Defines t8code internal functions that are useful for geometry implementations. More...

#include <t8.h>

Functions
void	t8_geom_compute_linear_geometry (t8_eclass_t tree_class, const double tree_vertices, const double ref_coords, const size_t num_coords, double *out_coords)
	Compute the linear geometry of a tree at a given reference coordinate. More...

void	t8_geom_compute_linear_axis_aligned_geometry (t8_eclass_t tree_class, const double tree_vertices, const double ref_coords, const size_t num_coords, double *out_coords)
	Compute the linear, axis-aligned geometry of a tree at a given reference coordinate. More...

void	t8_geom_linear_interpolation (const double coefficients, const double corner_values, int corner_value_dim, int interpolation_dim, double *evaluated_function)
	Interpolates linearly between 2, bilinearly between 4 or trilineraly between 8 points. More...

void	t8_geom_triangular_interpolation (const double coefficients, const double corner_values, int corner_value_dim, int interpolation_dim, double *evaluated_function)
	Triangular interpolation between 3 points (triangle) or 4 points (tetrahedron) using barycentric coordinates. More...

void	t8_geom_get_face_vertices (t8_eclass_t tree_class, const double tree_vertices, int face_index, int dim, double face_vertices)
	Copies the vertex coordinates of a tree face in zorder into a separate array. More...

void	t8_geom_get_edge_vertices (t8_eclass_t tree_class, const double tree_vertices, int edge_index, int dim, double edge_vertices)
	Copies the vertex coordinates of a tree edge in zorder into a separate array. More...

void	t8_geom_get_ref_intersection (int edge_index, const double *ref_coords, double ref_intersection[2])
	Calculates a point of intersection in a triangular reference space. More...

double	t8_geom_get_triangle_scaling_factor (int edge_index, const double tree_vertices, const double glob_intersection, const double *glob_ref_point)
	Calculates the scaling factor for edge displacement along a triangular tree face depending on the position of the global reference point. More...

double	t8_geom_get_scaling_factor_of_edge_on_face_tet (int edge_index, int face_index, const double *ref_coords)
	Calculates the scaling factor for the displacement of an edge over a face of a tetrahedral element. More...

void	t8_geom_get_tet_face_intersection (const int face_index, const double *ref_coords, double face_intersection[3])
	Calculates the face intersection of a ray passing trough the reference coordinates and the opposite vertex of that face for a tetrahedron. More...

int	t8_vertex_point_inside (const double vertex_coords[3], const double point[3], const double tolerance)
	Check if a point lies inside a vertex. More...

int	t8_line_point_inside (const double p_0, const double vec, const double *point, const double tolerance)
	Check if a point is inside a line that is defined by a starting point p_0 and a vector vec. More...

int	t8_triangle_point_inside (const double p_0[3], const double v[3], const double w[3], const double point[3], const double tolerance)
	Check if a point is inside of a triangle described by a point p_0 and two vectors v and w. More...

int	t8_plane_point_inside (const double point_on_face[3], const double face_normal[3], const double point[3])
	Check if a point lays on the inner side of a plane of a bilinearly interpolated volume element. More...

Detailed Description

Defines t8code internal functions that are useful for geometry implementations.

Function Documentation

◆ t8_geom_compute_linear_axis_aligned_geometry()

void t8_geom_compute_linear_axis_aligned_geometry	(	t8_eclass_t	tree_class,
		const double *	tree_vertices,
		const double *	ref_coords,
		const size_t	num_coords,
		double *	out_coords
	)

Compute the linear, axis-aligned geometry of a tree at a given reference coordinate.

This function is faster than t8_geom_compute_linear_geometry, but only works for axis-aligned trees of T8_ECLASS_LINE, T8_ECLASS_QUAD and T8_ECLASS_HEX.

Parameters

[in]	tree_class	The eclass of the tree.
[in]	tree_vertices	Array with the tree vertex coordinates.
[in]	ref_coords	The reference coordinates of the point.
[in]	num_coords	Number of points to evaluate.
[out]	out_coords	The output coordinates.

◆ t8_geom_compute_linear_geometry()

void t8_geom_compute_linear_geometry	(	t8_eclass_t	tree_class,
		const double *	tree_vertices,
		const double *	ref_coords,
		const size_t	num_coords,
		double *	out_coords
	)

Compute the linear geometry of a tree at a given reference coordinate.

Parameters

[in]	tree_class	The eclass of the tree.
[in]	tree_vertices	Array with the tree vertex coordinates.
[in]	ref_coords	The reference coordinates of the point.
[in]	num_coords	Number of points to evaluate.
[out]	out_coords	The output coordinates.

◆ t8_geom_get_edge_vertices()

void t8_geom_get_edge_vertices	(	t8_eclass_t	tree_class,
		const double *	tree_vertices,
		int	edge_index,
		int	dim,
		double *	edge_vertices
	)

Copies the vertex coordinates of a tree edge in zorder into a separate array.

Parameters

[in]	tree_class	The eclass of the tree.
[in]	tree_vertices	Array with the tree vertex coordinates.
[in]	edge_index	Index of the edge, which vertices should be copied.
[in]	dim	The dimension of the edge vertices.
[out]	edge_vertices	Coordinates of the edge vertices in zorder.

◆ t8_geom_get_face_vertices()

void t8_geom_get_face_vertices	(	t8_eclass_t	tree_class,
		const double *	tree_vertices,
		int	face_index,
		int	dim,
		double *	face_vertices
	)

Copies the vertex coordinates of a tree face in zorder into a separate array.

Parameters

[in]	tree_class	The eclass of the tree.
[in]	tree_vertices	Array with the tree vertex coordinates.
[in]	face_index	Index of the face, which vertices should be copied.
[in]	dim	The dimension of the face vertices.
[out]	face_vertices	Coordinates of the face vertices in zorder.

◆ t8_geom_get_ref_intersection()

void t8_geom_get_ref_intersection	(	int	edge_index,
		const double *	ref_coords,
		double	ref_intersection[2]
	)

Calculates a point of intersection in a triangular reference space.

The intersection is the extension of a straight line passing through a reference point and the opposite vertex of the edge. /|\ / | \ o -> reference point / o \ x -> intersection point / | \ /____x____\

Parameters

[in]	edge_index	Index of the edge, the intersection lies on.
[in]	ref_coords	Array containing the coordinates of the reference point.
[out]	ref_intersection	Coordinates of the intersection point.

◆ t8_geom_get_scaling_factor_of_edge_on_face_tet()

double t8_geom_get_scaling_factor_of_edge_on_face_tet	(	int	edge_index,
		int	face_index,
		const double *	ref_coords
	)

Calculates the scaling factor for the displacement of an edge over a face of a tetrahedral element.

Parameters

[in]	edge_index	Index of the edge, whose displacement should be scaled.
[in]	face_index	Index of the face, the displacement should be scaled on.
[in]	ref_coords	Array containing the coordinates of the reference point.

Returns: The scaling factor of the edge displacement on the face at the point of the reference coordinates.

◆ t8_geom_get_tet_face_intersection()

void t8_geom_get_tet_face_intersection	(	const int	face_index,
		const double *	ref_coords,
		double	face_intersection[3]
	)

Calculates the face intersection of a ray passing trough the reference coordinates and the opposite vertex of that face for a tetrahedron.

The coordinates of the face intersection are reference coordinates: [0,1]^3.

Parameters

[in]	face_index	Index of the face, on which the intersection should be calculated.
[in]	ref_coords	Array containing the coordinates of the reference point.
[out]	face_intersection	Three dimensional array containing the intersection point on the face in reference space.

◆ t8_geom_get_triangle_scaling_factor()

double t8_geom_get_triangle_scaling_factor	(	int	edge_index,
		const double *	tree_vertices,
		const double *	glob_intersection,
		const double *	glob_ref_point
	)

Calculates the scaling factor for edge displacement along a triangular tree face depending on the position of the global reference point.

Parameters

[in]	edge_index	Index of the edge, whose displacement should be scaled.
[in]	tree_vertices	Array with the tree vertex coordinates.
[in]	glob_intersection	Array containing the coordinates of the intersection point of a line drawn from the opposite vertex through the glob_ref_point onto the edge with edge_index.
[in]	glob_ref_point	Array containing the coordinates of the reference point mapped into the global space.

◆ t8_geom_linear_interpolation()

void t8_geom_linear_interpolation	(	const double *	coefficients,
		const double *	corner_values,
		int	corner_value_dim,
		int	interpolation_dim,
		double *	evaluated_function
	)

Interpolates linearly between 2, bilinearly between 4 or trilineraly between 8 points.

Parameters

[in]	coefficients	An array of size at least dim giving the coefficients used for the interpolation
[in]	corner_values	An array of size 2^dim * 3, giving for each corner (in zorder) of the unit square/cube its function values in space.
[in]	corner_value_dim	The dimension of the corner_values.
[in]	interpolation_dim	The dimension of the interpolation (1 for linear, 2 for bilinear, 3 for trilinear)
[out]	evaluated_function	An array of size corner_value_dim, on output the result of the interpolation.

◆ t8_geom_triangular_interpolation()

void t8_geom_triangular_interpolation	(	const double *	coefficients,
		const double *	corner_values,
		int	corner_value_dim,
		int	interpolation_dim,
		double *	evaluated_function
	)

Triangular interpolation between 3 points (triangle) or 4 points (tetrahedron) using barycentric coordinates.

Parameters

[in]	coefficients	An array of size interpolation_dim giving the coefficients used for the interpolation
[in]	corner_values	An array of size 3 * corner_value_dim for interpolation_dim == 2 or 4 * corner_value_dim for interpolation_dim == 3, giving the function values of the triangle/tetrahedron for each corner (in zorder)
[in]	corner_value_dim	The dimension of the corner_values.
[in]	interpolation_dim	The dimension of the interpolation (2 for triangle, 3 for tetrahedron)
[out]	evaluated_function	An array of size corner_value_dim, on output the result of the interpolation.

◆ t8_line_point_inside()

int t8_line_point_inside	(	const double *	p_0,
		const double *	vec,
		const double *	point,
		const double	tolerance
	)

Check if a point is inside a line that is defined by a starting point p_0 and a vector vec.

Parameters

[in]	p_0	Starting point of the line
[in]	vec	Direction of the line (not normalized)
[in]	point	The coordinates of the point to check
[in]	tolerance	A double > 0 defining the tolerance

Returns: 0 if the point is outside, 1 otherwise.

◆ t8_plane_point_inside()

int t8_plane_point_inside	(	const double	point_on_face[3],
		const double	face_normal[3],
		const double	point[3]
	)

Check if a point lays on the inner side of a plane of a bilinearly interpolated volume element.

the plane is described by a point and the normal of the face.

Parameters

[in]	point_on_face	A point on the plane
[in]	face_normal	The normal of the face
[in]	point	The point to check

Returns: 0 if the point is outside, 1 otherwise.

◆ t8_triangle_point_inside()

int t8_triangle_point_inside	(	const double	p_0[3],
		const double	v[3],
		const double	w[3],
		const double	point[3],
		const double	tolerance
	)

Check if a point is inside of a triangle described by a point p_0 and two vectors v and w.

Parameters

[in]	p_0	The first vertex of a triangle
[in]	v	The vector from p_0 to p_1 (second vertex in the triangle)
[in]	w	The vector from p_0 to p_2 (third vertex in the triangle)
[in]	point	The coordinates of the point to check
[in]	tolerance	A double > 0 defining the tolerance

Returns: 0 if the point is outside, 1 otherwise.

◆ t8_vertex_point_inside()

int t8_vertex_point_inside	(	const double	vertex_coords[3],
		const double	point[3],
		const double	tolerance
	)

Check if a point lies inside a vertex.

Parameters

[in]	vertex_coords	The coordinates of the vertex
[in]	point	The coordinates of the point to check
[in]	tolerance	A double > 0 defining the tolerance

Returns: 0 if the point is outside, 1 otherwise.

Functions

Detailed Description

Function Documentation

◆ t8_geom_compute_linear_axis_aligned_geometry()

◆ t8_geom_compute_linear_geometry()

◆ t8_geom_get_edge_vertices()

◆ t8_geom_get_face_vertices()

◆ t8_geom_get_ref_intersection()

◆ t8_geom_get_scaling_factor_of_edge_on_face_tet()

◆ t8_geom_get_tet_face_intersection()

◆ t8_geom_get_triangle_scaling_factor()

◆ t8_geom_linear_interpolation()

◆ t8_geom_triangular_interpolation()

◆ t8_line_point_inside()

◆ t8_plane_point_inside()

◆ t8_triangle_point_inside()

◆ t8_vertex_point_inside()