Civil Engineering Reference
In-Depth Information
Node shifted
(a)
(b)
(c)
Figure 4.78
Insertion of intersection nodes: (a) interior node; (b) edge node; (c) corner node.
Missing edge
Edge recovered
Figure 4.79
Segment recovered by edge swaps.
during mesh generation. Alternatively, a robust method is available ensuring that elements
generated are always on the triangulated surface. The steps are summarised as follows.
i.
Incorporating the intersection line to each surface.
This process is easy and fast as the
element associated with each intersection node is recorded in the neighbour-tracing pro-
cess. An intersection node can be classified into three cases according to its position
relative to the element, as shown in Figure 4.78. (a) The node is at the interior of the
element - the element is divided into three triangles; (b) the node is on an edge of the
element - the edge will be split, and two new elements are generated; and (c) the node is
close to a vertex of the element - the vertex is shifted to the intersection node, and no ele-
ment is created. Intersection line segments are incorporated into the surface by inserting
intersection nodes one by one following the sequence along the intersection line (loop/
chain). In case some intersection line segments are missing after the node insertion pro-
cess, they can be easily recovered by swapping of edges, as shown in Figure 4.79.
ii.
Mesh optimisation along the intersection line.
Excessive nodes are removed or repo-
sitioned along the intersection lines. Elements near the intersection lines are improved
by node repositioning and a swap of diagonals. In fact, all the techniques employed to
improve a planar triangular mesh can be applied. However, in the optimisation, due care
has to be exercised to maintain surface features and surface curvatures, and this can be
achieved by simply verifying the geometry of the patch of elements involved in the process.
4.5.7 Work examples
Six examples of various surface characteristics are presented in this section to illustrate how
intersections are determined by tracing neighbours of intersecting triangles (TNOIT) on a
relatively slow PC machine with a CPU speed of 150 MHz and 128-MB RAM. In the first
example, three spheres consisting, respectively, of 192, 672 and 3584 triangular facets are
