Graphics Reference
In-Depth Information
of the shape of object
B
, and even if object
B
moves. The ability to move objects
around interactively at render time was a remarkable accomplishment.
10.1.6 PRT Limitations
PRT was originally developed to represent low frequency light transfer. The goal
was to render a Lambertian object under diffuse lighting conditions, including
shadows and interreflection effects, in real time. Spherical harmonics do a good
job representing this kind of illumination. An advantage of the SH approach is
that relatively few directional samples are needed to get a good approximation
with low-degree SH basis functions. This is useful for broad area light sources,
which have a large solid angle and therefore would otherwise require a lot of
point samples. Furthermore, diffuse lighting generally creates diffuse shadowing,
which means the spatial variation in illumination changes slowly. Consequently,
the positional dependence can be represented by interpolating relatively sparse
samples. Moreover, the computation is well suited to hardware implementation
given precomputed transfer functions.
With high-frequency lighting, which arises from small light sources, shadow
edges get sharper. As a result, the illumination has to be densely sampled across
the surface to properly capture the appearance. This substantially increases the
storage requirements as well as the precomputation time. In addition, high-
frequency lighting requires a high-order SH approximation to capture the true
nature of the light. If there is only one light source, and it is small, the represen-
tation is inefficient. A small source requires fewer point samples, so it is more
reasonable to just sample the source directly at render time. That is, the bene-
fit of the precomputation drops as the light source decreases in size. However,
precomputation of high-frequency lighting can still be effective, especially for in-
direct lighting. Rendering caustics, which normally requires a very large number
of samples, can benefit from precomputation.
High-frequency reflection, i.e., highly specular reflection, causes problems
with SH representation as well. Even though reflection does not generally in-
crease the spatial frequency of the incident light, reflections of other scene
elements can have high frequency detail (consider a mirror surface reflecting
an object having a finely detailed texture). In terms of the transfer matrix, the
number of columns corresponds to the dimension of the incident light vector
;
the number of rows corresponds to that of the outgoing light vector
r
. Increasing
the specularity increases the required dimension of the outgoing vector, which
in turn increases the number of rows in the matrix. In summary, spherical har-
monic approximations work well for low-frequency lighting and reflection, but
are poorly suited to medium- and high-frequency effects. A fundamental problem
