Graphics Reference
In-Depth Information
we'll call
impulses,
and everything else. Impulse scattering is characterized by
the idea that radiance along some incoming ray is transformed to radiance along a
small number (one or two, typically) of outgoing rays. Such scattering cannot be
represented by an integral like the one in the reflectance equation unless we admit
the possibility of “delta functions” in the scattering function
f
s
. Nonetheless, we'll
continue to write the transformation from incoming to scattered light in the form
of the scattering equation (i.e., as an integral), and will consider, in Section 29.6,
the consequences of impulses in
f
s
after developing the main ideas.
Similarly, although the emitted light in a scene typically comes from physical
objects like lamps or the sun, which have nonzero size, it's convenient (and tra-
ditional) to allow point lights in a scene as well. These amount to impulses in
L
e
,
and must also be handled specially. These, too, will be discussed in Section 29.6.
We'll be discussing
light,
the flow of photons in a scene, extensively. But
we also want to talk about light
sources
, which are informally called lights in
expressions like “point light” and “area light.” To keep these two notions distinct,
we'll use the term
luminaire
to mean a light source throughout this chapter.
To discuss light transport, we need to use quite a lot of notation, which we'll
reuse in subsequent chapters. We summarize these symbols in Table 29.1, even
though some are given full definitions only later in the chapter.
Table 29.1: Symbols used in light transport and rendering.
Symbol
Meaning
E
The eye point.
P
A surface point in the scene, often the first one encountered by a
ray from the eye, but sometimes used generically.
Q
,
Q
j
A point on the surface of a luminaire or some other source of light
arriving at
P
, such as an illuminated reflective surface.
M
The set of all surfaces in the scene.
The unit normal vector at
P
, which we've denoted
n
(
P
)
previ-
ously, or the same thing for
Q
;using
n
P
slightly reduces the com-
plexity of equations.
n
P
,
n
Q
A ray pointing from
P
toward some source of light.
v
i
A ray pointing from
P
in the direction in which reflected light
from
v
o
v
i
exits, typically toward
E
.
A generic name for a unit vector, typically based at
P
.
v
L
(
P
,
)
The radiance at a surface point
P
in direction
.
v
v
L
e
(
P
,
)
The light emitted at point
P
in direction
; zero except when
P
is
v
v
a point of a luminaire.
L
ref
(
P
,
v
)
The light reflected at
P
in direction
v
.
L
r
(
P
,
)
v
The light reflected or transmitted (refracted) at
P
in direction
v
.
L
=
L
e
+
L
r
.
f
s
The bidirectional scattering distribution function.
f
r
The bidirectional reflectance distribution function.
f
s
The “impulse” part of
f
s
, corresponding to transmission or mirror
reflection.
f
s
The finite part of
f
s
, corresponding to nonmirror reflection.
