Civil Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
Figure 4.57
Ellipse packing and mesh generation for the wavy surface: (a) packing ellipses; (b) triangulation;
(c) curved surface mapped from mesh (b); (d) boundary created by surface intersection.
In the last example, the discrepancy in the required sizes at neighbouring points to the
actual length is about 12% (
Avg1
). The average number of iteration is equal to 4. Figure
4.57c shows the meshed curved surface produced by mapping the anisotropic mesh of Figure
4.57b. In 3D space, the boundary of the surface can be conveniently defined through a sur-
face intersection process, as shown in Figure 4.57d.
Remarks:
The ellipse packing has turned the mesh generation problem into a problem of
fitting objects of simple geometrical shape. The size and the orientation of the ellipses are
governed by the local metric, which provides a visual inspection of the point distribution with
respect to the specified metric field (unit metric contour). Owing to the simple geometry of an
ellipse, determination of intersection has been reduced to a distance check by a simple func-
tion f
ij
between adjacent ellipses Ci
i
and C
j
on the generation front. Moreover, relative to the
usual intersection check, the distance function used is much less stringent for which there is a
large tolerance for the fitting process resulting in a robust and efficient alternative other than
a direct generation of anisotropic meshes by proper well-established mesh generation schemes.
4.4 DIRECT MESH GENERATION ON SURFACE
Direct three-dimensional surface mesh generation forms elements directly on the curved
surface without the need for a parametric representation of the underlying geometry. In the
case where a parametric representation is not available or where the surface parameterisa-
tion is poor, direct 3D surface mesh generation can be applied. Lau and Lo (1996) presented
an ADF scheme for the generation of triangular meshes on curved surface in 3D space. By
this method, surface normal and tangents are computed to determine the direction of the
generation front. A number of surface projections are required to bring a proposed node
point back on to the surface. Intersection checks are also needed to make sure that triangles
