Sampling with Hammersley and Halton Points

1 January 1997

journal article
research article
Published by Taylor & Francis in Journal of Graphics Tools

Vol. 2 (2) , 9-24
https://doi.org/10.1080/10867651.1997.10487471

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 stochasticlooking 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 for the point sets, not just on the two-dimensional plane but also on a spherical surface. The sampling scheme is also applied to ray tracing, with a significant improvement in error over standard sampling techniques.

Keywords

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