Civil Engineering Reference
In-Depth Information
This important characteristic ensures that the choice of origin can be arbitrary and would
not affect the resulting mesh, which is governed only by the underlying metric requirement.
The meshes shown in Figure 4.54b and d is generated with the origin located at two differ-
ent positions, one inside the α-curve and the other outside the α-curve.
The next examples are about the application of anisotropic meshing to curved surfaces. In
general, curved surfaces can be represented by a bivariate mapping of the form
S
=
S
(x, y, z) =
S
(u, v) such that x = x(u, v), y = (u, v), z = z(u, v)
The size and the orientation of the ellipses in the pack are controlled by the unit metric
field of curved surface
S
, which can be computed following the procedure described in
Section 4.2.6. The parametric surface shown in Figure 4.55a and b with two distinct peaks
is defined by
22
xu yv zu ve
1u v
= =+
−−
2
2
=
,
,
(
3
)
In this example, the discrepancy in the required sizes at neighbouring points to the actual
length is about 12% (
Avg1
). The average number of iteration is relatively few, which is equal
to 4. Figure 4.55c shows the surface mesh mapped from the anisotropic mesh of Figure
4.55b. In 3D space, the boundary of the surface is defined by a surface intersection process,
as shown in Figure 4.55d.
(a)
(b)
(c)
(d)
Figure 4.55
Ellipse packing and mesh generation for curved surface 'Two Peaks': (a) ellipses packed on para-
metric domain; (b) anisotropic mesh on parametric domain; (c) curved surface mapped from
mesh (b); (d) boundary created by surface intersection.
