Graphics Reference
In-Depth Information
Inline Exercise 27.11:
One of the implicit assumptions in the definition of
the BRDF is that it is measured and used at a scale larger than the scale of
the largest variation in the underlying material. Thus, it makes some sense
to measure the BRDF of granite for use in aerial sensing applications, where
a single pixel sensor may record light reflected from many square meters of
granite surface, but it does not make sense to use that same BRDF in trying
to predict the appearance of a microscopic picture of granite. Suppose that we
have modeled some object with local variation in appearance—a piece of paper
with printing on it, or a flat metal tray with fingerprints around the rim—and
we wish to make a picture of it from a distance so that the entire object will
occupy just a few pixels on the imaging sensor. It's natural to use MIP mapping
for this.
(a) Argue why it is reasonable to average the spatially varying BRDF over a
region of the surface to estimate a BRDF for the larger surface region, at least
in the case of the paper and the flat metal tray.
(b) Argue that even in the case of a flat surface, it's
not
generally reasonable
to average the model parameters (such as the Phong exponent, or the Cook-
Torrance specular color, or the index of refraction), and then use these averaged
values to estimate the BRDF of the larger surface region.
(c) Suppose that your surface has a fairly constant BRDF (like the curved tile
on a Spanish tile roof), but the underlying surface has substantial curvature at
a smaller scale than one imager pixel (i.e., a Spanish tile rooftop that projects
to just a few imager pixels). How would you compute a BRDF for the larger
surface?
One benefit to using an explicit physically or empirically based model in rep-
resenting a BSDF is that such models often have a few parameters that may
be amenable to intuitive understanding. For example, the Phong exponent can
be described as representing “shininess,” and the diffuse and specular reflectiv-
ity as representing the “lightness” of the surface. Of course, the parameters may
not match our intuition completely; the Phong exponent, for instance, affects the
appearance of a surface a great deal when it's changed from 1 to 2, but hardly
at all when it's changed from 51 to 52. (Offering the user an adjustment for the
logarithm
of the Phong exponent proves to be far more intuitive: 0 corresponds to
diffuse, and 6 to “very shiny.”) Similarly, the index of refraction of a material and
its dielectric properties are not intuitively understood by most people, but we can
offer an intuitive control that ranges from “metallic” to “plastic” by combining
parameters in the Cook-Torrance model [Str88].
One more reason for using models with intuitive parameters is that we some-
times want to measure a material, and then create a new material that's quite simi-
lar, but not exactly the same. Fitting a model to the measured data, and then giving
the designer intuitive controls to adjust, is far more likely to produce good results
than giving the designer the opportunity to edit the measured data directly.
