Graphics Reference
In-Depth Information
SH basis functions
Light source
CG object
Figure 10.3
Lighting using SH basis functions.
the SH expansion. In short, spherical harmonic representations are not suited for
high-frequency (highly specular) environments.
It is worth mentioning that low-frequency SH approximations are useful in
themselves. For example, the order-0 approximation is just a constant—the av-
erage value of the function over the entire sphere. In Chapter 7 it was explained
how the SH approximation is one way of filtering an environment map.
Figure 10.3 illustrates the idea of illuminating an object from a set of light
sources. Alternatively, the incident illumination might be from an environment
map or some other computed radiance distribution. The figure on the right il-
lustrates schematically how the terms in the corresponding spherical harmonics
approximation increase in frequency. The first-order term is constant.
10.1.2 Radiance Transfer and Light Vectors
An advantage of using spherical harmonics, or any other fixed set of basis func-
tions, is that the representation of the incident light (or whatever signal is being
approximated) reduces to a set of basis function coefficients. These coefficients
can be collected into a single vector. In the case of an order-
n
SH approximation,
as in Equation (10.2), this vector is
=(
1
,
2
,...,
n
2
)
.
In the context of PRT, the vector
is called a
light vector
. Spherical harmon-
ics can be used to approximate any spherical function, or for that matter, any
hemispherical function. Both the incident radiance at a surface point and the out-
going radiance can be approximated with a spherical harmonics expansion, and
thus expressed as a light vector. The light vector for the outgoing radiance can
be regarded as a function of the incident light vector; this is known as a
trans-
