Illumination in the Presence of Weak Singularities

Approximating illumination by point light sources, as done in many professional applications, allows for efficient algorithms, but suffers from the problem of the weak singularity: Besides avoiding numerical exceptions caused by the division by the squared distance between the point light source and the point to be illuminated, the estimator should be unbiased and of finite variance. We first illustrate that the common practice of clipping weak singularities to a reasonable value yields clearly visible bias. Then we present a new global illumination algorithm that is unbiased and as simple as a path tracer, but elegantly avoids the problem of the weak singularity. In order to demonstrate its performance, the algorithm has been integrated in an interactive global illumination system.