahedron embedded in R^3
inline void compute_facet_normal_tetrahedron_3d(double n[3],
const double a[3],
const double det,
bool direction)
{
// Compute facet normals from the facet scale factor constants
n[0] = direction ? a[0] / det : -a[0] / det;
n[1] = direction ? a[1] / det : -a[1] / det;
n[2] = direction ? a[2] / det : -a[2] / det;
}
///--- Compute circumradius ---
/// Compute circumradius for interval embedded in R^1
inline void compute_circumradius_interval_1d(double & circumradius,
double volume)
{
// Compute circumradius; in 1D it is equal to half the cell length
circumradius = volume / 2.0;
}
/// Compute circumradius for interval embedded in R^2
inline void compute_circumradius_interval_2d(double & circumradius,
double volume)
{
// Compute circumradius of interval in 2D (1/2 volume)
circumradius = volume / 2.0;
}
/// Compute circumradius for interval embedded in R^3
inline void compute_circumradius_interval_3d(double & circumradius,
double volume)
{
// Compute circumradius of interval in 3D (1/2 volume)
circumradius = volume / 2.0;
}
/// Compute circumradius for triangle embedded in R^2
inline void compute_circumradius_triangle_2d(double & circumradius,
const double vertex_coordinates[6],
const double J[4],
double volume)
{
// Compute circumradius of triangle in 2D
const double v1v2 = std::sqrt( (vertex_coordinates[4] - vertex_coordinates[2])*(vertex_coordinates[4] - vertex_coordinates[2])
+ (vertex_coordinates[5] - vertex_coordinates[3])*(vertex_coordinates[5] - vertex_coordinates[3]) );
const double v0v2 = std::sqrt(J[3]*J[3] + J[1]*J[1]);
const double v0v1 = std::sqrt(J[0]*J[0] + J[2]*J[2]);
circumradius = 0.25*(v1v2*v0v2*v0v1) / volume;
}
/// Compute circumradius for triangle embedded in R^3
inline void compute_circumradius_triangle_3d(double & circumradius,
const double vertex_coordinates[9],
const double J[6],
double volume)
{
// Compute circumradius of triangle in 3D
const double v1v2 = std::sqrt( (vertex_coordinates[6] - vertex_coordinates[3])*(vertex_coordinates[6] - vertex_coordinates[3])
+ (vertex_coordinates[7] - vertex_coordinates[4])*(vertex_coordinates[7] - vertex_coordinates[4])
+ (vertex_coordinates[8] - vertex_coordinates[5])*(vertex_coordinates[8] - vertex_coordinates[5]));
const double v0v2 = std::sqrt( J[3]*J[3] + J[1]*J[1] + J[5]*J[5]);
const double v0v1 = std::sqrt( J[0]*J[0] + J[2]*J[2] + J[4]*J[4]);
circumradius = 0.25*(v1v2*v0v2*v0v1) / volume;
}
/// Compute circumradius for tetrahedron embedded in R^3
inline void compute_circumradius_tetrahedron_3d(double & circumradius,
const double vertex_coordinates[12],
const double J[9],
double volume)
{
// Compute circumradius
const double v1v2 = std::sqrt( (vertex_coordinates[6] - vertex_coordinates[3])*(vertex_coordinates[6] - vertex_coordinates[3])
+ (vertex_coordinates[7] - vertex_coordinates[4])*(vertex_coordinates[7] - vertex_coordinates[4])
+ (vertex_coordinates[8] - vertex_coordinates[5])*(vertex_coordinates[8] - vertex_coordinates[5]) );
const double v0v2 = std::sqrt(J[1]*J[1] + J[4]*J[4] + J[7]*J[7]);
const double v0v1 = std::sqrt(J[0]*J[0] + J[3]*J[3] + J[6]*J[6]);
const double v0v3 = std::sqrt(J[2]*J[2] + J[5]*J[5] + J[8]*J[8]);
const double v1v3 = std::sqrt( (vertex_coordinates[ 9] - vertex_coordinates[3])*(vertex_coordinates[ 9] - vertex_coordinates[3])
+ (vertex_coordinates[10] - vertex_coordinates[4])*(vertex_coordinates[10] - vertex_coordinates[4])
+ (vertex_coordinates[11] - vertex_coordinates[5])*(vertex_coordinates[11] - vertex_coordinates[5]) );
const double v2v3 = std::sqrt( (vertex_coordinates[ 9] - vertex_coordinates[6])*(vertex_coordinates[ 9] - vertex_coordinates[6])
+ (vertex_coordinates[10] - vertex_coordinates[7])*(vertex_coordinates[10] - vertex_coordinates[7])
+ (vertex_coordinates[11] - vertex_coordinates[8])*(vertex_coordinates[11] - vertex_coordinates[8]) );
const double la = v1v2*v0v3;
const double lb = v0v2*v1v3;
const double lc = v0v1*v2v3;
const double s = 0.5*(la+lb+lc);
const double area = std::sqrt(s*(s-la)*(s-lb)*(s-lc));
circumradius = area / (6.0*volume);
}
///--- Compute max facet edge lengths ---
/// Compute min edge length in facet of tetrahedron embedded in R^3
inline void compute_min_facet_edge_length_tetrahedron_3d(double & min_edge_length,
unsigned int facet,
const double vertex_coordinates[12])
{
// TODO: Extract compute_facet_edge_lengths_tetrahedron_3d(), reuse between min/max functions
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] = (vertex_coordinates[3*vertex1 + 0] - vertex_coordinates[3*vertex0 + 0])*(vertex_coordinates[3*vertex1 + 0] - vertex_coordinates[3*vertex0 + 0])
+ (vertex_coordinates[3*vertex1 + 1] - vertex_coordinates[3*vertex0 + 1])*(vertex_coordinates[3*vertex1 + 1] - vertex_coordinates[3*vertex0 + 1])
+ (vertex_coordinates[3*vertex1 + 2] - vertex_coordinates[3*vertex0 + 2])*(vertex_coordinates[3*vertex1 + 2] - vertex_coordinates[3*vertex0 + 2]);
}
min_edge_length = std::sqrt(std::min(std::min(edge_lengths_sqr[1], edge_lengths_sqr[1]), edge_lengths_sqr[2]));
}
///--- Compute max facet edge lengths ---
/// Compute max edge length in facet of tetrahedron embedded in R^3
inline void compute_max_facet_edge_length_tetrahedron_3d(double & max_edge_length,
unsigned int facet,
const double vertex_coordinates[12])
{
// TODO: Extract compute_facet_edge_lengths_tetrahedron_3d(), reuse between min/max functions
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] = (vertex_coordinates[3*vertex1 + 0] - vertex_coordinates[3*vertex0 + 0])*(vertex_coordinates[3*vertex1 + 0] - vertex_coordinates[3*vertex0 + 0])
+ (vertex_coordinates[3*vertex1 + 1] - vertex_coordinates[3*vertex0 + 1])*(vertex_coordinates[3*vertex1 + 1] - vertex_coordinates[3*vertex0 + 1])
+ (vertex_coordinates[3*vertex1 + 2] - vertex_coordinates[3*vertex0 + 2])*(vertex_coordinates[3*vertex1 + 2] - vertex_coordinates[3*vertex0 + 2]);
}
max_edge_length = std::sqrt(std::max(std::max(edge_lengths_sqr[0], edge_lengths_sqr[1]), edge_lengths_sqr[2]));
}
#endif
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