Graphics Reference
In-Depth Information
propriate format. The original PRT method represents the incident and reflected
light in terms of a spherical-harmonics expansion, which is a linear combination
of SH basis functions as described in Chapter 7. Even though the SH basis func-
tions themselves are nonlinear, they can be computed on a GPU or precomputed
and passed to the GPU at render time. This enables dynamic real-time rendering
of objects, including effects such as shadowing and interreflection, that was not
possible before the creation of the PRT technique.
PRT has gathered a great deal of attention since it was first introduced in 2002,
and has had a substantial impact in the field of real-time rendering. The original
PRT method had many limitations: the approximated light could only represent
very soft shadows under diffuse lighting, specular reflection was included only to
a limited extent, and the shapes of the objects had to be fixed (although they could
move with respect to each other). Much of the subsequent work has involved
generalizing the basic method and improving its versatility. New approaches have
been proposed that replaced the SH basis functions with more general basis sets,
such as wavelets. Sloan, Kautz, and Snyder, who originally developed the method,
have been actively involved in this subsequent research, and have published sev-
eral improvements to the original method. This final chapter introduces the basic
PRT method, and explores some of the subsequent developments in precomputed
transfer for rendering.
10.1 PRT Fundamentals
The work described in the original PRT paper was primarily concerned with a
single object illuminated by a distant environment map. The reflected radiance
(or the outgoing radiance, in general) at a set of sample points on the object is
represented by an expansion in spherical harmonics, which represents the outgo-
ing radiance from any viewpoint. The coefficients of the SH approximation can
be calculated quickly from the incident illumination using precomputed
transfer
functions
. This allows the object to be rendered at interactive rates as the view-
point and incident illumination are controlled by a user of the rendering system.
Shadowing and interreflection are included in the precomputation and therefore
change according to the lighting. The paper also describes how the method can
be applied to more than one object, where there is significant shadowing and in-
terreflection between the objects.
10.1.1 Light Approximations using SH Basis Functions
Spherical harmonics (SH) were introduced in Chapter 7 in the context of ap-
proximating and filtering environment maps as functions on a sphere. Specifi-
