Civil Engineering Reference
In-Depth Information
(a)
(b)
Figure 3.35
Creation of interior points by means of background grid: (a) rectangular grid; (b) triangular grid.
Solid line = domain boundary, broken line = triangulation of boundary points.
kernel. Instead of point insertion, points at the interior of the domain can be connected up
rapidly by means of standard templates. The remaining points near the domain boundary
can be processed by the point insertion kernel. Alternatively, a triangular grid of equilat-
eral triangles can be employed to produce better quality triangles without differentiation
between internal nodes or boundary nodes in the insertion process by the Delaunay inser-
tion kernel, as shown in Figure 3.35b (Lo and Liu 2002).
3.5.6.5.2.2 QUADTREE PARTITION
The idea of Quadtree partition of space has been introduced in Section 3.4. A rectangular
box that is large enough to contain the given domain is created. A Quadtree partition of the
rectangular box is carried out in compliance with the nodal spacing specification, as shown in
Figure 3.36a. Corner points and mid-side points of the cells can be triangulated by standard
templates or inserted by the Delaunay insertion kernel. As corner points of a cell are cyclic, in
the insertion process, the centroids of the cells are also inserted to avoid numerical problems.
However, similar to the regular grid, a recursively refined triangular grid analogous to the
(a)
(b)
Figure 3.36
Creation of interior points by recursive spatial partition: (a) quadtree decomposition; (b) recur-
sive triangular grid.
