Civil Engineering Reference
In-Depth Information
4. If the two intersecting triangles are on a common plane, there is no need to compute
the intersection. In other words, intersections will only be calculated if the two tri-
angles concerned are not on a common plane, in which case they can be again clas-
sified into types 1, 2 and 3, as described above. However, if the boundary edge is
involved, the intersection has to be calculated along the boundary part, as shown in
Figure 4.63d. Two triangles are on a common plane, IJ is a boundary edge, and the
intersection line segment PQ between triangles S
1
and T
1
has to be recorded. Figure
4.64 shows the intersection between a planar surface with an internal opening (Figure
4.74a) and a cylindrical surface with a closed bottom plate (Figure 4.74b). The outer
loop is the result of the intersection between the vertical cylindrical surface and the
flat surface. The inner loop is the intersection between the interior boundary of the flat
surface and the bottom plate of the cylinder, as shown in Figure 4.74c and d.
Intersection lines can be constructed by linking up individual line segments to form open
chains or closed loops. In the tracing process, if the intersection line goes back to the starting
point, a closed loop will be formed; otherwise, a chain can be defined with the end points on
the boundary of the surface. Figure 4.75a shows the loop of intersection between two spheres
of Figure 4.71a. There are 114 line segments in the intersection loop, as shown in Figure 4.75b.
Figure 4.75c and d shows the intersection loop and the neighbouring triangles on the two sur-
faces. Figure 4.76 shows the intersection of two open surfaces. The intersection line in the form
(a)
(b)
(d)
(c)
Figure 4.74
Intersection of planar surfaces: (a) planar surface with an internal opening; (b) cylindrical surface
with a bottom plate; (c) cylindrical surface on top of the planar surface; (d) resulting intersec-
tion loops.
(a)
(b)
(c)
(d)
Figure 4.75
Intersection loop and neighbouring triangles: (a) triangles collected by neighbour tracing;
(b) loop of intersection segments; (c) ring of intersecting triangles of the first surface; (d) ring of
intersecting triangles of the second surface.
