Civil Engineering Reference
In-Depth Information
Table 8.22
Summary of the statistics of the examples 1 to 5
Example
1
2
3
4
5
Objects
Plate
Cube
Plate
String
String
String
Hand
Plate
Cuboid
Machine
NN
192
125
2255
3366
3366
3366
6222
1953
60
21,241
NE
588
288
9600
11,248
11,248
11,248
22,391
7200
144
71,222
NF
308
240
2400
5226
5226
5226
12,440
2800
104
39,200
NI
192
421
613
744
624
NL
4
7
11
5
3
NFT
92
96
202
258
336
334
513
280
35
548
NZ
5
4
8
7
12
12
6
6
4
2
NR 1 4 11 2 1
NT 1570 22,624 24,948 25,099 73,931
NB 788 7896 11,120 13,928 38,696
T1 0.01 0.01 0.01 0.02 0.02
T2 0.10 0.26 0.29 0.48 0.82
Figures 8.123a-f 8.124a-i 8.125a-d 8.126a-e 8.127a-d
Note: NN = number of nodes in the object; NE = number of tetrahedral elements in the object; NF = number of triangles
on the boundary surface; NI = number of intersection points/segments; NL = number of intersection loops; NFT = number
of faces triangulated; NZ = number of zones (patches) on the boundary surface; NR = number of regions (volumes) of
intersection; NB = number of faces on the boundary of the merged object; T1 = CPU time in seconds for intersection;
T2 = total CPU time for mesh merging.
up four intersection loops, which divide the boundary of the hollow cube into four zones
(patches) and that of the plate into five zones, as shown in Figure 8.123a and b. One region
in the form of a shortened hollow cube bounded by 528 triangles from four cut surfaces and
four intersection loops is recovered, as shown in Figure 8.123c. The hollow cube, in which
there are fewer elements, is taken as the slave object. When compatibility is restored on the
top and the bottom surfaces of the region of intersection, the volume of intersection could be
taken out from the hollow cube, as shown in Figure 8.123d. On the other hand, if the solid
plate is taken as the slave object, the volume of intersection can be taken from the plate to
divide it into two regions, as shown in Figure 8.123e. The hollow cube and the solid plate
could be merged either by putting objects in Figure 8.123a and d or objects in Figure 8.123b
and e together, and the resulting object is shown in Figure 8.123f.
The penetration of a string into a wooden board is considered in Example 2. Full details
for all the steps of the merging process will be given in this interesting example as many
regions of intersection are found in the intersection of the objects. The string in the form
of a curved solid object is downloaded from the public domain (INRIA GAMMA 2007),
which consists of 3366 nodes, 11,248 tetrahedral elements and 5226 triangular facets on the
boundary surface. The board is first decomposed into hexahedral elements, each of which
is further divided into six tetrahedral elements, and the resulting tetrahedral mesh consists
of 2255 nodes, 9600 tetrahedra and 2400 triangles on the boundary surface. In the inter-
action of these two objects, there are 421 intersection points (segments) from which seven
closed loops can be retrieved, as shown in Figure 8.124a and b. The intersection segments
cut across 202 triangles on the surface of the wooded board, each of which is triangulated
in turn, and new tetrahedral elements are formed. The modified mesh consists of 10,615
tetrahedra and 3242 triangles on the surface, as shown in Figure 8.124c. As for the string,
258 triangles are intersected by the loops, and the intersected triangles are triangulated to
incorporate the intersection segment into the tetrahedral mesh. The triangular facets on the
boundary surface increases from 5226 to 6068, as shown in Figure 8.124d. The boundary
