Graphics Reference
In-Depth Information
B
Sample
A
C
E
2
Sample
E
1
Figure 2.9
The irradiance interpolation scheme of Ward et al. works by interpolating sample points in
overlapping discs. (After [Ward et al. 88].)
a somewhat regular rectangular grid. In contrast, samples in MCPT are poorly
suited to interpolation. The method does not record the values of the secondary
sample points; they are discarded after they are added to the summation for the
particular pixel. But even if the values are stored, they occur at scattered points,
which poses a more difficult interpolation problem.
In the late 1980s Greg Ward and his colleagues developed a novel scheme
for interpolating stored surface irradiance samples—now known as
irradiance
caching
—that is well suited to ray tracing [Ward et al. 88]. The method works
by computing the irradiance at a collection of surface points by Monte Carlo
integration over the hemisphere of directions above the surface (recall that diffuse
reflection depends only on the irradiance).
The method maintains bounds on the expected accuracy of the integration,
and the sample points are chosen judiciously so that the number of samples can
be kept minimal while maintaining a prescribed accuracy.
Ward's interpolation scheme is based on circular regions centered at sample
points at which the irradiance has been calculated. Figure 2.9 illustrates. When a
point lies in overlapping regions (point
A
in the figure), irradiance is interpolated
from the sample values at the centers of the overlapping circles (
E
1
and
E
2
in
the figure). At a point inside a single region (point
B
), irradiance is extrapolated
by weighting the sample value (
E
2
) of the circle, under the assumption that the
irradiance changes slowly inside each circle. Irradiance outside any region (point
C
) cannot be approximated from the existing samples, so it must be computed by
tracing rays.
The basic questions are how to choose sample points, and how to weight their
contributions. To answer this, the authors first consider a “worst case” arrange-
ment where each point is contained in sphere with a light (luminous) hemisphere
and a dark hemisphere, arranged so the boundary between the two lies directly
