Civil Engineering Reference
In-Depth Information
(i)
Figure 8.124
(Continued) Merging of a wooden board and a string. (i) Final mesh of merging the board and
the string.
Table 8.23
Relationship between intersection loops, surfaces and regions for example 2
Loop
Master surfaces
Slave surfaces
Cut surfaces
Region
L
1
S
1
S
2
S
3
S
2
S
3
R
1
S
4
S
4
S
5
S
5
L
2
S
1
S
3
S
3
R
2
S
5
L
3
S
1
S
4
S
5
S
6
S
4
R
2
L
4
S
1
S
5
S
6
S
7
S
5
S
7
R
3
L
5
S
1
S
6
S
3
S
6
S
3
R
1
S
1
S
2
L
6
S
1
S
7
S
1
S
7
S
2
R
4
S
6
S
2
L
7
S
1
S
8
S
2
S
8
R
4
follows a similar path based on the relationship between intersection loops and cut sur-
faces, as depicted in Table 8.23. Finally, all four region
s
of intersection are recovered such
that R
2
is b
o
unded by 356 triangles from S
3
, S
4
and
S
5
; R
3
is b
o
unded by 314 triangles
from S
5
and
S
7
; and R
4
is bounded by 376 triangles from S
7
, S
8
and
S
2
. Cavities are created at
the cutting surfaces of the regions by taking tetrahedra away from the slave object (string),
and MG is carried out at the cavities so as to restore compatibility at the cutting surfaces S
2
,
S
3
, S
4
, S
5
, S
6
, S
7
and S
8
of the master object, as shown in Figure 8.124g. A new object or mesh
is resulted by subtracting all the regions of intersection from the slave object, as shown in
Figure 8.124h. The reduced slave object can now be readily combined with the master object
with full compatibility at the cutting surfaces, as shown in Figure 8.124i.
Example 3 demonstrates the intersection of two identical strings put rather arbitrarily
together. Owing to the twisting of the curved boundary of the two strings, there are many
intersection segments that could be grouped into 11 loops. The boundaries of the master
object and the slave object are each partitioned into 12 zones, as shown in Figure 8.125a
and b. Eleven regions are identified, as shown in Figure 8.125c, and the merging of the two
strings is shown in Figure 8.125d.
A hand penetrating a flat board is considered in Example 4. The hand, which consists
of 6222 nodes, 22,391 tetrahedra and 12,440 triangles on the boundary surface, is down-
loaded from the public domain. The board is created by first generating hexahedral elements,
