Graphics Reference
In-Depth Information
not valid in this case. The proof of Equation (8.12) involves a frequency domain
analysis, and requires that the BRDF has a lower frequency than the illumination
pattern. In essence, this means that the BRDF lobes are at least as wide as the
apparent angle of the checkerboard squares of the light source. For most scenes
this is a reasonable assumption, but if the scene has strongly specular elements,
separation cannot be performed. Of course, the frequency of the lighting pattern
can always be increased to match the frequency of the BRDF, but the lighting
frequency has to be well above the image pixel frequency because the separation
depends on being able to discern lit and unlit pixels in the captured images.
Participatingmedia and scattering.
The derivation above omits volumet-
ric scattering; i.e., there is no scattering of light between surface patches. How-
ever, an adjustment to the argument generalizes the result to scenes involving a
participating medium. The effects of scattering can be separated into two types
(
Figure 8.42
)
. The first effect is scattering between surface patches, which is part
of GI computation and can be accomplished by integrating over rays incident at a
surface point. The averaging assumption applies in this situation much as it does
in the integration over patches, so the indirect component can be separated in the
same way.
The second effect is the in-scattering toward the viewpoint (camera), which
makes the participating medium itself visible. This is computed by integrating
over each ray in the set of rays forming the line of sight of a pixel. For this
computation it is helpful to (hypothetically) divide the scene volume into voxels
corresponding to the squares of the checkerboard illumination. Each voxel is
then either directly illuminated in full, or not directly illuminated at all. Each ray
through a pixel can be expected to hit approximately a fraction
α
lit voxels, and
Patch
i
Patch
j
Patch
j
Patch
i
(a)
(b)
Figure 8.42
Effects of a scattering medium.
