Civil Engineering Reference
In-Depth Information
Borouchaki (1998) proposed a more complicated scheme to remove a penetrating edge in
which three Steiner points are introduced at various positions on the cutting edge; however,
while this offers a plausible solution in removing a penetrating edge, it cannot be considered
as an optimal process as far as the number of Steiner points is concerned.
5.3.3.2.5 Step 5: Insert Steiner points to edges and faces
For those intersection points on boundary edges being cut across by a face or on boundary
faces being penetrated through by an edge, which cannot be simply removed by element
swaps, Steiner points are introduced on the face to restore the geometry of the missing
quantities. For a missing boundary edge, Steiner points are inserted at the position of all
the irreducible intersection points breaking each of the cutting faces into three triangles, as
shown in Figure 5.22. Each missing boundary edge is recovered as a series of line segments
separated by Steiner points. As for missing boundary faces, Steiner points are introduced
on the face concerned, and the face is triangulated with the Steiner points as internal nodes
such that the boundary face is represented as a concatenation of smaller triangles, as shown
in Figure 5.23. Nevertheless, a more elegant way to introduce Steiner points is to insert them
by means of the Delaunay point insertion kernel.
5.3.3.2.6 Step 6: Removing Steiner points on boundary edges
Steiner points inserted on boundary edges for their geometrical recovery (geometrically pres-
ent) have to be completely removed (relocated) for topological integrity with the original
boundary surface. This task, however, is relatively easier than originally thought as we only
have to deal with one side of the boundary surface, i.e. the side within the object; as for the
outside part, we don't have to care much as elements outside the boundary surface will be
discarded anyway to reveal the final meshed object. There should be at least two Steiner
points on an edge for recovery as one intersection point is always reducible. Hence, sup-
pose there are three Steiner points on a boundary edge, which can be lifted off the surface
one by one, as shown in Figure 5.24a. Upon the removal of the Steiner points, edge AB and
Steiner points
Q
P
Figure 5.22
Inserting Steiner points to an edge.
C
Steiner
points
B
A
Figure 5.23
Inserting Steiner points on a triangular facet.
