Algebraic methods and arithmetic filtering for exact predicates on circle arcs

Olivier Devillers 1 Alexandra Fronville 1 Bernard Mourrain 1 Monique Teillaud 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The purpose of this paper is to present a new method to design exact geometric predicates in algorithms dealing with curved objects such as circular arcs. We focus on the comparison 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 leading to fast implementation as shown by the experimental results.
Document type :
Journal articles
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download

https://hal.inria.fr/inria-00166709
Contributor : Olivier Devillers <>
Submitted on : Wednesday, August 8, 2007 - 6:19:37 PM
Last modification on : Saturday, January 27, 2018 - 1:31:40 AM
Long-term archiving on : Friday, April 9, 2010 - 12:31:21 AM

File

cercle.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Olivier Devillers, Alexandra Fronville, Bernard Mourrain, Monique Teillaud. Algebraic methods and arithmetic filtering for exact predicates on circle arcs. Computational Geometry, Elsevier, 2002, 22, pp.119-142. ⟨10.1016/S0925-7721(01)00050-5⟩. ⟨inria-00166709⟩

Share

Metrics

Record views

291

Files downloads

446