Graphics Reference
In-Depth Information
portance Sampling Using a Factored Representation” [Lawrence et al. 04]. The
method performs importance sampling efficiently by separating the BRDF into
a 2D function that depends only on viewing direction, and a 1D function that
depends on a function of the incident angles
i
.
Although a BRDF generally depends on four variables, some BRDFs con-
tain redundancy. A notable example arises when the surface reflection does not
change (much) as the surface is rotated around the surface normal. In this case,
the reflection is said to be
isotropic
.
1
An isotropic BRDF depends on three variables: the polar angles
θ
i
and
φ
θ
i
,
θ
r
and the
.
2
Many real surfaces exhibit isotropic
or nearly isotropic reflection. Plastic, polished metal, paper, human skin, and most
painted surfaces are typical examples of isotropic surfaces. In contrast, some
surface reflection is distinctly
anisotropic
. Surfaces that have an oriented sur-
face roughness usually exhibit anisotropic reflection. Fine oriented scratches in
brushed or milled metal cause reflection to vary with rotation: a brushed metal ob-
ject looks entirely different, depending on whether the view direction aligns with
the scratches or is perpendicular to them. Woven cloths also exhibit anisotropic
reflection, as their appearance depends on the orientation of the woven threads.
difference of the azimuthal angles
|
φ
−
φ
|
r
i
8.1.2 Basic BRDF models
BRDFs for two special kinds of surface reflection, ideal diffuse reflection and
ideal mirror reflection, were developed in Chapter 1 and are reviewed here. A
Lambertian surface exhibits ideal diffuse reflection: incident illumination is re-
flected uniformly in all directions.The reflected radiance in any direction is pro-
portional to the incident radiance, regardless of incident direction. The BRDF of
a Lambertian surface is therefore a constant, given by
f
r
=
ρ
d
(
x
)
,
π
where
is the albedo (Lambertian reflectance), the ratio of radiant exitance
to the incident irradiance as defined in Equation (1.12). (The factor of 1
ρ
d
(
x
)
comes
in converting radiant exitance to radiance.) An ideal mirror surface reflects all the
light coming from one direction to the direction of mirror reflection. The BRDF
of a perfect mirror therefore acts as a Dirac
/
π
δ
, where the value of
f
r
is “infinity”
1
The term
isotropic
is also used in the context of light scattering to mean that the scattering is
uniform in all directions (see Chapter 3). The word is derived from the Greek
iso
, meaning “equal”
and
tropos
, loosely meaning “turn.” In general, “isotropic” refers to anything that stays constant under
rotation.
2
Recent research into isotropic BRDFs suggests that some can be adequately represented as a
function of only
two
variables [Stark et al. 05, Edwards et al. 06].
