Robust Adaptive Floating-Point Geometric Predicates

Robust Adaptive Floating-Point Geometric Predicates (1996) (Make Corrections) (19 citations)
Jonathan Richard ShewchukSymposium on Computational Geometry

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Abstract: Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floating-point numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary precision arithmetic that have a strong advantage over other software techniques in computations that manipulate values of extended but small precision. Second, they are adaptive; their running time depends... (Update)

Context of citations to this paper: More

.... geometry and solid modelling communities, there has been a lot of work on the related problem of robust geometric computing [45, 56, 57, 91, 95, 99, 105, 107]. These techniques are not applicable to our problem since they attempt to avoid errors caused by numerical imprecision...

...we end up with consist in evaluating the sign of algebraic expressions (sections 2.2.2 and 3. 1) The reader is referred to [20, 1] for recent developments in this area. # 1 # 2 Figure 1: a)Intersection of two toleranced polygons (b)Worst case example of intersection...

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BibTeX entry: (Update)

J.R. Shewchuk. Robust Adaptive Floating-Point Geometric Predicates. In Proc. 12th Annu. ACM Sympos. Comput. Geom., pages 141--150, Philadelphia, PA, USA, June 1996. http://citeseer.nj.nec.com/shewchuk96robust.html More

@inproceedings{ shewchuk96robust,
    author = "Jonathan Richard Shewchuk",
    title = "Robust Adaptive Floating-Point Geometric Predicates",
    booktitle = "Symposium on Computational Geometry",
    pages = "141-150",
    year = "1996",
    url = "citeseer.nj.nec.com/shewchuk96robust.html" }

Citations (may not include all citations):
223 Primitives for the Manipulation of General Subdivisions and .. (context) - Guibas, Stolfi - 1985
91 What Every Computer Scientist Should Know About Floating-Poi.. - Goldberg - 1991
58 Quality Mesh Generator and Delaunay Triangulator (context) - Shewchuk, Engineering - 1996
51 Efficient Exact Arithmetic for Computational Geometry - Fortune, Van Wyk - 1993
49 Two Algorithms for Constructing a Delaunay Triangulation (context) - Lee, Schachter - 1980
48 dimensional Delaunay Tessellation with Application to Vorono.. (context) - Watson, n- - 1981
43 Evaluating Signs of Determinants Using Single-Precision Arit.. - Avnaim, Boissonnat et al. - 1995
36 Efficient Delaunay Triangulation Using Rational Arithmetic (context) - Karasick, Lieber et al. - 1991
28 A Floating-Point Technique for Extending the Available Preci.. (context) - Dekker - 1971
20 Algorithms for Arbitrary Precision Floating Point Arithmetic - Priest - 1991
16 A Portable High Performance Multiprecision Package - Bailey - 1993
11 The Art of Computer Programming: Seminumerical Algorithms (context) - Knuth - 1981
4 rd Annual Symposium on Foundations of Computer Science (context) - Clarkson, Effective - 1992
3 University of California at Berkeley (context) - of, Arithmetics et al. - 1992
2 To appear in Transactions on Mathematical Software (context) - Yields, Integer et al. - 1996

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