Numerical Integration for Radiosity in the Presence of Singularities
Peter Schröder
Abstract
The radiosity method for computing global illumination in Lambertian
environments requires the computation of form factors. These are given by
integrals for which some closed form solutions exist. In general however
the integrals need to be approximated numerically. Various schemes have
been proposed for this computation. Most of these are based on proximity
assumptions which break down when surfaces are close to one another. More
recently researchers have introduced higher order Galerkin methods to solve
the radiosity equation. These methods generalize the notion of form factors
and complicate the evaluation of the involved integrals. In the present
paper we examine the behavior of previous form factor approximations as
well as the generalized form factors of higher order methods near the
singularity of the radiosity kernel. We introduce a new technique of
constructing quadrature rules specifically adapted to the singularity.
These rules are based on exact constant-constant transport and we report on
experiments showing the performance of these new rules.
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