NAG Library Function Document

nag_mesh2d_delaunay (d06abc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{nvb}$ – IntegerInput

On entry: the number of vertices in the input boundary mesh.

Constraint: $\mathbf{nvb}\ge 3$.

2:    $\mathbf{nvint}$ – IntegerInput

On entry: the number of fixed interior mesh vertices to which a weight will be applied.

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

3:    $\mathbf{nvmax}$ – IntegerInput

On entry: the maximum number of vertices in the mesh to be generated.

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

4:    $\mathbf{nedge}$ – IntegerInput

On entry: the number of boundary edges in the input mesh.

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

5:    $\mathbf{edge}\left[3\times \mathbf{nedge}\right]$ – const IntegerInput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{edge}\left[\left(j-1\right)\times 3+i-1\right]$.

On entry: the specification of the boundary edges. $\mathbf{edge}\left[\left(j-1\right)\times 3\right]$ and $\mathbf{edge}\left[\left(j-1\right)\times 3+1\right]$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{edge}\left[\left(j-1\right)\times 3+2\right]$ is a user-supplied tag for the $j$th boundary edge and is not used by nag_mesh2d_delaunay (d06abc). Note that the edge vertices are numbered from $1$ to nvb.

Constraint: $1\le \mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]\le \mathbf{nvb}$ and $\mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3\right]\ne \mathbf{edge}\left[\left(\mathit{j}-1\right)\times 3+1\right]$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{nedge}$.

6:    $\mathbf{nv}$ – Integer *Output

On exit: the total number of vertices in the output mesh (including both boundary and interior vertices). If $\mathbf{nvb}+\mathbf{nvint}=\mathbf{nvmax}$, no interior vertices will be generated and $\mathbf{nv}=\mathbf{nvmax}$.

7:    $\mathbf{nelt}$ – Integer *Output

On exit: the number of triangular elements in the mesh.

8:    $\mathbf{coor}\left[2\times \mathbf{nvmax}\right]$ – doubleInput/Output

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{coor}\left[\left(j-1\right)\times 2+i-1\right]$.

On entry: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2\right]$ contains the $x$ coordinate of the $\mathit{i}$th input boundary mesh vertex, for $\mathit{i}=1,2,\dots ,\mathbf{nvb}$. $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2\right]$ contains the $x$ coordinate of the $\left(\mathit{i}-\mathbf{nvb}\right)$th fixed interior vertex, for $\mathit{i}=\mathbf{nvb}+1,\dots ,\mathbf{nvb}+\mathbf{nvint}$. For boundary and interior vertices, $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2+1\right]$ contains the corresponding $y$ coordinate, for $\mathit{i}=1,2,\dots ,\mathbf{nvb}+\mathbf{nvint}$.

On exit: $\mathbf{coor}\left[\left(\mathit{i}-1\right)\times 2\right]$ will contain the $x$ coordinate of the $\left(\mathit{i}-\mathbf{nvb}-\mathbf{nvint}\right)$th generated interior mesh vertex, for $\mathit{i}=\mathbf{nvb}+\mathbf{nvint}+1,\dots ,\mathbf{nv}$; while $\mathbf{coor}\left[\left(i-1\right)\times 2+1\right]$ will contain the corresponding $y$ coordinate. The remaining elements are unchanged.

9:    $\mathbf{conn}\left[3\times \left(2\times \mathbf{nvmax}+5\right)\right]$ – IntegerOutput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{conn}\left[\left(j-1\right)\times 3+i-1\right]$.

On exit: the connectivity of the mesh between triangles and vertices. For each triangle $\mathit{j}$, $\mathbf{conn}\left[\left(\mathit{j}-1\right)\times 3+\mathit{i}-1\right]$ gives the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{nelt}$. Note that the mesh vertices are numbered from $1$ to nv.

10:  $\mathbf{weight}\left[\mathit{dim}\right]$ – const doubleInput

Note: the dimension, dim, of the array weight must be at least $\max \left(1,\mathbf{nvint}\right)$.

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 $\mathbf{nvint}>0$, $\mathbf{weight}\left[\mathit{i}-1\right]>0.0$, for $\mathit{i}=1,2,\dots ,\mathbf{nvint}$.

11:  $\mathbf{npropa}$ – IntegerInput

On entry: 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 Section 9.

Constraint: $\mathbf{npropa}\ne 0$.

12:  $\mathbf{itrace}$ – IntegerInput

On entry: the level of trace information required from nag_mesh2d_delaunay (d06abc).

$\mathbf{itrace}\le 0$

No output is generated.

$\mathbf{itrace}\ge 1$

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 $\mathbf{itrace}=0$, unless you are experienced with finite element mesh generation.

13:  $\mathbf{outfile}$ – const 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.

14:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

On entry, $\mathbf{nedge}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nedge}\ge 1$.

On entry, $\mathbf{npropa}=0$.

On entry, $\mathbf{nvb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nvb}\ge 3$.

On entry, $\mathbf{nvint}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nvint}\ge 0$.

NE_INT_2

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

NE_INT_3

On entry, $\mathbf{nvb}=〈\mathit{\text{value}}〉$, $\mathbf{nvint}=〈\mathit{\text{value}}〉$ and $\mathbf{nvmax}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nvmax}\ge \mathbf{nvb}+\mathbf{nvint}$.

NE_INT_4

On entry, $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)=〈\mathit{\text{value}}〉$, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathit{J}=〈\mathit{\text{value}}〉$ and $\mathbf{nvb}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\ge 1$ and $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)\le \mathbf{nvb}$, where $\mathbf{edge}\left(\mathit{I},\mathit{J}\right)$ denotes $\mathbf{edge}\left[\left(\mathit{J}-1\right)\times 3+\mathit{I}-1\right]$.

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.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_MESH_ERROR

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

An error has occurred during the generation of the interior mesh. Check the inputs of the boundary.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NOT_CLOSE_FILE

Cannot close file $〈\mathit{\text{value}}〉$.

NE_NOT_WRITE_FILE

Cannot open file $〈\mathit{\text{value}}〉$ for writing.

NE_REAL_ARRAY_INPUT

On entry, $\mathbf{weight}\left[\mathit{I}-1\right]=〈\mathit{\text{value}}〉$ and $\mathit{I}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{weight}\left[\mathit{I}-1\right]>0.0$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (d06abce.c)

10.2

Program Data

Program Data (d06abce.d)

10.3

Program Results

Program Results (d06abce.r)