Civil Engineering Reference
In-Depth Information
Figure 3.85
Triangular mesh converted to quadrilateral mesh.
Splitting
Angle greater than 3π/2
Figure 3.86
Splitting boundary triangles to avoid large obtuse angles.
triangular elements. With post-processing mesh optimisation, the quality of the resulting
quadrilateral mesh is quite promising with a β coefficient at 0.706 (Section 3.9.3.1).
Remarks:
In order to avoid the formation of quadrilaterals with large obtuse angles, adja-
cent boundary triangles with a combined angle greater than some threshold, say 3π/2, are
split, as shown in Figure 3.86. This process of splitting boundary triangles is repeated until
no more combined angle from two adjacent boundary triangles is greater than the threshold
value of 3π/2.
As shown in Figure 3.79, in case both triangles ACL and CBR are feasible options to
merge with base triangle ABC without violating the parity requirement (even number of seg-
ments on a closed loop) of the merging fronts, the triangle that results in a quadrilateral of
better quality will be selected. During the process of merging triangles, the merging fronts
will be combined or further split into sub-fronts, and it is important to ensure that an even
number of segments on each frontal closed loop is always maintained.
