Civil Engineering Reference
In-Depth Information
Seed triangle
Intersection loops
Figure 8.112
Partition into zones by marching towards the bounding loops.
S
1
Ω
S
2
S
1
Ω
S
2
V
S
3
S
3
Figure 8.113
Region of intersection bounded by surface patches.
surface patch, and each triangle in this patch will be given the same surface label. The same
procedure can be repeated when there are triangular elements remaining on the boundary
surface unlabelled. Again, any remaining triangular element could be taken as the seed ele-
ment to grow into
a
nother surface patch. When all the triangular facets on the boundary
surfaces ∂Ω and
∂
have been processed, each of the boundary surface will be partitioned
into a number of surface patches by the intersection loops, as shown in Figure 8.112.
With
t
he introduction of boundary-surface partitio
n
by intersection loops into patches
S
i
and
S
i
, the volume of intersection between Ω and can be conven
ie
ntly identified and
defined. Let V be one
o
f the regions of intersection between Ω and ; V is bounded by
surfa
c
e patches S
i
and
S
i
. As shown in Fig
u
re 8.113, V is bounded by surface patches S
2
, S
3
and
S
2
from ∂Ω and
∂
. Objects Ω and can be merged together by ensuring that each
intersection region V is compatible at the boundary-surface patches.
8.6.2.4 Identification of intersection volumes (regions)
The identification of regions of intersection between two tetrahedral meshes is b
a
sed on the
obser
va
tion that each intersection region is bounded by surface patches Si
i
and
S
i
from ∂Ω
and
∂
separated by intersection loops. Starting from intersection loop,
ℓ
∈
L
, determine the
two surface patches Si
i
and S
j
⊂ ∂Ω attached to
ℓ
. As intersection loops are boundary lines of
penetr
a
tion from one volum
e
into a
n
other
,
identify between Si
i
and S
j
the cutting surface into
mesh . Let S
i
and S
j
⊂ ∂Ω,
S
i
and
S
j
∂
be the surface patches connected to intersection
loop
ℓ
, as shown in Figure 8.111, wh
er
e arrows are pointing towards the volume interior.
S
i
is a cut surface if it penetrates into , for which dihedral angle θ between triangles BAD
and ABE following the rotation axis BA is smaller than angle ϕ between triangles BAD and
ABC following the same rotation axis BA.
