Sampling with Hammersley and Halton Points

Abstract: The Hammersley and Halton point sets, two well known low discrepancy sequences, have been used for quasi-Monte Carlo integration in previous research. A deterministic formula generates a uniformly distributed and stochastic-looking sampling pattern, at low computational cost. The Halton point set is also useful for incremental sampling. In this paper, we discuss detailed implementation issues and our experience of choosing suitable bases of the point sets, not just on the 2D plane,but also on a spherical surface. The sampling scheme is also applied to ray tracing, with a significant improvement in error.


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