Examining the Distribution of Sampling Point Sets on Sphere for Monte Carlo Image Rendering

This paper presents a study of several non-uniform and uniform techniques for sampling of unit sphere and gives an comparative analysis on uniform sampling techniques. Each sampling technique generates point sets distributed on sphere. We are interested to examine the quality of their distributions, which could impact on the Monte Carlo image creation. Generalized discrepancy is designed as a measure for equidistribution of point sets on spherical sampling patterns as well as applied to analyze sampling techniques used in rendering. We generate sphere sampling patterns using various random number generators and Halton low discrepancy sequence. The generalized discrepancy is computed for increasing number of points for each sampling pattern. Finally, the results for different uniform sampling techniques are studied and analyzed by comparison of the uniformity of distributions.