Civil Engineering Reference
In-Depth Information
413 nodes and 822 triangles. There are merely 11 points in the initial background Delaunay
mesh, to which the boundary surface of the screw model is inserted to produce a Delaunay
mesh of 424 nodes and 2807 tetrahedra. Seventy-two boundary edges out of 1273 are miss-
ing in the first triangulation. In spite of fewer triangles on the initial boundary surface, the
recovery process requires 11 triangulations before all 1950 boundary faces are recovered in
the final Delaunay mesh of 988 nodes and 5896 tetrahedral elements, as shown in Figure 5.60.
The convergence characteristics and the statistics of the important parameters of the three
examples are listed in Table 5.3.
Table 5.3
Convergence statistics of examples 1, 2 and 3
Example 1
Example 2
Example 3
Object
String
Hand
Screw
Number of nodes
2613
6222
413
Number of triangles
5226
12,440
822
Number of edges
7839
18,660
1233
Number of spatial points
300
967
11
DT1:
Number of points
2913
7189
424
Number of tetrahedra
23,503
43,205
2807
Number of missing edges
1074
17
72
DT2:
Number of points
3987
7206
601
Number of tetrahedra
32,804
43,306
3824
Number of missing edges
462
2
150
DT3:
Number of points
4449
7208
763
Number of tetrahedra
35,072
43,315
4631
Number of missing edges
61
1
30
DT4:
Number of points
4510
7209
798
Number of tetrahedra
35,434
43,320
4842
Number of missing edges
15
0
44
Number of missing faces
0
0
16
Number of triangles
8420
12,554
1570
DT5:
Number of points
4525
864
Number of tetrahedra
35,535
5192
Number of missing edges
0
30
Number of missing faces
0
12
Number of triangles
8450
1702
DT =
Delaunay triangulation
DT10:
Number of points
987
Number of tetrahedra 5889
Number of missing edges 1
DT11:
Number of points
988
Number of tetrahedra 5896
Number of missing edges 0
Number of missing faces 0
Number of triangles 1950
Note: Number of missing faces = missing faces not connected to missing
edges; Number of triangles = number of triangles on the refined boundary
surface.
