Graphics Reference
In-Depth Information
in any viewing direction is therefore computed directly from the SH expansion,
which eliminates the need for interpolating the radiance in the viewing direction.
A drawback, however, is that the accuracy and visual quality of the represen-
tation depends on the intrinsic properties of spherical harmonics. The fact that
more specular reflection and increased detail in the environment map or a small
light source all increase the requisite order of the SH expansion is a serious prob-
lem. The irradiance environment map technique described in Chapter 7 uses an
order-3 approximation, but this is not sufficient for PRT even if the reflection is
totally diffuse simply because it does not represent shadowing well enough. The
“standard” PRT approach employs an order-5 approximation, which results in
25-dimensional light vectors and 25
25 transfer matrices. Merely doubling the
frequency to an order-10 approximation results in a 100
×
100 transfer matrix at
each sample point. The storage cost alone makes this impractical.
×
Using PCA.
The spherical harmonics representation eliminates interpolation in
the viewing direction, but not in the sample points on the surface. This means
that the surface points may have to be sampled densely enough for the interpola-
tion to be useful. Each sample point
p
requires (at least) a 25
25 exit transfer
matrix, so the storage requirements can be a problem. Much of this storage is
likely redundant; on smoother parts of the surface, the exit transfer matrices are
not likely to change very fast. A few representative sample points are therefore
likely to suffice, from which the values at other sample points can be interpo-
lated. In this case, the exit transfer matrices themselves are what is interpolated.
Another benefit of this approach of selecting representative sample points is that
when rendering the entire surface, only a few of the full matrix computations are
necessary. This makes it much easier to perform real-time rendering.
×
Exit Transfer Matrix
Signal
25
625
25
Figure 10.10
Signal construction.
