Graphics Reference
In-Depth Information
thought of as two points: one on the “outside” and the other on the “inside.” Light
traveling northward at the outer point is either reflected or transmitted, while light
traveling northward at the inner point is arriving there and is about to be trans-
mitted or reflected by the glass-air interface. As we suggested, we can enhance
the notion of the light field to take three arguments—a point, a direction, and a
normal vector that defines the “outside” for this point—but in the remainder of
this chapter, we're going to instead discuss only reflection (except at a few care-
fully indicated points), since (a) the two-points-in-one-place idea complicates the
notation, which is complex enough already, and (b) the actual changes in the pro-
grams that we'll see in Chapter 32 to account for transmission are relatively minor
and straightforward. As for the matter of keeping two separate copies of the north
pole, in practice, as we'll discuss in Chapter 32, we'll only keep a single copy of
the geometry, and there will be no explicit representation of the light field; on the
other hand, the meaning of an arriving light ray, and how it is treated, will depend
on the dot product of its direction with the unit normal n , resulting in several
if-else clauses in our programs.
Figure 31.5: Light from above the
sphere both reflects and refracts,
as does light in the inside of the
sphere.
We'll continue to write f s for the scattering function, however, but you'll need
to remember that in the case of transmission, some
v ·
n terms may need absolute-
value signs on them.
Notation: In some papers, L in is L ( P ,
) . Jensen uses L r
for reflected radiance, L i for incoming radiance, and L t for transmitted radi-
ance. RTR does the same thing. RTR uses L i and L o , with the direction chang-
ing based on the subscript. Shirley uses k i and k o for our w i and w o ; Arvo calls
L i and L o “field” and “surface” radiance. By the way, what we call the radiance
field is also called the “plenoptic function” and the “light field.”
) and L out is L ( P ,
v
v
) in a
scene by saying that the radiance at some surface point, in some direction, is a sum
of (a) the radiance emitted at that point in that direction, and (b) all the incoming
light at that point that is scattered in that direction. This equation has the form
The rendering equation characterizes the radiance field ( P ,
)
L ( P ,
v
v
L = E + T ( L ) .
(31.27)
Recall the meaning of the terms:
E is the emitted radiance field, with E ( P ,
v
)= 0 unless P is a point of
some luminaire, and
v
is a direction in which that luminaire emits light
from P .
T ( L ) is the scattered radiance field due to L ; T ( L )( P ,
v o ) is the light scat-
tered from the point P in the direction
v o when the radiance field for the
whole scene is L . 1
To be specific, T is defined by
v o )=
v i S + ( P )
T ( L )( P ,
L ( P ,
v i ) f s ( P ,
v i ,
v o )(
v i ·
n ( P )) d
v i .
(31.28)
1. We use the letter T rather than S (for “scattering”) because S will be used later in
describing various light paths.
 
 
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