Civil Engineering Reference
In-Depth Information
Tetrahedron DEFG
5
C
4
2
1
B
A
8
6
3
7
1
,
2
,
3
,
5
: Cuboid;
4
: prism;
6
: pyramid;
7
,
8
: tetrahedron
Figure 8.16
Object composed of eight chambers.
facets. The tasks to be performed are to verify the validity of the data, to construct the
boundary and interior partition surfaces, to give each triangular facet a consistent orienta-
tion according to the surface to which it belongs, to identify the volume bounded by surfaces
and to carry out a geometrical check for intersections, touches and sharp angles.
The first object tested is made of an artificial assembly of planar surfaces in which eight
compartments can be identified, as shown in Figure 8.16. A triangular facet ABC and a tetra-
hedron DEFG were added deliberately to test the ability of the computer program in detect-
ing free edges and intersections. Several objects were downloaded from the repertoire of the
GAMMA project of INRIA in France and were put to tests. The second object composed of
5226 triangular facets in the form of a twisted cable is shown in Figure 8.17. In spite of the
strange form, only one closed surface and one volume could be identified, and no intersec-
tion, sharp angle or touch was found. The aeroplane shown in Figure 8.18 is the third object
studied. The analysis indicates that some of the elements on the surface are of very bad shape,
and there is also a significant change of element size over the surface. Two touches and 106
sharp angles less than 2° were found, and the aeroplane turned out to be one of the most dif-
ficult objects for boundary recovery discussed in Section 5.3. The fourth example is a mould
whose surface is represented by 10,098 triangular facets, as shown in Figure 8.19; 1396
redundant triangles were found and removed before they could be triangulated into tetrahe-
dra. The fifth example is taken from a model of a bust of Victor Hugo, as shown in Figure
8.20. Fifty-two free edges were found; it was revealed that the facets did not form a closed
Figure 8.17
A string of 5226 triangles.
