Line Sampling for Direct Illumination

Abstract

Computing direct illumination efficiently is still a problem of major significance in computer graphics. The evaluation involves an integral over the surface areas of the light sources in the scene. Because this integral typically features many discontinuities, introduced by the visibility term and complex material functions, Monte Carlo integration is one of the only general techniques that can be used to compute the integral. In this paper, we propose to evaluate the direct illumination using line samples instead of point samples. A direct consequence of line sampling is that the two-dimensional integral over the area of the light source is reduced to a one-dimensional integral. We exploit this dimensional reduction by relying on the property that commonly used sampling patterns, such as stratified sampling and low-discrepancy sequences, converge faster when the dimension of the integration domain is reduced. We show that, while line sampling is generally more computationally intensive than point sampling, the variance of a line sample is smaller than that of a point sample, resulting in a higher order of convergence.