Civil Engineering Reference
In-Depth Information
L
1
∆
i
L
2
L
3
Inverse
relationship
E
n
E
3
E
2
Line L
E
1
Figure 8.3
Find the elements connected to an edge.
8.1.3.3 Elimination of redundant triangles
Elimination of redundant elements in
B
can be conveniently done by examining the elements
around each edge. Let Δ
i
and Δ
j
be two triangles connected to a particular edge; if Δ
i
= Δ
j
or (P
i1
, P
i2
, P
i3
) = (P
j1
, P
j2
, P
j3
) in any order, then Δ
k
will be eliminated, where k = max(i, j).
8.1.3.4 Surface construction
Surfaces can be constructed one at a time starting from any triangular element in
B
. The
following are the procedures of surface construction:
1. An open surface of one single triangle (seed) with a boundary consisting of three edges
of the triangle is initiated, as shown in Figure 8.4a.
2. The triangles connected to the edges of the construction front are identified and added
to the current unclosed surface of triangular facets, as shown in Figure 8.4b.
3. The boundary edges are those edges without neighbours (free edges) or edges shared
by more than two triangles, as shown in Figure 8.4c. A surface is obtained if the con-
struction front is reduced to zero, as shown in Figure 8.5.
(b)
(a)
L
1
L
2
L
3
Connected edge n = 4
Free edge n = 1
(c)
Figure 8.4
Connected edges and free edges: (a) seed triangle; (b) neighbouring triangles; (c) boundary edges.
