We show how importance-driven refinement and a wavelet basis can be co
mbined to provide an efficient solution to the global illumination pro
blem with glossy and diffuse reflections. Importance is used to focus
the computation on the interactions having the greatest impact on the
visible solution. Wavelets are used to provide an efficient representa
tion of radiance, importance, and the transport operator. We discuss a
number of choices that must be made when constructing a finite elemen
t algorithm for glossy global illumination. Our algorithm is based on
the standard wavelet decomposition of the transport operator and makes
use of a four-dimensional wavelet representation for spatially and an
gularly varying radiance distributions. We use a final gathering step
to improve the visual quality of the solution. Features of our impleme
ntation include support for curved surfaces as well as texture-mapped
anisotropic emission and reflection functions.