Civil Engineering Reference
In-Depth Information
Figure 5.58b. The boundary surface of the string is then inserted into the tetrahedral mesh.
The first DT of the boundary surface and the spatial points consists of 2913 points and
23,503 tetrahedral elements, in which 1074 edges are found missing. Nodes are introduced
to the missing edges and other related edges following the bisection of the longest edges, and
as a result, there are 3987 nodes and 32,804 tetrahedra in the second DT. The number of
missing edges is reduced to 462, for which exactly 462 nodes are needed for edge recovery.
In the fifth and the last DT of 4525 points and 35,535 tetrahedra, there is no more missing
edge, as shown in Figure 5.58c. Coincidentally, there is also no missing face in the DT, and
the final recovered boundary surface after refinement consists of 8450 triangles for which it
is discretised into 20,078 tetrahedral elements, as shown in Figure 5.58d.
The second example is a hand model defined by a closed surface of 6222 nodes and
12,440 triangular facets. There are 967 points in the initial background Delaunay mesh,
to which the boundary surface of the hand model is inserted to produce a Delaunay mesh
of 7189 nodes and 43,205 tetrahedra. Only 17 boundary edges out of 18,660 are missing
in the first triangulation. The boundary recovery takes altogether four iterations or DTs to
arrive at a final tetrahedral mesh, in which all the 12,554 boundary faces are present, as
shown in Figure 5.59. The third example is a simpler model of a screw, which is composed of
(b)
(a)
(c)
Figure 5.59
Example 2, boundary recovery of a hand model: (a) hand model; (b) final Delaunay mesh;
(c) tetrahedral mesh.
(a)
(b)
(c)
Figure 5.60
Example 3, boundary recovery of a screw model: (a) screw model; (b) final Delaunay mesh;
(c) tetrahedral mesh.
