Civil Engineering Reference
In-Depth Information
Figure 3.61
Delaunay triangulation of the boundary nodes.
Unmeshed
region
Base segment
Generation front
Meshed region
Figure 3.62
An intermediate stage of mesh generation.
a constrained DT of the generation front. At a typical stage, a line segment is selected from
the generation front as the base segment for the construction of a triangular element.
An interior node is generated, which forms the best triangle with the base segment in
terms of element shape quality and node spacing requirement, as shown in Figure 3.63.
This node is inserted to the unmeshed region of a constrained DT by means of the standard
Delaunay insertion kernel. The non-Delaunay triangles of the unmeshed region with respect
to the inserted node are removed from the triangulation, and the cavity left behind is filled
up by triangles formed by the interior node and the boundary of the cavity, as shown in
Figure 3.64. The triangle connected to the base segment is transferred from the unmeshed
region to the meshed region. In case no interior node is needed for the base line segment
under consideration, the triangle connected to the base segment is simply removed from the
unmeshed region to the meshed region, and the generation front is updated accordingly in
the same way as the insertion of an interior node. Line segments on the generation front
are considered in turn until there is no more line segment left on the generation front, and
by then, the unmeshed region will shrink to nothing, and the meshed region is a triangular
mesh of the given domain, as shown in Figure 3.65. In this example, a very simple node gen-
eration scheme has been employed for the generation of the interior nodes to show the basic
