Graphics Reference
In-Depth Information
Chapter 31
In this chapter we discuss the theory of solving the rendering equation, concentrat-
ing on the mathematics of various approaches and on what kinds of approxima-
tions are involved in these approaches, deferring the implementation details to the
next chapter. Fortunately, much of the mathematics can be understood by analogy
with far simpler problems. When we render, we're trying to compute values of
L
, the radiance field, or expressions involving combinations (typically integrals)
of many values of
L
. Thus, the unknown is the whole
function L
. That's in sharp
contrast to the equations like
3
x
2
+
x
=
13
(31.1)
that we see in algebra class, where the unknown,
x
, is a single number. Nonethe-
less, such simple equations provide a useful model for the approximations made
in the more complicated task of finding
L
; we discuss these first, and then go on
to apply these ideas to rendering.
There's no hope of solving the rendering equation exactly for any scene with even
a moderate degree of complexity. Instead, we are forced to
approximate
solu-
tions. There are four common forms of approximation that are routinely used in
graphics:
• Approximating the equation
• Restricting the domain
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