Graphics Reference
In-Depth Information
common, which amount to a fixed-sample strategy). We can integrate over the
lens area to get depth-of-field effects and chromatic aberration. For a scene that's
moving, we can simulate the effect of a shutter that's open for some period of
time by integrating over a fixed “time window.” All of these ideas were described
in a classic paper by Cook et al. [CPC84], which called the process distributed
ray tracing. Because of possible confusion with notions of distributed processing,
we prefer the term
distribution ray tracing
which Cook now uses to describe
the algorithm [Coo10]. We'll discuss the particular sampling strategies used in
distribution ray tracing in Chapter 32.
In short: To render a realistic image in the general case, we need to average, in
some way, many values, each of which is
L
(
P
,
)
for some point
P
of the image
v
S
2
.
plane and some direction
v
∈
We'll now briefly discuss radiosity—an approach that produces renderings for
certain scenes very effectively—and then return to the more general scenes that
require sampling methods and discuss how to effectively estimate the value
L
(
P
,
)
in the algorithms that work on those scenes.
The radiosity method for rendering differs from the methods we've seen in
Chapter 15; in those methods, we started with the imaging rectangle and said,
“We need to compute the light that arrives here, so let's cast rays into the scene
and see where they hit, and compute the light arriving at the hit point by various
methods.” Whether we did this one pixel at a time or one light at a time or one
polygon at a time was a matter of implementation efficiency. The key thing is that
we said, “Start from the imaging rectangle, and use
that
to determine which parts
of the light transport to compute.” A radically different approach is to simulate
the physics directly: Start with light emitted from light sources, see where it ends
up, and for the part that ends up falling on the imaging rectangle, record it. This
approach was taken by Appel [App68], who cast light rays into the scene and
then, at the image plane location of the intersection point (if it was visible), drew
a small mark (a “+” sign). In areas of high illumination there were many marks; in
areas of low illumination, almost none. By taking a black-and-white photograph
of the result (which was drawn with a pen on plotter paper) and then examining
the
negative
for the photograph, he produced a rendering of the incident light.
Radiosity takes a similar approach, concentrating first on the light in the scene,
and only later on the image produced. Because the surfaces in the scene are
assumed Lambertian, the transformation from a representation of the surface radi-
ance at all points of the scene to a final rendering is relatively easy.
The radiosity approach has two important characteristics.
v
•
It's a solution to a
subproblem,
in the sense that it only applies to Lam-
bertian reflectors, and is generally applied to scenes with only Lambertian
emitters.
•
It's a “discretization” approach: The problem of computing
L
(
P
,
v
o
)
for
S
+
(
P
)
is reduced to computing a finite set of values.
The scene is partitioned into small patches, and we compute a radiosity
value for each of these finitely many patches.
every
P
∈
M
and
v
o
∈
