Civil Engineering Reference
In-Depth Information
Figure 4.56a and b shows the ellipse packing and the corresponding anisotropic triangu-
lar mesh of the Klein bottle. The Klein bottle is defined by the following parametric surface
(Borouchaki et al. 2000a)
61
cosu
(
+
sinu
)
+
rcosucosvif
0
≤≤
u
π
x
=
61
cosu
(
+
sinu
)
−
r
cosv
if
π
≤≤2
u
π
16
sinu
+
rsinucosvif
0
≤ ≤
≤≤
u
π
y
=
16
sinu
if
π
u
2
π
z = rsinv,
r = 4 − 2 cosu,
over the square 0 ≤ u, v ≤ 2π
For this example, the error in the required sizes at neighbouring points to the actual length
is also 12% (
Avg1
). The average number of iterations is also equal to 4. Figure 4.56c shows
the surface mesh obtained through the mapping of the anisotropic mesh of Figure 4.56b.
Figure 4.57a and b shows the ellipse packing and the corresponding anisotropic triangular
mesh of a wavy curved surface. The parametric surface is defined by Borouchaki et al. (1999)
x = u
3
+ 10u,
y = v
3
+ 10v,
z = 100sinucosv
(a)
(b)
(c)
Figure 4.56
Ellipse packing and mesh generation for curved surface Klein bottle: (a) ellipses packed on para-
metric domain; (b) anisotropic mesh on parametric domain; (c) surface mesh of Klein bottle.
