Civil Engineering Reference
In-Depth Information
segments. The merging front will shrink whenever two triangles are combined to form a
quadrilateral, and the entire process terminates when the merging front is reduced to zero,
and all the triangles have been processed. The conversion process can be divided into three
distinct phases, which are described in Sections 3.9.4.1 to 3.9.4.4.
3.9.4.1 Initialisation of the merging front
Before the merging process starts, an initial merging front has to be set up, which is the
collection of all the boundary segments, as shown in Figure 3.78. The orientation of the
merging front follows that of the boundary segments, such that the unmerged triangles are
lying on the left-hand side of the merging front. The merging front will be updated during
the conversion process by adding and deleting line segments to and from the merging front.
Sub-fronts may also be formed from time to time, and the merging process is completed
when no more triangles are left, and all fronts are reduced to nothing.
3.9.4.2 Merging of triangles
A quadrilateral is formed when two triangles on the merging front are combined, and the
details of such a procedure are given as follows.
i. A segment AB on the merging front is selected as the base segment for the construction
of a quadrilateral, as shown in Figure 3.79a.
ii. Let triangle ABC be the triangle connected to segment AB; two triangular elements
ACL and CBR, which can possibly merge with triangle ABC on the two sides, are
identified.
iii. If node C does not divide the merging front into two sub-fronts, either triangle ACL or
CBR can be considered to combine with triangle ABC to form a quadrilateral. Suppose
vthat triangle ACL is taken; if node L does not divide the merging front into sub-fronts
Simply connected domain
Multi-connected domain
Figure 3.78
The domain boundary is taken as the initial merging front.
C
C
L
C
R
R
D
SFL
SFR
A
B
A
B
(a)
(b)
(c)
Figure 3.79
Merging of triangles into quadrilaterals: (a) node C does not divide the merging front;
(b) node C divides the merging front; (c) node R divides the merging front.
