Algebraic methods and arithmetic filtering for exact predicates on circle arcs

Olivier Devillers 1 Alexandra Fronville 2 Bernard Mourrain 2 Monique Teillaud 1
1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
2 SAGA - Algebraic Systems, Geometry and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The purpose of this paper is to present a new method to de- sign exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the com- parison of the abscissae of two intersection points of circle arcs, which is known to be a difficult predicate involved in the computation of arrangements of circle arcs. We present an algorithm for deciding the x-order of intersections from the signs of the coefficients of a polynomial, obtained by a general approach based on resultants. This method allows the use of efficient arithmetic and filtering techniques lead- ing to fast implementation as shown by the experimental results.
Type de document :
Communication dans un congrès
Annual Symposium on Computational Geometry, 2000, Hong Kong, China. pp.139-147, 〈http://www.cse.ust.hk/tcsc/scg00.html〉. 〈10.1145/336154.336194〉
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https://hal.inria.fr/hal-01179417
Contributeur : Olivier Devillers <>
Soumis le : mercredi 22 juillet 2015 - 14:30:36
Dernière modification le : samedi 27 janvier 2018 - 01:30:59

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Olivier Devillers, Alexandra Fronville, Bernard Mourrain, Monique Teillaud. Algebraic methods and arithmetic filtering for exact predicates on circle arcs. Annual Symposium on Computational Geometry, 2000, Hong Kong, China. pp.139-147, 〈http://www.cse.ust.hk/tcsc/scg00.html〉. 〈10.1145/336154.336194〉. 〈hal-01179417〉

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