p4est_geometry.h File Reference

Transform from tree-local "reference" coordinate system to global "physical space" coordinates. More...

#include <p4est_connectivity.h>

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Data Structures
struct	p4est_geometry
	Encapsulates a custom transformation from tree-local coordinates to user defined physical space. More...

Typedefs
typedef struct p4est_geometry	p4est_geometry_t
	This object encapsulates a custom geometry transformation.
typedef void(*	p4est_geometry_X_t) (p4est_geometry_t *geom, p4est_topidx_t which_tree, const double abc[3], double xyz[3])
	Forward transformation from the tree-local coordinates to physical space. More...
typedef void(*	p4est_geometry_destroy_t) (p4est_geometry_t *geom)
	Destructor prototype for a user-allocated p4est_geometry_t. More...

Functions
void	p4est_geometry_destroy (p4est_geometry_t *geom)
	Can be used to conveniently destroy a geometry structure. More...
p4est_geometry_t *	p4est_geometry_new_connectivity (p4est_connectivity_t *conn)
	Create a geometry structure based on the vertices in a connectivity. More...
void	p4est_geometry_connectivity_X (p4est_geometry_t *geom, p4est_topidx_t which_tree, const double abc[3], double xyz[3])
	Geometric coordinate transformation for geometry created with p4est_geometry_new_connectivity. More...
p4est_geometry_t *	p4est_geometry_new_icosahedron (p4est_connectivity_t *conn, double R)
	Create a geometry for mapping the sphere using 2d connectivity icosahedron. More...
p4est_geometry_t *	p4est_geometry_new_shell2d (p4est_connectivity_t *conn, double R2, double R1)
	Create a geometry for mapping the annulus. More...
p4est_geometry_t *	p4est_geometry_new_disk2d (p4est_connectivity_t *conn, double R0, double R1)
	Create disk2d geometry associated to disk2d connectivity. More...
p4est_geometry_t *	p4est_geometry_new_sphere2d (p4est_connectivity_t *conn, double R)
	Create sphere geometry associated to cubed connectivity. More...

Detailed Description

Transform from tree-local "reference" coordinate system to global "physical space" coordinates.

These are used in p4est_vtk.h to write global coordinate meshes to disk.

We provide several example geometries for use. You may also implement your own geometry as you see fit.

Note

For geometry purposes, each tree has the local coordinate system . For legacy/p8est compatibility reasons the local coordinates are always represented as a triple abc[3]. For a 2D quadtree mesh the local coordinates are abc[0] and abc[1] and the third coordinate abc[2] should be ignored.

Typedef Documentation

p4est_geometry_destroy_t

typedef void(* p4est_geometry_destroy_t) (p4est_geometry_t *geom)

Destructor prototype for a user-allocated p4est_geometry_t.

It is invoked by p4est_geometry_destroy. If the user chooses to reserve the structure statically, there is no need to provide it.

p4est_geometry_X_t

typedef void(* p4est_geometry_X_t) (p4est_geometry_t *geom, p4est_topidx_t which_tree, const double abc[3], double xyz[3])

Forward transformation from the tree-local coordinates to physical space.

Note

The two-dimensional connectivities built into p4est have 3D vertex coordinates that can be used in the transformation if so desired. However, connectivities are not in general required to have vertex coordinate information.

Parameters

[in]	geom	associated geometry
[in]	which_tree	tree id inside forest
[in]	abc	tree-local coordinates: . For 2D meshes abc[2] should never be accessed.
[out]	xyz	cartesian coordinates in physical space after geometry

Function Documentation

p4est_geometry_connectivity_X()

void p4est_geometry_connectivity_X	(	p4est_geometry_t *	geom,
		p4est_topidx_t	which_tree,
		const double	abc[3],
		double	xyz[3]
	)

Geometric coordinate transformation for geometry created with p4est_geometry_new_connectivity.

This is defined by tri/binlinear interpolation from vertex coordinates.

May also be used as a building block in custom geometric coordinate transforms. See for example p4est_geometry_sphere2d_X or p4est_geometry_disk2d_X.

Parameters

[in]	geom	associated geometry
[in]	which_tree	tree id inside forest
[in]	abc	tree-local reference coordinates : [0,1]^3. Note: abc[2] is only accessed by the P4_TO_P8 version
[out]	xyz	Cartesian coordinates in physical space after geometry

Warning

The associated geometry is assumed to have a connectivity as its *user field, and this connectivity is assumed to have vertex information in its *tree_to_vertex field.

p4est_geometry_destroy()

void p4est_geometry_destroy

(

p4est_geometry_t *

geom

)

Can be used to conveniently destroy a geometry structure.

The user is free not to call this function at all if they handle the memory of the p4est_geometry_t in their own way.

Examples

simple/simple2.c.

p4est_geometry_new_connectivity()

p4est_geometry_t * p4est_geometry_new_connectivity

(

p4est_connectivity_t *

conn

)

Create a geometry structure based on the vertices in a connectivity.

The transformation is constructed using bilinear interpolation.

Parameters

[in]

conn

A connectivity with vertex coordinate information. We do not take ownership and expect this structure to stay alive.

Returns

Geometry structure; use with p4est_geometry_destroy.

p4est_geometry_new_disk2d()

p4est_geometry_t * p4est_geometry_new_disk2d	(	p4est_connectivity_t *	conn,
		double	R0,
		double	R1
	)

Create disk2d geometry associated to disk2d connectivity.

Parameters

[in]	conn	The result of p4est_connectivity_new_disk2d.
[in]	R0	radius of the inner circle.
[in]	R1	radius of the outer circle (external border).

This geometry is meant to be used with the disk2d connectivity, which is a 5-tree connectivity to map the spherical disk.

Examples

simple/simple2.c.

p4est_geometry_new_icosahedron()

p4est_geometry_t * p4est_geometry_new_icosahedron	(	p4est_connectivity_t *	conn,
		double	R
	)

Create a geometry for mapping the sphere using 2d connectivity icosahedron.

Parameters

[in]	conn	The result of p4est_connectivity_new_icosahedron.
[in]	R	The radius of the sphere.

Examples

simple/simple2.c.

p4est_geometry_new_shell2d()

p4est_geometry_t * p4est_geometry_new_shell2d	(	p4est_connectivity_t *	conn,
		double	R2,
		double	R1
	)

Create a geometry for mapping the annulus.

This a direct adaptation of geometric shell in 3d.

Parameters

[in]	conn	The result of p4est_connectivity_new_shell2d.
[in]	R1	radius of the inner circle (internal border).
[in]	R2	radius of the outer circle (external border).

Examples

simple/simple2.c.

p4est_geometry_new_sphere2d()

p4est_geometry_t * p4est_geometry_new_sphere2d	(	p4est_connectivity_t *	conn,
		double	R
	)

Create sphere geometry associated to cubed connectivity.

Parameters

[in]	conn	The result of p4est_connectivity_new_cubed.
[in]	R	radius of the sphere

This geometry is meant to be used with the cubed connectivity p4est_connectivity_new_cubed, which is a 6-tree connectivity, to map the sphere.

Examples

simple/simple2.c.