Algebraic methods and arithmetic filtering for exact predicates on circle arcs

Authors:
Olivier Devillers;Alexandra Fronville;Bernard Mourrain;Monique Teillaud
Affiliations:
INRIA Sophia Antipolis, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France;INRIA Sophia Antipolis, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France;INRIA Sophia Antipolis, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France;INRIA Sophia Antipolis, 2004 Route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France
Venue:
Computational Geometry: Theory and Applications
Year:
2002

Citing 7
Cited 7

Towards exact geometric computation

Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Efficient algorithms for line and curve segment intersection using restricted predicates

SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Robust Proximity Queries: An Illustration of Degree-Driven Algorithm Design

SIAM Journal on Computing
Matrices in elimination theory

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Look — a Lazy Object-Oriented Kernel for geometric computation

Proceedings of the sixteenth annual symposium on Computational geometry
Generalized resultants over unirational algebraic varieties

Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Robust Plane Sweep for Intersecting Segments

SIAM Journal on Computing

Root comparison techniques applied to computing the additively weighted Voronoi diagram

SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Controlled perturbation for arrangements of circles

Proceedings of the nineteenth annual symposium on Computational geometry
Optimal adaptive algorithms for finding the nearest and farthest point on a parametric black-box curve

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Towards and open curved kernel

SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The predicates of the Apollonius diagram: algorithmic analysis and implementation

Computational Geometry: Theory and Applications - Special issue on robust geometric algorithms and their implementations
Exact and efficient 2D-arrangements of arbitrary algebraic curves

Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Predicates for line transversals to lines and line segments in three-dimensional space

Proceedings of the twenty-fourth annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

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.