Two-dimensional triangular meshes. More...

Data Structures
struct	_tri2d
	Representation of a two-dimensional triangular mesh. More...

struct	_tri2dref
	Representation of the refinement relationship between two meshes. More...

Typedefs
typedef struct _tri2d	tri2d
	Two-dimensional triangulat mesh.

typedef tri2d *	ptri2d
	Pointer to tri2d object.

typedef const tri2d *	pctri2d
	Pointer to constant tri2d object.

typedef struct _tri2dref	tri2dref

typedef tri2dref *	ptri2dref
	Pointer to tri2dref object.

typedef const tri2dref *	pctri2dref
	Pointer to constant tri2dref object.

typedef struct _tri2dbuilder	tri2dbuilder
	Tool for constructing tri2d meshes.

typedef tri2dbuilder *	ptri2dbuilder

Functions
ptri2d	new_tri2d (uint vertices, uint edges, uint triangles)
	Create a partially initialized tri2d mesh. More...

void	del_tri2d (ptri2d t2)
	Delete a tri2d object. More...

ptri2d	new_unitsquare_tri2d ()
	Create a mesh containing two triangles representing the unit square, $[-1,1] \times [-1,1]$ . More...

ptri2d	new_unitcircle_tri2d ()
	Create a mesh containing four triangles representing the unit square, $[-1,1] \times [-1,1]$ . More...

ptri2d	new_lshape_tri2d ()
	Create a mesh containing six triangles representing a L-shaped domain with vertices . More...

ptri2d	new_ushape_tri2d ()
	Create a mesh containing twentyfour triangles representing a U-shaped domain. More...

void	write_tri2d (pctri2d t2, const char *name)
	Write a triangular mesh to a file. More...

ptri2d	read_tri2d (const char *name)
	Read a triangular mesh from a file. More...

void	getvertices_tri2d (pctri2d t2, uint tn, uint v[])
	Find the vertices of a triangle. More...

void	fixnormals_tri2d (ptri2d t2)
	Ensure that the vertices of boundary edges are in counter-clockwise order as seen from outside of the mesh. More...

void	check_tri2d (pctri2d t2)
	Perform various consistency checks. More...

ptri2d	refine_tri2d (pctri2d t2, ptri2dref *t2r)
	Regular refinement of a triangular mesh. More...

void	del_tri2dref (ptri2dref t2r)
	Delete a tri2dref object. More...

void	draw_cairo_tri2d (pctri2d t2, const char *filename, bool mark_refedges, int mark_triangle)
	Draw a tri2d mesh. More...

void	smooth_unitcircle_tri2d (ptri2d t2)
	Smooth a tri2d unitcircle. More...

ptri2dbuilder	new_tri2dbuilder (uint vertices)
	Create a new tri2dbuilder object. More...

void	del_tri2dbuilder (ptri2dbuilder tb)
	Delete a tri2dbuilder object. More...

real(*	getx_tri2dbuilder (ptri2dbuilder tb))[2]
	Obtain array of vertex coordinates in tri2dbuilder object. More...

void	addtriangle_tri2dbuilder (ptri2dbuilder tb, uint v0, uint v1, uint v2)
	Add a triangle to a tri2dbuilder object. More...

ptri2d	buildmesh_tri2dbuilder (ptri2dbuilder tb)
	Create a tri2d mesh from the geometrical and topological information stored in a tri2dbuilder object. More...

Detailed Description

Two-dimensional triangular meshes.

Typedef Documentation

typedef tri2dbuilder* ptri2dbuilder

Pointer to tri2dbuilder object

typedef struct _tri2dref tri2dref

Refinement data for triangular meshes

Function Documentation

void addtriangle_tri2dbuilder	(	ptri2dbuilder	tb,
		uint	v0,
		uint	v1,
		uint	v2
	)

Add a triangle to a tri2dbuilder object.

Parameters

tb	Target tri2dbuilder object.
v0	Index of first vertex.
v1	Index of second vertex.
v2	Index of third vertex.

ptri2d buildmesh_tri2dbuilder ( ptri2dbuilder tb )

Create a tri2d mesh from the geometrical and topological information stored in a tri2dbuilder object.

Once the mesh has been created, the corresponding tri2dbuilder object can be deleted.

Parameters

tb	Source tri2dbuilder object.

Returns: tri2d mesh.

void check_tri2d ( pctri2d t2 )

Perform various consistency checks.

Parameters

t2 Mesh

Returns: Number of inconsistencies found

void del_tri2d ( ptri2d t2 )

Delete a tri2d object.

Parameters

t2	Object to be deleted

void del_tri2dbuilder ( ptri2dbuilder tb )

Delete a tri2dbuilder object.

Parameters

tb	Object to be deleted.

void del_tri2dref ( ptri2dref t2r )

Delete a tri2dref object.

Parameters

t2r	Object to be deleted

void draw_cairo_tri2d	(	pctri2d	t2,
		const char *	filename,
		bool	mark_refedges,
		int	mark_triangle
	)

Draw a tri2d mesh.

Parameters

t2	This grid will be drawn.
filename	In this fill the mesh will be drawn.
mark_refedges
mark_triangle

void fixnormals_tri2d ( ptri2d t2 )

Ensure that the vertices of boundary edges are in counter-clockwise order as seen from outside of the mesh.

Parameters

t2	Mesh, offending boundary edges will be reordered

Returns: Number of edges that have been fixed.

void getvertices_tri2d	(	pctri2d	t2,
		uint	tn,
		uint	v[]
	)

Find the vertices of a triangle.

Due to the hierarchical representation of geometric objects, we cannot access the vertices of a triangle directly. This function finds the vertices and returns them in a specific order: v[i] is the vertex opposite the i-th edge.

Parameters

t2	Mesh
tn	Number of the triangle
v	Will be filled with vertex numbers.

real(* getx_tri2dbuilder ( ptri2dbuilder tb ) )[2]

Obtain array of vertex coordinates in tri2dbuilder object.

Since tri2dbuilder is an opaque class, this function is provided for setting the coordinates of the vertices.

Parameters

tb	tri2dbuilder object.

Returns: Pointer to array of with tb->vertices entries of type real [2] representing the vertex coordinates.

ptri2d new_lshape_tri2d ( )

Create a mesh containing six triangles representing a L-shaped domain with vertices $(-1,-1), (0,-1), (1,-1), (-1,0), (0,0), (1,0), (-1,1) and (0,1)$ .

Returns: tri2d mesh representing the L-shaped domain

ptri2d new_tri2d	(	uint	vertices,
		uint	edges,
		uint	triangles
	)

Create a partially initialized tri2d mesh.

All arrays are created, but are not filled with meaningful values.

Parameters

vertices	Number of vertices
edges	Number of edges
triangles	Number of tetrahedra

Returns: Partially initialized tri2d mesh

ptri2dbuilder new_tri2dbuilder ( uint vertices )

Create a new tri2dbuilder object.

Parameters

vertices Number of vertices of the new mesh.

Returns: tri2dbuilder object with no edges or triangles.

ptri2d new_unitcircle_tri2d ( )

Create a mesh containing four triangles representing the unit square, $[-1,1] \times [-1,1]$ .

Returns: tri2d mesh representing the unit square.

ptri2d new_unitsquare_tri2d ( )

Create a mesh containing two triangles representing the unit square, $[-1,1] \times [-1,1]$ .

Returns: tri2d mesh representing the unit square.

ptri2d new_ushape_tri2d ( )

Create a mesh containing twentyfour triangles representing a U-shaped domain.

Returns: tri2d mesh representing the U-shape.

ptri2d read_tri2d ( const char * name )

Read a triangular mesh from a file.

Parameters

name Filename

Returns: tri2d object describing the mesh

ptri2d refine_tri2d	(	pctri2d	t2,
		ptri2dref *	t2r
	)

Regular refinement of a triangular mesh.

The mesh is globally refined using regular refinement.

Parameters

t2	Coarse mesh
t2r	If not null, the target pointer will be set to a new tri2dref object describing the refinement relationship

Returns: Refined mesh

void smooth_unitcircle_tri2d ( ptri2d t2 )

Smooth a tri2d unitcircle.

Smooth a tri2d mesh representing a unit circle. The vertices of the smooth unit circle are shifted to the boundary.

Parameters

t2	mesh representing the unitsquare, will be overwritten with smooth mesh.

void write_tri2d	(	pctri2d	t2,
		const char *	name
	)

Write a triangular mesh to a file.

Parameters

t2	Source mesh
name	Filename

Data Structures

Typedefs

Functions

Detailed Description

Typedef Documentation

Function Documentation