An Implementation Algorithm of 2D Sobol Sequence Fast, Elegant, and Compact
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Date
2024
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
We present a novel algorithm to evaluate 2D Sobol samples, bringing the time complexity for m-bit resolution to O(log(m)) instead of O(m), thus gaining tangible performance boost. We take advantage of the geometric structure of the underlying Pascal matrix to factor it into diagonally-running matrices that are efficient to implement using bit-wise operations. We extend the method to inversion in global Sobol sampling. The algorithms form a flexible framework, able to generate several wellknown sample sequences as special cases. We compare the speed performance and memory footprint of our algorithms to state of the art implementations.
Description
@inproceedings{10.2312:sr.20241147,
booktitle = {Eurographics Symposium on Rendering},
editor = {Haines, Eric and Garces, Elena},
title = {{An Implementation Algorithm of 2D Sobol Sequence Fast, Elegant, and Compact}},
author = {Ahmed, Abdalla G. M.},
year = {2024},
publisher = {The Eurographics Association},
ISSN = {1727-3463},
ISBN = {978-3-03868-262-2},
DOI = {10.2312/sr.20241147}
}