Graphics Reference
In-Depth Information
f
s
)
2
]
over the domain, and use
that
as
a measure of error. But that only makes sense if the BSDF is sending light to the
eye. What if it's reflecting light onto
another
surface that will in turn reflect it to
the eye? Then maybe the original
L
2
difference is the better measure of goodness.
After all, at some distance from the surface (especially if it's at all curved), the
fine details of the BSDF are “blurred out” so that the reflected light distribution is
fairly uniform, as we'll see in Section 31.20.
Some of the simplest models, like the Phong model, don't fit observed data
very well, but they have good empirical characteristics (a large lobe in about the
right direction for specular reflection, intuitive parameters). Others, like the Lafor-
tune model, provide better
L
2
fit, and have the additional benefit of being amenable
to sampling in certain common ways (see Section 27.14). Still others, like the
spherical harmonic representation, allow for efficient nonprobabilistic evaluation
of the reflectance integral. In deciding which to use, you need to consider your
eventual purpose.
perhaps integrate something like
log[(
f
−
The BSDF of a surface is typically not constant as a function of position. The
BSDF for a piece of paper might be nearly constant, but when it has print on it
the printed parts will have much smaller total reflectance. Objects like wood have
structural texture like grain at a scale of about 1 millimeter, and further cellular
texture at a scale perhaps 100 times smaller. The BSDFs for the different kinds of
wood fiber are quite different. Some of the richness of wood comes from strong
subsurface scattering by linear structures like wood fibers; if the orientation of
these fibers varies, as it does in burls, for instance, this can introduce another kind
of variation in the reflectance of the material.
Let's examine two approaches to modeling a wall painted with latex paint,
such as you might find in any office. Typically such a surface has some texture,
in the nongraphics sense: There are bumps on the order of 0.1mm, separated by a
typical distance of 2mm. The paint surface, even on the bumps, is reasonably flat
at a scale of 10 wavelengths of light, so it's reasonable to use a BSDF representa-
tion. We'll assume that the latex paint has a perfect Lambertian BSDF, but we'll
need to record, in a texture map, the variation of the albedo from point to point,
and the variation of the normal vector. That entails a total of three dimensions of
high-resolution texture map (one for albedo, two for the normal vector variation),
or perhaps a procedural texture.
Alternatively, we could imagine treating the wall as truly flat, and measuring
the BSDF at each point of the wall. On the sides of the bumps, we'd find that
the BSDF was different from what it is at the bottoms of valleys, etc.; if we rep-
resent each BSDF as a sum of spherical harmonics, say, 50 harmonics, then to
represent the entire wall we'd need 50 dimensions of texture map to record each
harmonic coefficient. (We're assuming a white paint, to avoid the worry of spectral
dependence.)
Clearly the first model is preferable in this case. But if we instead consider
something like a granite wall surface, where the material is made up of an aggre-
gate of other materials, each with a different reflectance property, a spatially vary-
ing BSDF might be a completely reasonable approach: Perhaps a suitably factored
model would be a good solution; perhaps the variation of the BSDF will occur
mostly in one or two factors so that the others can be treated as constants, saving
a great deal of space.
