NAG Library Routine Document

D06DBF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     EPS – REAL (KIND=nag_wp)Input

On entry: the relative precision of the restitching of the two input meshes (see Section 8).

Suggested value: $0.001$.

Constraint: $\mathbf{EPS}>0.0$.

2:     NV1 – INTEGERInput

On entry: the total number of vertices in the first input mesh.

Constraint: $\mathbf{NV1}\ge 3$.

3:     NELT1 – INTEGERInput

On entry: the number of triangular elements in the first input mesh.

Constraint: $\mathbf{NELT1}\le 2\times \mathbf{NV1}-1$.

4:     NEDGE1 – INTEGERInput

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

Constraint: $\mathbf{NEDGE1}\ge 1$.

5:     COOR1($2$,NV1) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{COOR1}\left(1,\mathit{i}\right)$ contains the $x$ coordinate of the $\mathit{i}$th vertex of the first input mesh, for $\mathit{i}=1,2,\dots ,\mathbf{NV1}$; while $\mathbf{COOR1}\left(2,\mathit{i}\right)$ contains the corresponding $y$ coordinate.

6:     EDGE1($3$,NEDGE1) – INTEGER arrayInput

On entry: the specification of the boundary edges of the first input mesh. $\mathbf{EDGE1}\left(1,j\right)$ and $\mathbf{EDGE1}\left(2,j\right)$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{EDGE1}\left(3,j\right)$ is a user-supplied tag for the $j$th boundary edge.

Constraint: $1\le \mathbf{EDGE1}\left(\mathit{i},\mathit{j}\right)\le \mathbf{NV1}$ and $\mathbf{EDGE1}\left(1,\mathit{j}\right)\ne \mathbf{EDGE1}\left(2,\mathit{j}\right)$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{NEDGE1}$.

7:     CONN1($3$,NELT1) – INTEGER arrayInput

On entry: the connectivity between triangles and vertices of the first input mesh. For each triangle $\mathit{j}$, $\mathbf{CONN1}\left(\mathit{i},\mathit{j}\right)$ gives the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{NELT1}$.

Constraints:

• $1\le \mathbf{CONN1}\left(i,j\right)\le \mathbf{NV1}$;
• $\mathbf{CONN1}\left(1,j\right)\ne \mathbf{CONN1}\left(2,j\right)$;
• $\mathbf{CONN1}\left(1,\mathit{j}\right)\ne \mathbf{CONN1}\left(3,\mathit{j}\right)$ and $\mathbf{CONN1}\left(2,\mathit{j}\right)\ne \mathbf{CONN1}\left(3,\mathit{j}\right)$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{NELT1}$.

8:     REFT1(NELT1) – INTEGER arrayInput

On entry: $\mathbf{REFT1}\left(\mathit{k}\right)$ contains the user-supplied tag of the $\mathit{k}$th triangle from the first input mesh, for $\mathit{k}=1,2,\dots ,\mathbf{NELT1}$.

9:     NV2 – INTEGERInput

On entry: the total number of vertices in the second input mesh.

Constraint: $\mathbf{NV2}\ge 3$.

10:   NELT2 – INTEGERInput

On entry: the number of triangular elements in the second input mesh.

Constraint: $\mathbf{NELT2}\le 2\times \mathbf{NV2}-1$.

11:   NEDGE2 – INTEGERInput

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

Constraint: $\mathbf{NEDGE2}\ge 1$.

12:   COOR2($2$,NV2) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{COOR2}\left(1,\mathit{i}\right)$ contains the $x$ coordinate of the $\mathit{i}$th vertex of the second input mesh, for $\mathit{i}=1,2,\dots ,\mathbf{NV2}$; while $\mathbf{COOR2}\left(2,\mathit{i}\right)$ contains the corresponding $y$ coordinate.

13:   EDGE2($3$,NEDGE2) – INTEGER arrayInput

On entry: the specification of the boundary edges of the second input mesh. $\mathbf{EDGE2}\left(1,j\right)$ and $\mathbf{EDGE2}\left(2,j\right)$ contain the vertex numbers of the two end points of the $j$th boundary edge. $\mathbf{EDGE2}\left(3,j\right)$ is a user-supplied tag for the $j$th boundary edge.

Constraint: $1\le \mathbf{EDGE2}\left(\mathit{i},\mathit{j}\right)\le \mathbf{NV2}$ and $\mathbf{EDGE2}\left(1,\mathit{j}\right)\ne \mathbf{EDGE2}\left(2,\mathit{j}\right)$, for $\mathit{i}=1,2$ and $\mathit{j}=1,2,\dots ,\mathbf{NEDGE2}$.

14:   CONN2($3$,NELT2) – INTEGER arrayInput

On entry: the connectivity between triangles and vertices of the second input mesh. For each triangle $\mathit{j}$, $\mathbf{CONN2}\left(\mathit{i},\mathit{j}\right)$ gives the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{NELT2}$.

Constraints:

• $1\le \mathbf{CONN2}\left(i,j\right)\le \mathbf{NV2}$;
• $\mathbf{CONN2}\left(1,j\right)\ne \mathbf{CONN2}\left(2,j\right)$;
• $\mathbf{CONN2}\left(1,\mathit{j}\right)\ne \mathbf{CONN2}\left(3,\mathit{j}\right)$ and $\mathbf{CONN2}\left(2,\mathit{j}\right)\ne \mathbf{CONN2}\left(3,\mathit{j}\right)$, for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{NELT2}$.

15:   REFT2(NELT2) – INTEGER arrayInput

On entry: $\mathbf{REFT2}\left(\mathit{k}\right)$ contains the user-supplied tag of the $\mathit{k}$th triangle from the second input mesh, for $\mathit{k}=1,2,\dots ,\mathbf{NELT2}$.

16:   NV3 – INTEGEROutput

On exit: the total number of vertices in the resulting mesh.

17:   NELT3 – INTEGEROutput

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

18:   NEDGE3 – INTEGEROutput

On exit: the number of boundary edges in the resulting mesh.

19:   COOR3($2$,$*$) – REAL (KIND=nag_wp) arrayOutput

Note: the second dimension of the array COOR3 must be at least $\mathbf{NV1}+\mathbf{NV2}$.

On exit: $\mathbf{COOR3}\left(1,\mathit{i}\right)$ will contain the $x$ coordinate of the $\mathit{i}$th vertex of the resulting mesh, for $\mathit{i}=1,2,\dots ,\mathbf{NV3}$; while $\mathbf{COOR3}\left(2,i\right)$ will contain the corresponding $y$ coordinate.

20:   EDGE3($3$,$*$) – INTEGER arrayOutput

Note: the second dimension of the array EDGE3 must be at least $\mathbf{NEDGE1}+\mathbf{NEDGE2}$. This may be reduced to $\mathbf{NEDGE3}$ once that value is known.

On exit: the specification of the boundary edges of the resulting mesh. $\mathbf{EDGE3}\left(i,j\right)$ will contain the vertex number of the $i$th end point ($i=1,2$) of the $j$th boundary or interface edge.

If the two meshes overlap, $\mathbf{EDGE3}\left(3,j\right)$ will contain the same tag as the corresponding edge belonging to the first and/or the second input mesh.

If the two meshes are adjacent,

(i)	if the $j$th edge is part of the partition interface, then $\mathbf{EDGE3}\left(3,j\right)$ will contain the value $1000\times k_1+k_2$ where $k_1$ and $k_2$ are the tags for the same edge of the first and the second mesh respectively;
(ii)	otherwise, $\mathbf{EDGE3}\left(3,j\right)$ will contain the same tag as the corresponding edge belonging to the first and/or the second input mesh.

21:   CONN3($3$,$*$) – INTEGER arrayOutput

Note: the second dimension of the array CONN3 must be at least $\mathbf{NELT1}+\mathbf{NELT2}$. This may be reduced to $\mathbf{NELT3}$ once that value is known.

On exit: the connectivity between triangles and vertices of the resulting mesh. $\mathbf{CONN3}\left(\mathit{i},\mathit{j}\right)$ will give the indices of its three vertices (in anticlockwise order), for $\mathit{i}=1,2,3$ and $\mathit{j}=1,2,\dots ,\mathbf{NELT3}$.

22:   REFT3($*$) – INTEGER arrayOutput

Note: the dimension of the array REFT3 must be at least $\mathbf{NELT1}+\mathbf{NELT2}$. This may be reduced to $\mathbf{NELT3}$ once that value is known.

On exit: if the two meshes form a partition, $\mathbf{REFT3}\left(\mathit{k}\right)$ will contain the same tag as the corresponding triangle belonging to the first or the second input mesh, for $\mathit{k}=1,2,\dots ,\mathbf{NELT3}$. If the two meshes overlap, then $\mathbf{REFT3}\left(\mathit{k}\right)$ will contain the value $1000\times {\mathit{k}}_1+{\mathit{k}}_2$ where ${\mathit{k}}_1$ and ${\mathit{k}}_2$ are the user-supplied tags for the same triangle of the first and the second mesh respectively, for $\mathit{k}=1,2,\dots ,\mathbf{NELT3}$.

23:   ITRACE – INTEGERInput

On entry: the level of trace information required from D06DBF.

$\mathbf{ITRACE}\le 0$

No output is generated.

$\mathbf{ITRACE}\ge 1$

Details about the common vertices, edges and triangles to both meshes are printed on the current advisory message unit (see X04ABF).

24:   IWORK(LIWORK) – INTEGER arrayWorkspace

25:   LIWORK – INTEGERInput

On entry: the dimension of the array IWORK as declared in the (sub)program from which D06DBF is called.

Constraint: $\mathbf{LIWORK}\ge 2\times \mathbf{NV1}+3\times \mathbf{NV2}+\mathbf{NELT1}+\mathbf{NELT2}+\mathbf{NEDGE1}+\mathbf{NEDGE2}+1024$.

26:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	$\mathbf{EPS}\le 0.0$,
or	$\mathbf{NV1}<3$,
or	$\mathbf{NELT1}>2\times \mathbf{NV1}-1$,
or	$\mathbf{NEDGE1}<1$,
or	$\mathbf{EDGE1}\left(i,j\right)<1$ or $\mathbf{EDGE1}\left(i,j\right)>\mathbf{NV1}$ for some $i=1,2$ and $j=1,2,\dots ,\mathbf{NEDGE1}$,
or	$\mathbf{EDGE1}\left(1,j\right)=\mathbf{EDGE1}\left(2,j\right)$ for some $j=1,2,\dots ,\mathbf{NEDGE1}$,
or	$\mathbf{CONN1}\left(i,j\right)<1$ or $\mathbf{CONN1}\left(i,j\right)>\mathbf{NV1}$ for some $i=1,2,3$ and $j=1,2,\dots ,\mathbf{NELT1}$,
or	$\mathbf{CONN1}\left(1,j\right)=\mathbf{CONN1}\left(2,j\right)$ or $\mathbf{CONN1}\left(1,j\right)=\mathbf{CONN1}\left(3,j\right)$ or $\mathbf{CONN1}\left(2,j\right)=\mathbf{CONN1}\left(3,j\right)$ for some $j=1,2,\dots ,\mathbf{NELT1}$,
or	$\mathbf{NV2}<3$,
or	$\mathbf{NELT2}>2\times \mathbf{NV2}-1$,
or	$\mathbf{NEDGE2}<1$,
or	$\mathbf{EDGE2}\left(i,j\right)<1$ or $\mathbf{EDGE2}\left(i,j\right)>\mathbf{NV2}$ for some $i=1,2$ and $j=1,2,\dots ,\mathbf{NEDGE2}$,
or	$\mathbf{EDGE2}\left(1,j\right)=\mathbf{EDGE2}\left(2,j\right)$ for some $j=1,2,\dots ,\mathbf{NEDGE2}$,
or	$\mathbf{CONN2}\left(i,j\right)<1$ or $\mathbf{CONN2}\left(i,j\right)>\mathbf{NV2}$ for some $i=1,2,3$ and $j=1,2,\dots ,\mathbf{NELT2}$,
or	$\mathbf{CONN2}\left(1,j\right)=\mathbf{CONN2}\left(2,j\right)$ or $\mathbf{CONN2}\left(1,j\right)=\mathbf{CONN2}\left(3,j\right)$ or $\mathbf{CONN2}\left(2,j\right)=\mathbf{CONN2}\left(3,j\right)$ for some $j=1,2,\dots ,\mathbf{NELT2}$,
or	$\mathbf{LIWORK}<2\times \mathbf{NV1}+3\times \mathbf{NV2}+\mathbf{NELT1}+\mathbf{NELT2}+\mathbf{NEDGE1}+\mathbf{NEDGE2}+1024$.

$\mathbf{IFAIL}=2$

Using the input precision EPS, the routine has detected fewer than two coincident vertices between the two input meshes. You are advised to try another value of EPS; if this error still occurs the two meshes are probably not stitchable.

$\mathbf{IFAIL}=3$

A serious error has occurred in an internal call to the restitching routine. You should check the input of the two meshes, especially the edge/vertex and/or the triangle/vertex connectivities. If the problem persists, contact NAG.

$\mathbf{IFAIL}=4$

The routine has detected a different number of coincident triangles from the two input meshes in the overlapping zone. You should check the input of the two meshes, especially the triangle/vertex connectivities.

$\mathbf{IFAIL}=5$

The routine has detected a different number of coincident edges from the two meshes on the partition interface. You should check the input of the two meshes, especially the edge/vertex connectivities.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (d06dbfe.f90)

9.2  Program Data

Program Data (d06dbfe.d)

9.3  Program Results

Program Results (d06dbfe.r)

Figure 1: The boundary and the interior interfaces of the two partitioned squares geometry

Figure 2: The interior mesh of the two partitioned squares geometry

Figure 3: The boundary and the interior interfaces (left); the interior mesh (right)
of the two overlapping squares geometry

Figure 4: The boundary and the interior interfaces of the double restitched geometry

Figure 5: The interior mesh of the double restitched geometry