Graphics Reference
In-Depth Information
Since these all just describe scattering (and lack of scattering, due to absorp-
tion), they are typically described by a scattering function. There are several vari-
ations, among them the bidirectional scattering distribution function (BSDF)
for surface scattering, the reflectance-only variant (BRDF) for purely opaque sur-
faces, the BTDF for purely transmissive surfaces, and the BSSDF for describing
both surface and shallow subsurface effects. BSDFs alone require fairly in-depth
discussion of a specific rendering algorithm and surface physics to describe prop-
erly. Fortunately, one can also get by with a fairly simple model and application
of it. A substantial portion of the pixels rendered in the past 30 years all used
variations on the same simplified model, and it will likely be with us for some
time.
In the following subsections we sketch the basic idea of a BSDF interface and
one of the simple phenomenologically based models in common use today for
opaque surfaces. We then return to some common approximations of transmission
using compositing instead of BSDFs.
14.9.1 Scattering Functions (BSDFs)
n
v i
v o
Scattering can be described by a function ( P ,
v o )
f s ( P ,
v o ) that repre-
v i ,
v i ,
sents the probability density of light propagating in direction
v i scattering to
direction
v o when it strikes the surface at point P (see Figure 14.25). In general, a
“brighter” or more reflective diffuse surface will have higher values of f s () .(The
precise definition of f s is given in Chapter 26.)
P
Figure
14.25:
The
vector
v
i
points toward the light source
(represented by the star), so light
propagates in direction v i .The
light
In writing f s ( P ,
v o ) , we are introducing notation that we'll use throughout
the discussion of rendering in the remainder of the topic. The function f s will
always represent scattering. P will often represent a point of some surface at
which we're computing scattering,
v i ,
scatters
at
P
and
leaves
v i is the direction from P to the source of
light arriving at P (thus, the light travels in direction
in
various
directions
v o .The
v i ), and
v o will be the
value f s ( P ,
v i ,
v o ) measures the
direction in which light leaves P .
scattering.
The use of f s is a mathematical convenience. In our programs, f s is typically
defined in terms of some “basic” scattering function f defined by how it scat-
ters light from a surface in the xz -plane whose outward normal vector is in the
positive- y direction. As an example, a surface that preferentially scatters light in
the normal direction could be modeled by
0
if
v i or
v o points in the
y halfplane
2
0
1
0
f ( k ,
v i ,
v o )=
v o ·
·
k
otherwise
(14.14)
y ,0 ) 2
= k
·
max(
v o ·
where k is a number between 0 and 1 describing how reflective the surface is (for
this simple case, it reflects all wavelengths equally well). The function f is large
when
v o is near the y -direction and small when it's near the xz -plane. When we
want to use f to represent the scattering from a surface that's not oriented with its
normal vector in the positive- y direction, we write f s so that it first transforms
v i
 
 
 
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