Civil Engineering Reference
In-Depth Information
Table 8.1
Statistics of boundary surfaces tested
Object
Partition
String
Avion
Mould
Hugo
Wheel
NP
21
2613
1879
4343
2028
1929
NB
53
5226
3762
10,098
4000
3870
NL
65
7893
5643
13,053
6062
5805
1
1
0.001
100
1
1
λ
S
1087
235
237
3205
470
10,814
A
min
12.5
0.0287
0.00011
0.00134
0.0109
0.00021
A
20.5
0.045
0.0629
0.3683
0.118
2.79
0.693
0.645
0.0188
0.281
0.135
0.00939
α
min
0.77
0.772
0.498
0.798
0.699
0.271
α
Angles <1
o
0
0
8
0
0
264
Touches
0
0
2
0
0
280
27.8
24.1
0.624
9.73
4.5
0.32
θ
min
41.7%
36.4%
0.498%
6.31%
5.8%
0.158%
δ
min
NS
18
1
1
1
1
1
NR
8
1
1
1
0
1
V
1187.5
56.9
54.4
1636
0
10884.8
Grid
3 × 6 × 3
51 × 51 × 15
67 × 67 × 22
48 × 48 × 42
28 × 41 × 36
23 × 21 × 34
Test /facet
10
15
34
84
12
47
Efficiency
6.5
526
111
155
505
123
CPUT (s)
0.00
0.03
0.04
0.11
0.00
0.07
Remark
Many touches,
sharp angles,
an object
challenging
to mesh
Note: NP = Number of points; NB = number of triangles; NL = number of edges;
λ
= co-ordinate scaling factor; S = total
surface area; A
min
= minimum size of a triangle; A = average size of triangles;
α
min
= minimum quality of a triangle;
α
= average
quality of triangles;
θ
min
= minimum angle in degree,
δ
min
= minimum touch; NS = number of surfaces identified; NR = number
of region formed; V = volume of the object; Grid = space partition for geometrical operations; Test/facet = average tests
performed for each triangle; Efficiency = ratio of CPU time between no grid and with grid; CPUT = CPU time of PC i7 CPU
870 at 2.93 Ghz running on XP mode.
Two free
edges and 12
intersections
found
Good-quality
smooth
surface
Poorly shaped
elements with
very small
size
encountered
Big change in
element size,
redundant
elements
found
Elements had
to be added
at the top
and at the
bottom
surface, and no volume could be defined. It was similar to an open cylinder, and triangular
facets had to be added at the top and at the bottom to close it up. The last example is a wheel
of 1929 nodes and 3870 triangles, as shown in Figure 8.21. This is a very poor boundary sur-
face of 264 angles less than 1° and 280 touches of distance less than 1% of the length of the
edge under consideration. The characteristics and the results of analysis of all these examples
are summarised in Table 8.1. It is found that the CPU time for checking intersections, touches
and sharp angles can be much reduced with the aid of a background grid.
8.2 MULTI-GRID INSERTION OF NON-UNIFORM
POINT DISTRIBUTIONS (2D)
8.2.1 Introduction
Uniform or mildly non-uniform distribution point sets can be efficiently handled by the
insertion scheme with the aid of a regular grid. However, for highly non-uniform point
distributions, the triangulation time may be many times more than what is required by
