Graphics Reference
In-Depth Information
If a point light hits a mirror surface or transmits through a translucent surface,
we can then compute the result of its scattering from the
next
diffuse surface, etc.
This eventually becomes a serious bookkeeping problem, and since point lights
are merely a convenient fiction, we ignore it: We compute only diffuse scattering
of point lights. Although addressing this properly in a ray-tracing-based renderer
is difficult, we'll see later that in the case of photon mapping, it's quite simple.
One useful compromise for point-light sources is to say that for the purpose of
emission directly toward the eye, the point source is actually a glowing sphere of
some small radius,
r
, while when it's used in the calculation of direct illumination,
it's treated as a point. This compromise, however, has the drawback that it requires
the design of the class for representing lights to know something about the kinds
of rays that will be interacting with it (i.e., an eye ray will be intersection-tested
against a small sphere, while a secondary ray will never meet the light source at
all), which violates encapsulation.
Recall the basic idea of ray tracing and path tracing: For each pixel of the image,
we shoot several rays from the eye through the pixel area. A typical ray (the red
one in Figure 32.5) hits the scene somewhere, and we compute the direct light
arriving there (the nearly vertical blue ray), and how it scatters back along the
ray toward the eye (gray). We then trace one or more recursive rays (such as the
yellow ray that hits the wall), and compute the radiance flowing back along
them,
and how it scatters back toward the eye, etc. Having computed the radiance back
toward the eye along each of the rays through our pixel, we take some sort of
weighted average and call that the pixel value.
Because of the usual description of ray tracing (“Start from the eye, and follow
a ray out into the scene until it hits a surface at some point
P
,and...”),we'lluse
the convention that the rays we discuss are always the result of tracing
from the
eye,
that is, the first ray points away from the eye, the second ray points away from
the first intersection toward a light or another intersection, etc. (see Figure 32.6).
Figure 32.5: Ray tracing.
Physical
direction
Algorithmic
direction
Figure 32.6: The algorithm works
from the eye toward the light
source (red); photons travel in
the opposite direction (blue).
On the other hand, the radiance we want to compute is the radiance that flows
along the ray in the other direction. If the eye ray
r
starts at the eye,
E
, and goes
in direction
)
,
that is, we want to compute the radiance in the
opposite
of
r
's direction. We'll
have various procedures like
Radiance3 estimateTotalRadiance(Ray r,
...)
; such functions always return the radiance flowing in the direction
opposite
that of
r
.
, meeting the scene at a point
P
, then we want to compute
L
(
P
,
−
v
v
We begin with a very simple path tracer, in which the image plane is divided
into rectangular areas, each of which corresponds to a pixel. If a ray toward the
eye passes through the
(
i
,
j
)
th rectangle, we treat the radiance as a sample of the
radiance arriving at that rectangle. Despite the simplicity of the path tracer, we'll
use a lot of symbols, which we list in Table 32.1; we'll define each one as we
encounter it.
