naginterfaces.library.mesh.dim2_​gen_​delaunay

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

dim2_gen_delaunay generates a triangular mesh of a closed polygonal region in $R^2$, 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://support.nag.com/numeric/nl/nagdoc_30/flhtml/d06/d06abf.html

Parameters

nvbint

The number of vertices in the input boundary mesh.

edgeint, array-like, shape $(3,\text{nedge})$

The specification of the boundary edges. $edge[0,j-1]$ and $edge[1,j-1]$ contain the vertex numbers of the two end points of the $j$th boundary edge. $edge[2,j-1]$ is a user-supplied tag for the $j$th boundary edge and is not used by dim2_gen_delaunay.

coorfloat, array-like, shape $(2,\text{nvmax})$

$coor[0,\text{i}-1]$ contains the $x$ coordinate of the $\text{i}$th input boundary mesh vertex, for $\text{i}=1,\dots ,nvb$. $coor[0,\text{i}-1]$ contains the $x$ coordinate of the $(\text{i}-nvb)$th fixed interior vertex, for $\text{i}=nvb+1,\dots ,nvb+\text{nvint}$. For boundary and interior vertices, $coor[1,\text{i}-1]$ contains the corresponding $y$ coordinate, for $\text{i}=1,2,\dots ,nvb+\text{nvint}$.

weightfloat, array-like, shape $\left(\text{nvint}\right)$

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 $npropa$ is used when the internal points are created. They are distributed in a geometric manner if $npropa$ 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.

$itrace\le 0$

No output is generated.

$itrace\ge 1$

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 $itrace=0$, 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 $nvb+\text{nvint}=\text{nvmax}$, no interior vertices will be generated and $nv=\text{nvmax}$.

neltint

The number of triangular elements in the mesh.

coorfloat, ndarray, shape $(2,\text{nvmax})$

$coor[0,\text{i}-1]$ will contain the $x$ coordinate of the $(\text{i}-nvb-\text{nvint})$th generated interior mesh vertex, for $\text{i}=nvb+\text{nvint}+1,\dots ,nv$; while $coor[1,i-1]$ will contain the corresponding $y$ coordinate. The remaining elements are unchanged.

connint, ndarray, shape $(3,2\times \text{nvmax}+5)$

The connectivity of the mesh between triangles and vertices. For each triangle $\text{j}$, $conn[\text{i}-1,\text{j}-1]$ gives the indices of its three vertices (in anticlockwise order), for $\text{j}=1,\dots ,nelt$, for $\text{i}=1,2,\dots ,3$.

Raises

NagValueError

(errno $1$)

On entry, $nvb=⟨value⟩$, $\text{nvint}=⟨value⟩$ and $\text{nvmax}=⟨value⟩$.

Constraint: $\text{nvmax}\ge nvb+\text{nvint}$.

(errno $1$)

On entry, $\text{nedge}=⟨value⟩$.

Constraint: $\text{nedge}\ge 1$.

(errno $1$)

On entry, $edge(\text{I},\text{J})=⟨value⟩$, $\text{I}=⟨value⟩$, $\text{J}=⟨value⟩$ and $nvb=⟨value⟩$.

Constraint: $edge(\text{I},\text{J})\ge 1$ and $edge(\text{I},\text{J})\le nvb$.

(errno $1$)

On entry, $nvb=⟨value⟩$.

Constraint: $nvb\ge 3$.

(errno $1$)

On entry, $\text{nvint}=⟨value⟩$.

Constraint: $\text{nvint}\ge 0$.

(errno $1$)

On entry, the end points of the edge $\text{J}$ have the same index $\text{I}$: $\text{J}=⟨value⟩$ and $\text{I}=⟨value⟩$.

(errno $1$)

On entry, $weight[\text{I}-1]=⟨value⟩$ and $\text{I}=⟨value⟩$.

Constraint: $weight[\text{I}-1]>0.0$.

(errno $1$)

On entry, $npropa=0$.

(errno $2$)

An error has occurred during the generation of the interior mesh. Check the definition of the boundary (arguments $coor$ and $edge$) as well as the orientation of the boundary (especially in the case of a multiple connected component boundary). Setting $itrace>0$ may provide more details.

(errno $3$)

An error has occurred during the generation of the boundary mesh. It appears that $\text{nvmax}$ is not large enough: $\text{nvmax}=⟨value⟩$.

(errno $3$)

An error has occurred during the generation of the boundary mesh. Check the definition of the boundary (arguments $coor$ and $edge$) as well as the orientation of the boundary (especially in the case of a multiple connected component boundary). Setting $itrace>0$ 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