@inproceedings{f5ce642e2b36438da0fcc3a00bd091af,

title = "Table based detection of degenerate predicates in free space construction",

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.",

keywords = "Degenerate predicates, Free space construction, Robustness",

author = "Victor Milenkovic and Elisha Sacks and Nabeel Butt",

note = "Funding Information: Supported by NSF CCF-1526335. Sacks and Butt supported by NSF CCF-1524455. Funding Information: Supported by NSF CCF-1526335. 2 Sacks and Butt supported by NSF CCF-1524455. Publisher Copyright: {\textcopyright} Victor Milenkovic, Elisha Sacks, and Nabeel Butt; licensed under Creative Commons License CC-BY 34th Symposium on Computational Geometry (SoCG 2018).; 34th International Symposium on Computational Geometry, SoCG 2018 ; Conference date: 11-06-2018 Through 14-06-2018",

year = "2018",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.SoCG.2018.61",

language = "English (US)",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "611--6114",

editor = "Toth, {Csaba D.} and Bettina Speckmann",

booktitle = "34th International Symposium on Computational Geometry, SoCG 2018",

address = "Germany",

}