Graphics Reference
In-Depth Information
Figure 10.2.
Losing small objects in ray tracing.
Figure 10.3.
Shooting rays with adaptive
supersampling.
ways to deal with this aliasing problem are (uniform) supersampling and stochastic
sampling. More thorough discussions can be found in [WatW92] and [Roge98].
Supersampling.
With this approach one simply sends out more rays and then aver-
ages the results. For example, one could send out k
2
rays for each pixel. More specif-
ically, if the resolution is m ¥ n, assume a virtual resolution of km ¥ kn and send out
a ray for each virtual pixel and then average the values of successive k ¥ k grids.
Although this approach does not solve the aliasing problem, it helps. According to
[Whit85], k = 4 seems to give adequate results. Two methods related to supersampling
that avoid the problem in simple ray tracing caused by sending out an infinitesimally
thin ray are
cone tracing
([Aman84]), where single rays are replaced by thin cones,
and
beam tracing
([HecH84]), where rays are replaced by bundles of parallel rays.
Adaptive Supersampling
([Whit80])
.
This is a variant of supersampling. The idea
here is that rather than blindly shooting off all the rays that supersampling requires,
one should concentrate where it counts. See Figure 10.3. One starts by tracing rays
through the four corners and center of a pixel, marked A-E in the figure. Next, one
compares the colors of the pairs of rays (A,E), (B,E), (C,E), and (D,E). One starts sub-
dividing and sending out more rays only where differences are detected. For example,
suppose that the values at the pairs (A,E) and (D,E) are similar, but the values at the
other pairs are substantially different. In this case, one should look at the quadrant
defined by E and B more closely. To do this, one sends out new rays through F, G, and
H shown in the figure. Again one compares the values in this quadrant and, if there
are any differences, then the subdivision process is continued until no substantial dif-
ferences between adjacent points are detected. Next, one would notice that the values
at C and E are different and apply the same recursive process to the E-C quadrant.
