Civil Engineering Reference
In-Depth Information
B
P
2
I
P
n−1
P
1
P
n
A
Figure 8.110
Dividing edge AB at I.
inite
nu
mber of intersection loops. Let
L
be the set of loo
ps
of intersection between ∂Ω
and
∂
, i.e.
L
= {, ,...,
12 N
L
such that
ℓ
i
∈ ∂Ω a
nd
i
∈∂
for 1 ≤ i ≤ N
L
, w
he
re N
L
is
the number of intersection loops between ∂Ω and
∂
. It is remarked that Ω and are the
modified tetrahedral meshes, which have undergone the surface triangulation, subdivision
of intersected tetrahedral elements and restoration of compatibility for adjacent triangulated
tetrahedral elements on the boundary, as described in Section 8.6.2.2.
The set of intersection loop
L
will partition naturally each of the boundary surfaces into
}
N
and
a num
b
er of zones of surface patches, as shown in Figure 8.111, such that
∂=
=
S
i
N
where S
i
and
S
i
are, respectively, surface partitions in ∂Ω and
∂
bounded by
intersection loop(s); N
Ω
and
N
i
1
∂=
=
S
i
i
1
are, respectively, the number of such surface patches in the
partition of ∂Ω and
∂
.
Based on the surface-neighbouring relationship, the surface partition by intersection
loops can be easily carried out by a pure topological proces
s.
Once we have the intersection
segments incorporated into the tetrahedral meshes Ω and , take any triangular facet on
the boundary surface by means of the adjacency relationship; the patch will grow from this
seed triangle by attaching more triangles to it until the entire patch is bounded by intersec-
tion segments. Such a patch of triangles will be given a label and recorded as an individual
Torus: two zones
Intersection loops
Torus: one zone
Sphere: three zones
Torus with a handle: one zone
F i g u r e 8 .111
Boundary surfaces partitioned into zones by intersection loops.
