naginterfaces.library.mesh.dim2_​gen_​delaunay

naginterfaces.library.mesh.dim2_gen_delaunay(nvb, edge, coor, weight, npropa, itrace, io_manager=None)[source]

dim2_gen_delaunay generates a triangular mesh of a closed polygonal region in , given a mesh of its boundary. It uses a Delaunay–Voronoi process, based on an incremental method.

For full information please refer to the NAG Library document for d06ab

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/d06/d06abf.html

Parameters
nvbint

The number of vertices in the input boundary mesh.

edgeint, array-like, shape

The specification of the boundary edges. and contain the vertex numbers of the two end points of the th boundary edge. is a user-supplied tag for the th boundary edge and is not used by dim2_gen_delaunay.

coorfloat, array-like, shape

contains the coordinate of the th input boundary mesh vertex, for . contains the coordinate of the th fixed interior vertex, for . For boundary and interior vertices, contains the corresponding coordinate, for .

weightfloat, array-like, shape

The weight of fixed interior vertices. It is the diameter of triangles (length of the longer edge) created around each of the given interior vertices.

npropaint

The propagation type and coefficient, the argument is used when the internal points are created. They are distributed in a geometric manner if is positive and in an arithmetic manner if it is negative. For more details see Further Comments.

itraceint

The level of trace information required from dim2_gen_delaunay.

No output is generated.

Output from the meshing solver is printed. This output contains details of the vertices and triangles generated by the process.

You are advised to set , unless you are experienced with finite element mesh generation.

io_managerFileObjManager, optional

Manager for I/O in this routine.

Returns
nvint

The total number of vertices in the output mesh (including both boundary and interior vertices). If , no interior vertices will be generated and .

neltint

The number of triangular elements in the mesh.

coorfloat, ndarray, shape

will contain the coordinate of the th generated interior mesh vertex, for ; while will contain the corresponding coordinate. The remaining elements are unchanged.

connint, ndarray, shape

The connectivity of the mesh between triangles and vertices. For each triangle , gives the indices of its three vertices (in anticlockwise order), for , for .

Raises
NagValueError
(errno )

On entry, , and .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, , , and .

Constraint: and .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, the end points of the edge have the same index : and .

(errno )

On entry, and .

Constraint: .

(errno )

On entry, .

(errno )

An error has occurred during the generation of the interior mesh. Check the definition of the boundary (arguments and ) as well as the orientation of the boundary (especially in the case of a multiple connected component boundary). Setting may provide more details.

(errno )

An error has occurred during the generation of the boundary mesh. It appears that is not large enough: .

(errno )

An error has occurred during the generation of the boundary mesh. Check the definition of the boundary (arguments and ) as well as the orientation of the boundary (especially in the case of a multiple connected component boundary). Setting may provide more details.

Notes

dim2_gen_delaunay generates the set of interior vertices using a Delaunay–Voronoi process, based on an incremental method. It allows you to specify a number of fixed interior mesh vertices together with weights which allow concentration of the mesh in their neighbourhood. For more details about the triangulation method, consult the D06 Introduction as well as George and Borouchaki (1998).

This function is derived from material in the MODULEF package from INRIA (Institut National de Recherche en Informatique et Automatique).

References

George, P L and Borouchaki, H, 1998, Delaunay Triangulation and Meshing: Application to Finite Elements, Editions HERMES, Paris