Civil Engineering Reference
In-Depth Information
Surface 1
Surface 2
Cell
Intersection
Figure 4.69
Intersection of triangles in a typical cell.
Surface S
Cell
d
y
d
z
d
x
L
z
L
x
L
y
Bounding
box
Figure 4.70
Background grid for triangulated surfaces.
thinner lines represent facets of the first surface, and thicker lines represent facets from the
second surface.
For completeness, the regular background introduced in Section 2.7 is also presented here
following the adopted notations. The dimensions of a typical cell is given by
L
N
L
N
L
N
y
x
z
d
=
,
d
=
,
d
=
x
y
z
x
y
z
where L
x
, L
y
and L
z
represent, respectively, the lengths on the three sides of the bounding
box, and N
x
, N
y
and N
z
represent, respectively, the number of divisions along the three prin-
cipal directions, as shown in Figure 4.70. The number of cells N = N
x
× N
y
× N
z
depends on
the amount of computer memory available. The size of a cell can be set equal to the average
length of the edges on the surface. However, the dimensions of the cells can be also adjusted
so that the use of available memory can be optimised.
4.5.2.1 Determination of cells intersected by a triangular facet
A typical triangular facet will intersect more than one cell in the background grid.
Considering each triangular facet in turn, the cells cut by the triangular facet under consid-
eration are recorded. At the end of the process, the list of triangular facets intersected with
each cell can be determined. The cells cut across by a triangular facet can be found by the
following procedure.
