Graphics Reference
In-Depth Information
Figure 10.9.
Form factors using
hemispheres.
Figure 10.10.
Form factors using
rectangles.
where Q ranges over all rectangles Q
st
that lie in the projection of A
j
onto the
hemicube. A three-dimensional version of the Cohen-Sutherland clipping algorithm
can be used to compute the projection of A
j
onto the hemicube. One can also handle
occlusions of patches. This is done on the R
ij
level, that is, for each rectangle Q
st
in
the projection, use the form factor of that patch A
j
that is closest. There is a similar-
ity with the z-buffer algorithm, except that here we maintain labels for the nearest
patch rather than a z-value. Figure 10.11 shows a cross-section of an example.
The formulas for the form factors DF
Q
in equation (10.11) are easy to compute.
For rectangles Q in the top of the hemicube we have
1
D
F
Q
=
D
A
.
2
(
)
2
2
p
xyl
++
This follows from the geometry shown in Figure 10.12. There are similar formulas for
Q in the side of the hemicube. For example, for Q in the plane x = 1, we have
