Graphics Reference
In-Depth Information
light fields, the outgoing light fields also sum. This linearity places very serious
restrictions on the kinds of transformations that can take place. It also means that
we can study the “response” of the object to incoming radiance along single rays,
and then integrate over a field of such rays to get the outgoing radiance field for
an arbitrary incoming field.
While intrinsically appealing, such a representation isn't really practical in
general: Writing down the response to all possible incoming light fields (even
single-ray responses!) requires too much memory. But it's worth holding on to the
idea that any representation we make must somehow encompass the “transformer-
of-light-fields” ideal just presented.
Some objects, such as fog, have no explicit geometry. But in the case where
an object
does
have some geometry, it's useful to “factor” the way it interacts with
light into
geometry
and
material
where by “material” we mean to suggest the
characteristics of the object that are independent of position. Thus, “aluminum” is
a material, and an aluminum sphere scatters light in the same way from its north
pole as from its south pole. This splitting into geometry and material represents
an enormous simplification and compression: We need to know how one tiny bit
of material scatters light, and then we reuse this knowledge at other points. Of
course, for this to work well, the object must be made of a homogeneous mate-
rial. If the material varies from point to point (e.g., as with a sedimentary rock),
a compromise solution is often workable: We describe a parameterized
class
of
materials, and associate (through texture mapping) some parameters to each point
of the surface so that at one surface point the material is red sandstone and at
another it's ochre sandstone, for instance.
Such factoring can be taken further. We sometimes factor the bidirectional
scattering distribution function (BSDF) into two parts: a “surface color” at each
point, and an underlying BSDF. To compute scattered light, we use the underly-
ing BSDF to compute how much light is scattered, and then compute the spec-
tral distribution of the outgoing light as a product of the spectral distribution of
the incoming light times this basic reflectance times the “surface color,” which is
really a per-wavelength reflectivity, typically represented by just three values (usu-
ally called “red,” “green,” and “blue”). You already saw an example of a BRDF-
like reflection model in Chapter 6—where we described a “lighting model” for
surfaces that involved diffuse and specular RGB colors, and how they got mul-
tiplied by incoming light to compute the color with which a surface should be
rendered—and in a more physically correct form in Chapter 14.
As we mentioned in the previous chapters, the single-point description of scatter-
ing is typically represented by a BRDF. For materials where the light-object inter-
action involves transmission, or takes place throughout the material rather than at
its surface (e.g., many cheeses), richer descriptions like the bidirectional scattering
distribution function (BSDF) or bidirectional surface scattering reflectance distri-
bution function (BSSRDF) are needed. For volumetric materials, like fog, even
more complex descriptions are needed. We'll concentrate on the surface-material
examples, but we will touch on the others as well. The questions to consider, as
we do so, are the following.
• What BRDF (or BSDF, or BSSRDF, etc.) is the one to use to model some
material?
