Graphics Reference
In-Depth Information
For mirror reflection, this is easy: We always return
v
r
, the mirror-reflected
version of
v
i
. For Lambertian scattering, we need to pick a direction on the hemi-
sphere, favoring the North Pole, and fading off in probability as we approach the
equator. Fortunately, using the Average Height principle, it's not too difficult to do
this. Section 30.3.8 gives the details.
For Blinn-Phong scattering, things are not so simple. Although it's possible to
sample directly from the BRDF by doing some careful computations, that's only
because of the nice power-of-a-cosine form; by the time other factors, like the
Fresnel term, get included such direct sampling is no longer possible. Far better is
to use an approach like that of Lawrence [Law04], which approximates the BRDF
with terms that are amenable to efficient sampling.
For ray tracing/path tracing, we have a similar problem, except that we're
given
v
o
)
.Andfor
direct computation of the reflectance integral, we may want to sample in propor-
tion to
f
s
(
v
o
and want to select
v
i
with density proportional to
f
s
(
v
i
,
n
)
.
The same arguments apply in these cases, except that in the Lambertian case
for the ray tracing/path tracing computation, instead of using the cosine-weighted
BRDF, we just need to sample in proportion to the BRDF, which is constant. In
other words, we just need to pick points uniformly on the hemisphere, which is
easy with the cylinder-sphere projection theorem.
v
i
,
v
o
)(
v
i
·
Phenomenological models tend to approximate well those things that we, as
humans, recognize as “phenomena.” But it's possible that other aspects of scat-
tering, when combined with light transport, produce other “phenomena” as well,
and if we suppress those aspects, these secondary phenomena will never be simu-
lated. The only way to know is to have a ground-truth representation of the scat-
tering, and compare results of simulations that use this ground truth to those that
use either phenomenological or physically based approximations to it, and see
whether the results differ significantly.
One such ground-truth representation is provided by the full BRDF measure-
ments made by Matusik et al. [MPBM03] of about one hundred isotropic materi-
als. For an isotropic material, the BRDF, represented in polar coordinates, depends
only on the
difference
between the longitude coordinates of
v
o
, so the data
can be tabulated in a three-index table (two latitudes, one longitude difference).
Tabulated at approximately one sample per degree, these tables have many entries
(
90
v
i
and
180
)
, each of which is an RGB triple. (The sampling near glossy
highlights is deliberately somewhat denser so that very shiny materials can be
accurately represented.)
Others have measured various anisotropic materials [War92], texture charac-
teristics of surfaces [DvGNK99], and more complex data like subsurface scatter-
ing distribution [JMLH01], and have developed image-based approaches to mea-
suring BRDFs without the high cost of a gonioreflectomer [MLW
+
99].
One value of these measurements is that they can be used to compare the
expressive power of various BRDF models: if optimally adjusting all the param-
eters of the Blinn-Phong model, for instance, only allowed you to get within
5% of the measured values, and that only for, say, 90% of all possible
(
×
90
×
v
o
)
pairs, you might conclude that the Blinn-Phong model was not sufficiently rich to
v
i
,
