Mesh generation in three dimensions - Finite Element Mesh Generation - page 274

Steiner points
at intersections
Figure 5.48 Inserting Steiner points at intersections of missing edges.
Figure 5.49 Final mesh and bounded region recovered.
insertion for the generation of conforming DTs. The main drawback of the boundary pro-
tection scheme is that an excessive number of Steiner points may be created for complex
boundary surfaces as the final conforming mesh can only be generated after a couple of
iterations. However, this approach can be useful for boundary surfaces, for which only geo-
metrical integrity is of primary concern but not topological integrity, and Steiner points are
allowed to stay on the boundary surface. On completion of the boundary recovery, the tri-
angular mesh within the boundary region can be retrieved by collecting triangles inside the
boundary contour, and such an element collection scheme for a bounded contour or surface
is given by the following algorithm.
5.4.3 Algorithm RBR: Retrieving bounded region
The following is a generic algorithm in collecting elements within a bounded region Ω .
Input: Mesh M = {T i , i = NT, T }, boundary B = {E i , i = NT, B };
Output: Zone label on M , Z = {Z i , i = 1, NT, T , Z i = 1 if Ti i ∈ Ω, Z i = 0 if Ti i ∉ Ω};