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Asymptotic speed-ups in constructive solid geometry

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Abstract

We convert constructive solid geometry input to explicit representations of polygons, polyhedra, or more generallyd-dimensional polyhedra, in time and space 0(nd), improving a previous0(nd logn) time bound. We then show that any Boolean formula can be preprocessed in time0(n log n/log logn) and linear space so that the value of the formula can be maintained, as variables are changed one by one, in time O(log n/log logn) per change; this speeds up certain output-sensitive algorithms for constructive solid geometry.

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Authors and Affiliations

  1. Department of Information and Computer Science, University of California, 92717, Irvine, CA, USA

    D. Eppstein

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  1. D. Eppstein
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Communicated by Chee-Keng Yap.

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Eppstein, D. Asymptotic speed-ups in constructive solid geometry. Algorithmica 13, 462–471 (1995). https://doi.org/10.1007/BF01190849

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  • DOI: https://doi.org/10.1007/BF01190849

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