Graphics Reference
In-Depth Information
many different parameter values, and it's important that it be robust regardless of
this wide range of inputs.
There
is
an alternative, however. If we actually know microgeometry perfectly,
and we know the index of refraction for every material, we can compute scat-
tering relatively simply—there's a reflection term and a transmission term, and
what's neither reflected nor transmitted is absorbed. As long as the microgeome-
try is of a scale somewhat larger than the wavelength of light that we're scattering,
this provides a complete model. Unfortunately, at present it's an impractical one,
for several reasons. First, representing microgeometry at the scale of microfacets
requires either an enormous amount of data or, if it's generated procedurally, an
enormous amount of computation. Second, if we accurately represent microge-
ometry, then every surface becomes mirrorlike at a small enough scale. To get the
appearance of diffuse reflection at a point
P
requires that thousands of rays hit the
surface near
P
, each scattering in its own direction. Ray-tracing a piece of chalk
suddenly requires a thousand rays per pixel instead of just one! Third, the exact
index of refraction for many materials is unknown or hard to measure, especially
the coefficient of extinction.
Our representation of scattering by summary statistics like the diffuse coeffi-
cient is a way to take this intractable model and make it workable, with only slight
losses in fidelity, based on the observation that the precise microgeometry almost
never matters in the final rendering; if we render 20 pieces of chalk with the same
macrogeometry, they'll all look essentially identical.
There's a third alternative between these two: You can store measured BRDF
data. Storing such data, at a reasonably fine level of detail, can be expensive.
(If your material has a glossy highlight that resembles the one produced by a
Phong exponent of 1000, then the BRDF drops from its peak value to half that
value in about 7
◦
, suggesting that you might need to sample at least every 2
◦
to faithfully capture it, requiring about 17,000 samples.) Drawing a direction
v
)
is far more problematic, but it is
feasible. You might think that you could have the best of both worlds by choos-
ing an explicit parametric representation (e.g., spherical harmonics, or perhaps
some generalized Phong-like model) and finding the best fit to the measured
data. This is a fairly common practice in the film industry today, and it works
well for some materials like metals, but it can produce huge errors for diffuse
surfaces when you use common analytic models that fail to model subsurface
effects accurately [NDM05]. Nonetheless, it's currently an active area of research,
one with considerable promise for simplifying the computation of the scattering
integral.
v
→
f
s
(
with probability proportional to
v
i
,
v
Figure 32.9 shows four simple scenes we'll use in evaluating renderers, both
drawn and ray-traced. The first, with its diffuse floor and back wall, and brightly
colored semidiffuse sphere, provides a nice, simple test of bounding volume hier-
archy, visibility, and rendering with reflection but not transmission. Since most of
the scattering in the scene is diffuse, it only provides limited testing of scattering
from multiple surfaces: We can't visually check multiple interobject reflections
the way we could in a scene with 12 mirrored spheres, for instance.
In the second scene, we've added a transparent sphere whose refractive
index is somewhat greater than that of air, to let us verify that transmissive
