Civil Engineering Reference
In-Depth Information
point insertion procedures can be found in the works of Yang et al. (2005), Si (2009, 2010)
and Si and Gaertner (2011).
5.4.2.1 Insert Steiner points at the mid-points of missing edges
As shown in Figure 5.44, nodes are introduced at the mid-points of all the 22 missing edges,
and a new DT is constructed. Not all the boundary edges are recovered in the new DT,
and quite surprisingly, there are 23 missing edges in the new DT, one more than we had
in the first triangulation. There are still missing boundary edges, because some originally
Delaunay boundary edges are rendered non-Delaunay by the introduction of Steiner points,
as shown in Figure 5.45. The same step was repeated five more times, and the process did
converge to produce DTs with 15, 10, 6, 1 and 0 missing edges. After six iterations, the final
DT containing all the boundary edges is shown in Figure 5.46. A triangular mesh of the
domain can now be retrieved by collecting all the triangles within the bounded region, as
shown in Figure 5.47. There are 163 nodes and 328 triangles in the entire mesh from which
163 triangles are retrieved to form the final mesh of the object. Steiner points have to be
removed from the boundary edges if a fully constrained DT is required; however, the pri-
mary purpose of introducing the boundary protection scheme is to show some possibilities
to generate conforming DTs rapidly in a robust manner.
Steiner points
at mid-points
Figure 5.44
Second Delaunay triangulation with 23 missing edges.
Edge AB is Delaunay if
points P and Q are not there
P
A
B
Q
Figure 5.45
Delaunay edges turned non-Delaunay by Steiner points.
