Civil Engineering Reference
In-Depth Information
where
M
is the mesh containing the bounded region
Ω
, and
B
contains the boundary edges
of
Ω
.
1. Pick any point within the bounded region
Ω
.
2. Identify the triangle T
k
containing the point (BASE) and include triangle T
k
to the
bounded region, i.e. set Z
k
= 1.
3. For each edge of triangle if
k
, if it is not a boundary edge (∉
B
), add it to the list of
frontal segments
F
= {F
i
, i = 1,n}, n = 1, 2 or 3, in setting up the initial front.
4. Take the last frontal segment F
n
and identify the two triangles connected to F
n
. One
triangle if
i
connecting F
n
from inside of the construction front
F
should already been
known; and the other triangle Ti
j
opposite to Ti
i
can be found by adjacency, as shown
in Figure 5.50. Delete F
n
from
F
by simply updating n, n ↦ n − 1.
5. Include triangle T
j
to
Ω
by setting Z
j
= 1.
6. For each edge E of triangle if
j
not connected to F
n
, if it is not a boundary edge (E ∉
B
),
update it with the construction front
F
, i.e.
F
=
F
∪ {E} if E ∉
F
,
F
=
F
− {E} if E ∈
F
.
7. If
F
is not empty, go to step 4.
If an exterior point close to the border of the square is picked, the elements between the
boundary of the domain and the edges of the square are collected, as shown in Figure 5.51.
F
n
E
T
i
T
j
F
Figure 5.50
Triangle T
j
absorbed by the generation front F.
Figure 5.51
Elements outside the domain are collected by picking an exterior point.
