This geometry maps the faces of an octahedron/icosahedron to a spherical surface. More...

#include <t8_geometry_examples.hxx>

Inheritance diagram for t8_geometry_triangulated_spherical_surface:

Public Member Functions
void	t8_geom_evaluate (t8_cmesh_t cmesh, t8_gloidx_t gtreeid, const double ref_coords, const size_t num_coords, double out_coords) const
	Map the faces of an octahedron/icosahedron to a spherical surface. More...

void	t8_geom_evaluate_jacobian (t8_cmesh_t cmesh, t8_gloidx_t gtreeid, const double ref_coords, const size_t num_coords, double jacobian) const
	Compute the jacobian of the t8_geom_evaluate map at a point in the reference space $ [0,1]^\mathrm{dim} $. More...

Public Member Functions inherited from t8_geometry_with_vertices
	t8_geometry_with_vertices (int dimension, std::string name)

virtual	~t8_geometry_with_vertices ()
	The destructor. More...

virtual void	t8_geom_load_tree_data (t8_cmesh_t cmesh, t8_gloidx_t gtreeid)
	Update a possible internal data buffer for per tree data. More...

virtual bool	t8_geom_tree_negative_volume () const
	Check if the currently active tree has a negative volume. More...

t8_geometry_type_t	t8_geom_get_type () const
	Get the type of this geometry. More...

Public Member Functions inherited from t8_geometry
	t8_geometry (int dim, std::string name)

virtual	~t8_geometry ()
	The destructor. More...

virtual void	t8_geom_point_batch_inside_element (t8_forest_t forest, t8_locidx_t ltreeid, const t8_element_t element, const double points, const int num_points, int *is_inside, const double tolerance) const
	Query whether a batch of points lies inside an element. More...

int	t8_geom_get_dimension () const
	Get the dimension of this geometry. More...

const std::string	t8_geom_get_name () const
	Get the name of this geometry. More...

const size_t	t8_geom_get_hash () const

Additional Inherited Members
Protected Attributes inherited from t8_geometry_with_vertices
t8_gloidx_t	active_tree

t8_eclass_t	active_tree_class

const double *	active_tree_vertices

Protected Attributes inherited from t8_geometry
int	dimension
	The dimension of reference space for which this is a geometry.

std::string	name
	The name of this geometry.

size_t	hash
	The hash of the name of this geometry.

Detailed Description

This geometry maps the faces of an octahedron/icosahedron to a spherical surface.

Member Function Documentation

◆ t8_geom_evaluate()

void t8_geometry_triangulated_spherical_surface::t8_geom_evaluate	(	t8_cmesh_t	cmesh,
		t8_gloidx_t	gtreeid,
		const double *	ref_coords,
		const size_t	num_coords,
		double *	out_coords
	)		const

virtual

Map the faces of an octahedron/icosahedron to a spherical surface.

Map the faces of an octahedron to a spherical surface.

Parameters

[in]	cmesh	The cmesh in which the point lies.
[in]	gtreeid	The global tree (of the cmesh) in which the reference point is.
[in]	ref_coords	Array of dimension x num_coords many entries, specifying a point in /f$ [0,1]^\mathrm{dim} /f$.
[in]	num_coords	The number of points to map.
[out]	out_coords	The mapped coordinates in physical space of ref_coords. The length is num_coords * 3.

This routine expects an input mesh of triangles arranged into an octahedron/icosahedron.

Parameters

[in]	cmesh	The cmesh in which the point lies.
[in]	gtreeid	The global tree (of the cmesh) in which the reference point is.
[in]	ref_coords	Array of dimension many entries, specifying a point in [0,1]^dimension.
[out]	out_coords	The mapped coordinates in physical space of ref_coords.

Implements t8_geometry.

◆ t8_geom_evaluate_jacobian()

void t8_geometry_triangulated_spherical_surface::t8_geom_evaluate_jacobian	(	t8_cmesh_t	cmesh,
		t8_gloidx_t	gtreeid,
		const double *	ref_coords,
		const size_t	num_coords,
		double *	jacobian
	)		const

inlinevirtual

Compute the jacobian of the t8_geom_evaluate map at a point in the reference space $ [0,1]^\mathrm{dim} $.

Parameters

[in]	cmesh	The cmesh in which the point lies.
[in]	glreeid	The global tree (of the cmesh) in which the reference point is.
[in]	ref_coords	Array of dimension x num_coords many entries, specifying points in $ [0,1]^\mathrm{dim} $.
[in]	num_coords	Amount of points of /f$ \mathrm{dim} /f$ to map.
[out]	jacobian	The jacobian at ref_coords. Array of size num_coords x dimension x 3. Indices $ 3 \cdot i$ , $ 3 \cdot i+1 $ , $ 3 \cdot i+2 $ correspond to the $ i $-th column of the jacobian (Entry $ 3 \cdot i + j $ is $ \frac{\partial f_j}{\partial x_i} $).

Implements t8_geometry.

The documentation for this struct was generated from the following files:

src/t8_geometry/t8_geometry_implementations/t8_geometry_examples.hxx
src/t8_geometry/t8_geometry_implementations/t8_geometry_examples.cxx

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ t8_geom_evaluate()

◆ t8_geom_evaluate_jacobian()