Snap Rounding Line Segments Efficiently in Two and Three Dimensions (1997)  (Make Corrections)  (8 citations)
Michael T. Goodrich, Leonidas J. Guibas, John Hershberger, Paul J. Tannenbaum
Symposium on Computational Geometry

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Abstract: We study the problem of robustly rounding a set S of n line segments in R 2 using the snap rounding paradigm. In this paradigm each pixel containing an endpoint or intersection point is called "hot," and all segments intersecting a hot pixel are re-routed to pass through its center. We show that a snap-rounded approximation to the arrangement defined by S can be built in an output-sensitive fashion, and that this can be done without first determining all the intersecting pairs of segments in... (Update)

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...under insertion and deletion of edges; they also give elementary proofs of basic topological properties of snap rounding. Goodrich et al. [7] give improved algorithms to snap round a set of intersecting edges, in the case when there are many intersections within a pixel....

...floating point arithmetic. Some examples of previous and related work on robust floating point geometric algorithms can be found in [17], 18] 22] 27] 32] and [33] Our motivating application is geometric modeling of molecules. Our software package is part of a toolbox...

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Hardware-Assisted Computation of Depth Contours - Krishnan, Mustafa..   (Correct)
Rounding Arrangements Dynamically - Guibas, Marimont (1995)   (Correct)
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0.8:   Backwards Analysis of Randomized Geometric Algorithms - Seidel (1992)   (Correct)
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6:   Verifiable Implementations of Geometric Algorithms Using Finite Precision Arithm.. (context) - Milenkovic - 1988
6:   Finite-Resolution Computational Geometry (context) - Greene - 1986
5:   Rounding arrangements dynamically - Guibas, Marimont - 1995

BibTeX entry:   (Update)

M. Goodrich, L. J. Guibas, J. Hershberger, and P. Tanenbaum. Snap rounding line segments efficiently in two and three dimensions. In Proceedings of the Thirteenth Annual ACM Symposium on Computational Geometry, pages 284--293, 1997. http://citeseer.nj.nec.com/goodrich97snap.html   More

@inproceedings{ goodrich97snap,
    author = "Michael T. Goodrich and Leonidas J. Guibas and John Hershberger and Paul J. Tanenbaum",
    title = "Snap Rounding Line Segments Efficiently in Two and Three Dimensions",
    booktitle = "Symposium on Computational Geometry",
    pages = "284-293",
    year = "1997",
    url = "citeseer.nj.nec.com/goodrich97snap.html" }
Citations (may not include all citations):
216   Primitives for the manipulation of general subdivisions and .. (context) - Guibas, Stolfi - 1985
133   Algorithms for reporting and counting geometric intersection.. (context) - Bentley, Ottmann - 1979
118   Simulation of simplicity: a technique to cope with degenerat.. - Edelsbrunner, Mucke - 1990
84   Randomized incremental construction of Delaunay and Voronoi .. (context) - Guibas, Knuth et al. - 1992
62   On range searching with semialgebraic sets - Agarwal, Matousek - 1994
53   Epsilon geometry: building robust algorithms from imprecise .. (context) - Guibas, Salesin et al. - 1989
50   Finite-resolution computational geometry (context) - Greene, Yao - 1986
47   Backwards analysis of randomized geometric algorithms - Seidel - 1993
41   Four results on randomized incremental constructions - Clarkson, Mehlhorn et al. - 1993
34   Double precision geometry: a general technique for calculati.. - Milenkovic - 1989
28   Towards implementing robust geometric computations (context) - Hoffmann, Hopcroft et al. - 1988
25   Numerical stability of algorithms for 2-d Delaunay triangula.. (context) - Fortune - 1995
25   Rounding arrangements dynamically - Guibas, Marimont - 1995
21   Numerical stability of algorithms for line arrangements - Fortune, Milenkovic - 1991
18   Randomized geometric algorithms - Clarkson - 1992
15   Evaluation of a new method to compute signs of determinants (context) - Avnaim, Boissonnat et al. - 1995
13   Robust proximity queries in implicit Voronoi diagrams - Liotta, Preparata et al. - 1996
11   Practical segment intersection with finite precision output - Hobby - 1993
9   Geometric algorithms in finite-precision arithmetic (context) - Sugihara, Iri - 1988
6   Two design principles of geometric algorithms in finite-prec.. (context) - Sugihara, Iri - 1989
5   Algorithms for reporting and counting geometric intersection.. (context) - Brown - 1981
3   A fast planar partition algorithm: part (context) - Mulmuley - 1988
2   A tail estimate for Mulmuley's segment intersection algorith.. (context) - Matousek, Seidel - 1992



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Dynamic Trees and Dynamic Point Location - Goodrich, Tamassia (1991)   (Correct)
On the Complexity of Optimization Problems for 3-Dimensional.. - Das, Goodrich (1995)   (Correct)
Bounded-Independence Derandomization of Geometric.. - Goodrich, Ramos (1996)   (Correct)

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