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Abstract: We consider whether restricted sets of geometric predicates support efficient algorithms to solve line and curve segment intersection problems in the plane. Our restrictions are based on the notion of algebraic degree, proposed by Preparata and others as a way to guide the search for efficient algorithms that can be implemented in more realistic computational models than the Real RAM. (Update)
Context of citations to this paper: More
...on their volume and diameter. For curve segments intersection, robustness problems led to the design of low degree algorithms [3, 4, 5], however an Omega Gamma n p k) lower bound was proven [3] in this context. Our result shows that it is possible to get around this...
.... References where the performance of geometric computations is measured also in terms of the required arithmetic precision include [2, 3, 4, 16]. The remainder of the paper is organized as follows. Preliminaries are in Section 2. A unifying approach to the computation of fi...
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BibTeX entry: (Update)
J.-D. Boissonnat and J. Snoeyink. Efficient algorithms for line and curve segment intersection using restricted predicates. In Proc. 15th Annu. ACM Sympos. Comput. Geom., pages 370--379, 1999. http://citeseer.ist.psu.edu/boissonnat99efficient.html More
@inproceedings{ boissonnat99efficient,
author = "Jean-Daniel Boissonnat and Jack Snoeyink",
title = "Efficient Algorithms for Line and Curve Segment Intersection Using Restricted Predicates",
booktitle = "Symposium on Computational Geometry",
pages = "370-379",
year = "1999",
url = "citeseer.ist.psu.edu/boissonnat99efficient.html" }
Citations (may not include all citations):1254 Computational Geometry: An Introduction (context) - Preparata, Shamos - 1985
169 Algorithms for reporting and counting geometric intersection.. (context) - Bentley, Ottmann - 1979
114 An optimal algorithm for intersecting line segments in the p.. (context) - Chazelle, Edelsbrunner - 1992
68 Towards exact geometric computation - Yap - 1997
59 Epsilon geometry: building robust algorithms from imprecise .. (context) - Guibas, Salesin et al. - 1989
49 Evaluating signs of determinants using single-precision arit.. - Avnaim, Boissonnat et al. - 1997
41 Exact geometric computation in LEDA - Burnikel, Konnemann et al. - 1995
40 Applications of a semi-dynamic convex hull algorithm (context) - Hershberger, Suri - 1992
38 Robust proximity queries: an illustration of degree-driven a.. - Liotta, Preparata et al. - 1997
32 Safe and effective determinant evaluation - Clarkson - 1992
29 An optimal algorithm for finding segment intersections (context) - Balaban - 1995
27 Static analysis yields efficient exact integer arithmetic fo.. - Fortune, Van Wyk - 1996
25 Exact Computation of Voronoi Diagrams and Line Segment Inter.. (context) - Burnikel - 1996
19 simple trapezoid sweep algorithm reporting redblue segment i.. - trapezoid, for et al. - 1994
17 A robust topology-oriented incremental algorithm for Voronoi.. (context) - Sugihara, Iri - 1994
16 On properties of floating point arithmetics: numerical stabi.. - Priest - 1992
15 Further comparison of algorithms for geometric intersection .. - Andrews - 1994
15 Computational geometry: a survey (context) - Lee, Preparata - 1984
15 Robust adaptive floating-point geometric predicates (context) - Shewchuk - 1996
12 Sign determination in Residue Number Systems (context) - Bronnimann, Emiris et al. - 1999
6 private communication (context) - Chan - 1998
4 Interval arithmetic yields efficient dynamic filters for com.. - Bronnimann, Burnikel et al. - 1998
4 Robust plane sweep for intersecting segments (context) - Boissonnat, Preparata - 1997
4 Counting and reporting redblue segment intersection (context) - Snoeyink, reporting et al. - 1994
1 Invited talk on computational geometry and software engineer.. (context) - Forrest - 1986
1 Verifiable Implementations of Geometric Algorithms Using Fin.. (context) - Milenkovic - 1988
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