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Towards Soft Exact Computation (Invited Talk)

  • Chee YapEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11661)

Abstract

Exact geometric computation (EGC) is a general approach for achieving robust numerical algorithms that satisfy geometric constraints. At the heart of EGC are various Zero Problems, some of which are not-known to be decidable and others have high computational complexity. Our current goal is to introduce notions of “soft- Open image in new window correctness” in order to avoid Zero Problems. We give a bird’s eye view of our recent work with collaborators in two principle areas: computing zero sets and robot path planning. They share a common Subdivision Framework. Such algorithms (a) have adaptive complexity, (b) are practical, and (c) are effective. Here, “effective algorithm” means it is easily and correctly implementable from standardized algorithmic components. Our goals are to outline these components and to suggest new components to be developed. We discuss a systematic pathway to go from the abstract algorithmic description to an effective algorithm in the subdivision framework.

Notes

Acknowledgements

The author is deeply grateful for the feedback and bug reports from Michael Burr, Matthew England, Rémi Imbach, Juan Xu and Bo Huang.

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Authors and Affiliations

  1. 1.Department of Computer ScienceCourant Institute, NYUNew YorkUSA

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