D06DBF joins together (restitches) two adjacent, or overlapping, meshes.
| SUBROUTINE D06DBF ( | EPS, NV1, NELT1, NEDGE1, COOR1, EDGE1, CONN1, REFT1, NV2, NELT2, NEDGE2, COOR2, EDGE2, CONN2, REFT2, NV3, NELT3, NEDGE3, COOR3, EDGE3, CONN3, REFT3, ITRACE, IWORK, LIWORK, IFAIL) |
| INTEGER | NV1, NELT1, NEDGE1, EDGE1(3,NEDGE1), CONN1(3,NELT1), REFT1(NELT1), NV2, NELT2, NEDGE2, EDGE2(3,NEDGE2), CONN2(3,NELT2), REFT2(NELT2), NV3, NELT3, NEDGE3, EDGE3(3,*), CONN3(3,*), REFT3(*), ITRACE, IWORK(LIWORK), LIWORK, IFAIL |
| double precision | EPS, COOR1(2,NV1), COOR2(2,NV2), COOR3(2,*) |
D06DBF joins together two adjacent, or overlapping, meshes. If the two meshes are adjacent then vertices belonging to the part of the boundary forming the common interface should coincide. If the two meshes overlap then vertices and triangles in the overlapping zone should coincide too.
This routine is partly derived from material in the MODULEF package from INRIA (Institut National de Recherche en Informatique et Automatique).
None.
- 1: EPS – double precisionInput
On entry: the relative precision of the restitching of the two input meshes (see
Section 8).
Suggested value:
0.001.
Constraint:
EPS>0.0.
- 2: NV1 – INTEGERInput
On entry:
the total number of vertices in the first input mesh.
Constraint:
NV1≥3.
- 3: NELT1 – INTEGERInput
On entry:
the number of triangular elements in the first input mesh.
Constraint:
NELT1≤2×NV1-1.
- 4: NEDGE1 – INTEGERInput
On entry:
the number of boundary edges in the first input mesh.
Constraint:
NEDGE1≥1.
- 5: COOR1(2,NV1) – double precision arrayInput
-
On entry: COOR11i contains the x co-ordinate of the ith vertex of the first input mesh, for i=1,2,…,NV1; while COOR12i contains the corresponding y co-ordinate.
- 6: EDGE1(3,NEDGE1) – INTEGER arrayInput
-
On entry: the specification of the boundary edges of the first input mesh. EDGE11j and EDGE12j contain the vertex numbers of the two end points of the jth boundary edge. EDGE13j is a user-supplied tag for the jth boundary edge.
Constraint:
1≤EDGE1ij≤NV1 and EDGE11j≠EDGE12j, for i=1,2 and j=1,2,…,NEDGE1.
- 7: CONN1(3,NELT1) – INTEGER arrayInput
-
On entry: the connectivity between triangles and vertices of the first input mesh. For each triangle j, CONN1ij gives the indices of its three vertices (in anticlockwise order), for i=1,2,3 and j=1,2,…,NELT1.
Constraints:
- 1≤CONN1ij≤NV1;
- CONN11j≠CONN12j;
- CONN11j≠CONN13j and CONN12j≠CONN13j, for i=1,2,3 and j=1,2,…,NELT1.
- 8: REFT1(NELT1) – INTEGER arrayInput
On entry: REFT1k contains the user-supplied tag of the kth triangle from the first input mesh, for k=1,2,…,NELT1.
- 9: NV2 – INTEGERInput
On entry:
the total number of vertices in the second input mesh.
Constraint:
NV2≥3.
- 10: NELT2 – INTEGERInput
On entry:
the number of triangular elements in the second input mesh.
Constraint:
NELT2≤2×NV2-1.
- 11: NEDGE2 – INTEGERInput
On entry:
the number of boundary edges in the second input mesh.
Constraint:
NEDGE2≥1.
- 12: COOR2(2,NV2) – double precision arrayInput
-
On entry: COOR21i contains the x co-ordinate of the ith vertex of the second input mesh, for i=1,2,…,NV2; while COOR22i contains the corresponding y co-ordinate.
- 13: EDGE2(3,NEDGE2) – INTEGER arrayInput
-
On entry: the specification of the boundary edges of the second input mesh. EDGE21j and EDGE22j contain the vertex numbers of the two end points of the jth boundary edge. EDGE23j is a user-supplied tag for the jth boundary edge.
Constraint:
1≤EDGE2ij≤NV2 and EDGE21j≠EDGE22j, for i=1,2 and j=1,2,…,NEDGE2.
- 14: CONN2(3,NELT2) – INTEGER arrayInput
-
On entry: the connectivity between triangles and vertices of the second input mesh. For each triangle j, CONN2ij gives the indices of its three vertices (in anticlockwise order), for i=1,2,3 and j=1,2,…,NELT2.
Constraints:
- 1≤CONN2ij≤NV2;
- CONN21j≠CONN22j;
- CONN21j≠CONN23j and CONN22j≠CONN23j, for i=1,2,3 and j=1,2,…,NELT2.
- 15: REFT2(NELT2) – INTEGER arrayInput
On entry: REFT2k contains the user-supplied tag of the kth triangle from the second input mesh, for k=1,2,…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,*) – double precision arrayOutput
Note: the second dimension of the array
COOR3
must be at least
NV1+NV2. This may be reduced to
NV3 once that value is known.
On exit: COOR31i will contain the x co-ordinate of the ith vertex of the resulting mesh, for i=1,2,…,NV3; while COOR32i will contain the corresponding y co-ordinate.
- 20: EDGE3(3,*) – INTEGER arrayOutput
Note: the second dimension of the array
EDGE3
must be at least
NEDGE1+NEDGE2. This may be reduced to
NEDGE3 once that value is known.
On exit: the specification of the boundary edges of the resulting mesh.
EDGE3ij will contain the vertex number of the
ith end point (
i=1,2) of the
jth boundary or interface edge.
If the two meshes overlap, EDGE33j 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 jth edge is part of the partition interface, then EDGE33j will contain the value 1000×k1+k2 where k1 and k2 are the tags for the same edge of the first and the second mesh respectively; |
| (ii) |
otherwise, EDGE33j 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
NELT1+NELT2. This may be reduced to
NELT3 once that value is known.
On exit: the connectivity between triangles and vertices of the resulting mesh. CONN3ij will give the indices of its three vertices (in anticlockwise order), for i=1,2,3 and j=1,2,…,NELT3.
- 22: REFT3(*) – INTEGER arrayOutput
Note: the dimension of the array
REFT3
must be at least
NELT1+NELT2. This may be reduced to
NELT3 once that value is known.
On exit: if the two meshes form a partition, REFT3k will contain the same tag as the corresponding triangle belonging to the first or the second input mesh, for k=1,2,…,NELT3. If the two meshes overlap, then REFT3k will contain the value 1000×k1+k2 where k1 and k2 are the user-supplied tags for the same triangle of the first and the second mesh respectively, for k=1,2,…,NELT3.
- 23: ITRACE – INTEGERInput
On entry: the level of trace information required from D06DBF.
- ITRACE≤0
- No output is generated.
- ITRACE≥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:
LIWORK≥2×NV1+3×NV2+NELT1+NELT2+NEDGE1+NEDGE2+1024.
- 26: IFAIL – INTEGERInput/Output
-
On entry:
IFAIL must be set to
0,
-1 or 1. If you are unfamiliar with this parameter you should refer to
Section 3.3 in the Essential Introduction for details.
On exit:
IFAIL=0 unless the routine detects an error (see
Section 6).
For environments where it might be inappropriate to halt program execution when an error is detected, the value
-1 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 -1 or 1 is used it is essential to test the value of IFAIL on exit.
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Not applicable.
D06DBF finds all the common vertices between the two input meshes using the relative precision of the restitching parameter
EPS. You are advised to vary the value of
EPS in the neighbourhood of
0.001 with
ITRACE≥1 to get the optimal value for the meshes under consideration.
For this routine two examples are presented. There is a single example program for D06DBF, with a main program and the code to solve the two example problems given in Example 1 (EX1) and Example 2 (EX2).
This example involves the unit square
0,12 meshed uniformly, and then translated by a vector
u→=
u1
u2
(using
D06DAF). This translated mesh is then restitched with the original mesh. Two cases are considered:
| (a) |
overlapping meshes (u1=15.0, u2=17.0), |
| (b) |
partitioned meshes (u1=19.0, u2=0.0). |
The mesh on the unit square has
400 vertices,
722 triangles and its boundary has
76 edges. In the overlapping case the resulting geometry is shown in
Figure 1 and
Figure 2. The resulting geometry for the partitioned meshes is shown in
Figure 3.
This example restitches three geometries by calling the routine D06DBF twice. The result is a mesh with three partitions. The first geometry is meshed by the Delaunay–Voronoi process (using
D06ABF), the second one meshed by an Advancing Front algorithm (using
D06ACF), while the third one is the result of a rotation (by
-π/2) of the second one (using
D06DAF). The resulting geometry is shown in
Figure 4 and
Figure 5.
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
