T. Kollig, A. Keller

• Approximating illumination by point light sources, as done in many professional applications, suffers from the problem of the weak singularity: Numerical exceptions caused by the division by the squared distance between the point light source and the point to be illuminated must be avoided. Multiple importance sampling overcomes these problems by combining multiple sampling techniques by weights. Such a set of weights is called a heuristic. So far the estimators resulting from a heuristic only have been analyzed for variance. Since the cost of sampling is not at all constant for different sampling techniques, it is possible to find more efficient heuristics, even though they may hove higher variance. Based on our new stratification heuristic, we present a robust and unbiased global illumination algorithm. By numerical examples, we show that it is more efficient than previous heuristics. The algorithm is as simple as a path tracer, but elegantly avoids the problem of the weak singularity.