Graphics Reference
In-Depth Information
Chapter 29
In this chapter we develop the
rendering equation,
which characterizes the light
transport in a scene. We do this first for a scene in which there is no transmissive
scattering, only reflection, and then generalize to handle transmission as well.
In all but the simplest cases, the rendering equation is impossible to solve
exactly. Approximation methods are therefore essential tools. The dominant
approximation method involves estimating certain integrals by so-called Monte
Carlo integration, that is, randomized integration algorithms, which we discuss
in the next chapter. To assist with understanding the convergence properties of
such algorithms, we can consider various kinds of light transport, some of which
are amenable to study with one technique, some with another. For instance,
a sequence of mirror reflections that conveys light from a point source to the
eye must be treated rather differently from a sequence of diffuse reflections
of illumination from an area light source. In fact, the phenomena produced by
various kinds of light-transport paths can also be quite different at a perceptual
level; we discuss this briefly, as well.
With the notion of the radiance field in hand, and that of the bidirectional
reflectance distribution function (BRDF), we can now discuss light transport in
general. We begin with the case of a scene consisting of empty space and purely
reflective objects (i.e., there is nothing that's partly transparent, and light reflects
from the surfaces of objects—there's no subsurface scattering to consider). The
scattering of light from an object is therefore described by the BRDF, which we'll
denote
f
r
(the “r” standing for “reflection”). This special case conveys the main
ideas but avoids some complexities. Having developed this first situation, we'll
generalize to other kinds of scattering, but with very few important changes.
We'll continue with the assumptions of Chapter 26, that the scattering of light
by a material comes in two parts: mirror and Snell-transmissive scattering, which
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