Table based detection of degenerate predicates in free space construction

Victor Milenkovic, Elisha Sacks, Nabeel Butt

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The key to a robust and efficient implementation of a computational geometry algorithm is an efficient algorithm for detecting degenerate predicates. We study degeneracy detection in constructing the free space of a polyhedron that rotates around a fixed axis and translates freely relative to another polyhedron. The structure of the free space is determined by the signs of univariate polynomials, called angle polynomials, whose coefficients are polynomials in the coordinates of the vertices of the polyhedra. Every predicate is expressible as the sign of an angle polynomial f evaluated at a zero t of an angle polynomial g. A predicate is degenerate (the sign is zero) when t is a zero of a common factor of f and g. We present an efficient degeneracy detection algorithm based on a one-time factoring of every possible angle polynomial. Our algorithm is 3500 times faster than the standard algorithm based on greatest common divisor computation. It reduces the share of degeneracy detection in our free space computations from 90% to 0.5% of the running time.

Original languageEnglish (US)
Title of host publication34th International Symposium on Computational Geometry, SoCG 2018
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages611-6114
Number of pages5504
Volume99
ISBN (Electronic)9783959770668
DOIs
StatePublished - Jun 1 2018
Event34th International Symposium on Computational Geometry, SoCG 2018 - Budapest, Hungary
Duration: Jun 11 2018Jun 14 2018

Other

Other34th International Symposium on Computational Geometry, SoCG 2018
CountryHungary
CityBudapest
Period6/11/186/14/18

Fingerprint

Polynomials
Computational geometry

Keywords

  • Degenerate predicates
  • Free space construction
  • Robustness

ASJC Scopus subject areas

  • Software

Cite this

Milenkovic, V., Sacks, E., & Butt, N. (2018). Table based detection of degenerate predicates in free space construction. In 34th International Symposium on Computational Geometry, SoCG 2018 (Vol. 99, pp. 611-6114). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2018.61

Table based detection of degenerate predicates in free space construction. / Milenkovic, Victor; Sacks, Elisha; Butt, Nabeel.

34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. p. 611-6114.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Milenkovic, V, Sacks, E & Butt, N 2018, Table based detection of degenerate predicates in free space construction. in 34th International Symposium on Computational Geometry, SoCG 2018. vol. 99, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, pp. 611-6114, 34th International Symposium on Computational Geometry, SoCG 2018, Budapest, Hungary, 6/11/18. https://doi.org/10.4230/LIPIcs.SoCG.2018.61
Milenkovic V, Sacks E, Butt N. Table based detection of degenerate predicates in free space construction. In 34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. p. 611-6114 https://doi.org/10.4230/LIPIcs.SoCG.2018.61
Milenkovic, Victor ; Sacks, Elisha ; Butt, Nabeel. / Table based detection of degenerate predicates in free space construction. 34th International Symposium on Computational Geometry, SoCG 2018. Vol. 99 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. pp. 611-6114
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