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Sweep methods for parallel computational geometry

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Abstract

In this paper we give efficient parallel algorithms for a number of problems from computational geometry by using versions of parallel plane sweeping. We illustrate our approach with a number of applications, which include:

  • General hidden-surface elimination (even if the overlap relation contains cycles).

  • CSG boundary evaluation.

  • Computing the contour of a collection of rectangles.

  • Hidden-surface elimination for rectangles.

There are interesting subproblems that we solve as a part of each parallelization. For example, we give an optimal parallel method for building a data structure for line-stabbing queries (which, incidentally, improves the sequential complexity of this problem). Our algorithms are for the CREW PRAM, unless otherwise noted.

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Communicated by M. Snir.

This research appeared in preliminary form inProc. 2nd ACM Symp. on Parallel Algorithms and Architectures, 1990, pp. 280–289. The research of M. T. Goodrich was supported by the National Science Foundation under Grants CCR-8810568, CCR-9003299, CCR-9300079, and IRI-9116843. The research of M. J. Ghouse and J. Bright was supported by the NSF and DARPA under Grant CCR-8908092.

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Goodrich, M.T., Ghouse, M.R. & Bright, J. Sweep methods for parallel computational geometry. Algorithmica 15, 126–153 (1996). https://doi.org/10.1007/BF01941685

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  • DOI: https://doi.org/10.1007/BF01941685

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