nag_mesh2d_front (d06acc) (PDF version)
d06 Chapter Contents
d06 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_mesh2d_front (d06acc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_mesh2d_front (d06acc) generates a triangular mesh of a closed polygonal region in 2, given a mesh of its boundary. It uses an Advancing Front process, based on an incremental method.

2  Specification

#include <nag.h>
#include <nagd06.h>
void  nag_mesh2d_front (Integer nvb, Integer nvint, Integer nvmax, Integer nedge, const Integer edge[], Integer *nv, Integer *nelt, double coor[], Integer conn[], const double weight[], Integer itrace, const char *outfile, NagError *fail)

3  Description

nag_mesh2d_front (d06acc) generates the set of interior vertices using an Advancing Front 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 Chapter 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).

4  References

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

5  Arguments

1:     nvbIntegerInput
On entry: the number of vertices in the input boundary mesh.
Constraint: nvb3.
2:     nvintIntegerInput
On entry: the number of fixed interior mesh vertices to which a weight will be applied.
Constraint: nvint0.
3:     nvmaxIntegerInput
On entry: the maximum number of vertices in the mesh to be generated.
Constraint: nvmaxnvb+nvint.
4:     nedgeIntegerInput
On entry: the number of boundary edges in the input mesh.
Constraint: nedge1.
5:     edge[3×nedge]const IntegerInput
On entry: the specification of the boundary edges. edge[j-1×3+0] and edge[j-1×3+1] contain the vertex numbers of the two end points of the jth boundary edge. edge[j-1×3+2] is a user-supplied tag for the jth boundary edge and is not used by nag_mesh2d_front (d06acc). Note that the edge vertices are numbered from 1 to nvb.
Constraint: 1edge[j-1×3+i-1]nvb and edge[j-1×3+0]edge[j-1×3+1], for i=1,2 and j=1,2,,nedge.
6:     nvInteger *Output
On exit: the total number of vertices in the output mesh (including both boundary and interior vertices). If nvb+nvint=nvmax, no interior vertices will be generated and nv=nvmax.
7:     neltInteger *Output
On exit: the number of triangular elements in the mesh.
8:     coor[2×nvmax]doubleInput/Output
On entry: coor[i-1×2+0] contains the x coordinate of the ith input boundary mesh vertex, for i=1,2,,nvb. coor[i-1×2+0] contains the x coordinate of the i-nvbth fixed interior vertex, for i=nvb+1,,nvb+nvint. For boundary and interior vertices, coor[i-1×2+1] contains the corresponding y coordinate, for i=1,2,,nvb+nvint.
On exit: coor[i-1×2+0] will contain the x coordinate of the i-nvb-nvintth generated interior mesh vertex, for i=nvb+nvint+1,,nv; while coor[i-1×2+1] will contain the corresponding y coordinate. The remaining elements are unchanged.
9:     conn[3×2×nvmax+5]IntegerOutput
On exit: the connectivity of the mesh between triangles and vertices. For each triangle j, conn[j-1×3+i-1] gives the indices of its three vertices (in anticlockwise order), for i=1,2,3 and j=1,2,,nelt. Note that the mesh vertices are numbered from 1 to nv.
10:   weight[dim]const doubleInput
Note: the dimension, dim, of the array weight must be at least max1,nvint.
On entry: 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.
Constraint: if nvint>0, weight[i-1]>0.0, for i=1,2,,nvint.
11:   itraceIntegerInput
On entry: the level of trace information required from nag_mesh2d_front (d06acc).
itrace0
No output is generated.
itrace1
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.
12:   outfileconst char *Input
On entry: the name of a file to which diagnostic output will be directed. If outfile is NULL the diagnostic output will be directed to standard output.
13:   failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, nedge=value.
Constraint: nedge1.
On entry, nvb=value.
Constraint: nvb3.
On entry, nvint=value.
Constraint: nvint0.
NE_INT_2
On entry, the endpoints of the edge j have the same index i: j=value and i=value.
NE_INT_3
On entry, nv=value, nvint=value and nvmax=value.
Constraint: nvb+nvintnvmax.
On entry, nvb=value, nvint=value and nvmax=value.
Constraint: nvmaxnvb+nvint.
NE_INT_4
On entry, EDGEi,j=value, i=value, j=value and nvb=value.
Constraint: EDGEi,j1 and EDGEi,jnvb, where EDGEi,j denotes edge[j-1×3+i-1].
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_MESH_ERROR
An error has occurred during the generation of the interior mesh. Check the inputs of the boundary.
NE_NOT_CLOSE_FILE
Cannot close file value.
NE_NOT_WRITE_FILE
Cannot open file value for writing.
NE_REAL_ARRAY_INPUT
On entry, weight[i-1]=value and i=value.
Constraint: weight[i-1]>0.0.

7  Accuracy

Not applicable.

8  Further Comments

The position of the internal vertices is a function position of the vertices on the given boundary. A fine mesh on the boundary results in a fine mesh in the interior. During the process vertices are generated on edges of the mesh Ti to obtain the mesh Ti+1 in the general incremental method (consult the d06 Chapter Introduction or George and Borouchaki (1998)).
You are advised to take care to set the boundary inputs properly, especially for a boundary with multiply connected components. The orientation of the interior boundaries should be in clockwise order and opposite to that of the exterior boundary. If the boundary has only one connected component, its orientation should be anticlockwise.

9  Example

In this example, a geometry with two holes (two wings inside an exterior circle) is meshed using a Delaunay–Voronoi method. The exterior circle is centred at the point 1.5,0.0 with a radius 4.5, the first wing begins at the origin and it is normalized, finally the last wing is also normalized and begins at the point 0.8,-0.3. To be able to carry out some realistic computation on that geometry, some interior points have been introduced to have a finer mesh in the wake of those airfoils.
The boundary mesh has 120 vertices and 120 edges (see Figure 1 top). Note that the particular mesh generated could be sensitive to the machine precision and therefore may differ from one implementation to another.

9.1  Program Text

Program Text (d06acce.c)

9.2  Program Data

Program Data (d06acce.d)

9.3  Program Results

Program Results (d06acce.r)

The boundary mesh (top), the interior mesh (bottom) of a  double wing inside a circle geometry
Figure 1: The boundary mesh (top), the interior mesh (bottom) of a
double wing inside a circle geometry

nag_mesh2d_front (d06acc) (PDF version)
d06 Chapter Contents
d06 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012