Civil Engineering Reference
In-Depth Information
Intersection segments exist
as edges of the triangulation
B
A
Q
P
C
D
Figure 8.108
Triangulating facet ABC.
Intersection segments
C
B
I
E
A
F
D
Figure 8.109
Tetrahedra ABCD and ABFE are not direct neighbours.
incorporated into the tetrahedral meshes, and boundary surface compatibility is estab-
lished a
s
each intersection segment is present in the resulting modified tetrahedral meshes
Ω and .
While compatibility is established on the boundary surfaces, compatibility between inter-
sected tetrahedral elements has to be checked. As shown in Figure 8.109, the adjacent inter-
sected tetrahedral elements on the boundary surface may not be direct neighbours of each
other. Referring to Figure 8.109, ABCD and ABFE are adjacent intersected tetrahedral ele-
ments on the boundary surface. However, tetrahedral elements ABCD and ABFE are not
direct neighbours to each other, and compatibility could not be maintained in tetrahedral
element ABDF, which also shares the common line segment AB. To restore compatibility,
simply divide each tetrahedral element between tetrahedra ABCD and ABFE sharing the
common line segment AB into two tetrahedral elements, in which ABDF is divided by inter-
section point I at edge AB into tetrahedra AIDF and IBDF. Such a process is a standard pro-
cedure in the optimisation and refinement of tetrahedral meshes, as shown in Figure 8.110.
8.6.2.3 Volume (region) of intersection
Based on the method of neighbour tracing in the determination of the intersection between
two boundary surfaces, as described in Section 8.6.2.1, intersections are represented as a
