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Static analysis yields efficient exact integer arithmetic for computational geometry
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Volume 15 ,  Issue 3  (July 1996) table of contents
Pages: 223 - 248  
Year of Publication: 1996
ISSN:0730-0301
Authors
Steven Fortune  AT&T Bell Laboratories, Murray Hill, NJ
Christopher J. Van Wyk  Dept. of Mathematics and Computer Sceince, Drew University, Madison, NJ
Publisher
ACM  New York, NY, USA
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Downloads (6 Weeks): 11,   Downloads (12 Months): 41,   Citation Count: 19
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REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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BENOUAMER, M. O., JAmLON, P., MICHELUCCI, D., AND MOREAU, J.-M. 1993. A "lazy" solution to imprecision in computational geometry. In Proceedings of the Fifth Canadian Conference on Computational Geometry (Waterloo, Ontario, Aug. 5-9), 73-78,
 
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BENOUAMER, M. O., MICHELUCCI, D., AND PEROCHE, B. 1994. Error-free boundary evaluation based on a lazy rational arithmetic: a detailed implementation. Comput.-Aided Des. 26, 6, 403-416.
 
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BENTLEY, J. L. AND OTTMANN, T.A. 1979. Algorithms for reporting and counting geometric intersections. IEEE Trans. Comput. 28, 9 (Sept.), 643-647.
 
7
 
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CHANG, J. AND MILENKOVIC, V. 1993. An experiment using LN for exact geometric computations. In Proceedings of the 5th Canadian Conference on Computational Geometry (Waterloo, Ontario, Aug. 5-9), 67-72.
 
9
CLARKSON, K.L. 1992. Safe and effective determinant evaluation. In the 33th Symposium on Foundations of Computer Science (Pittsburgh, PA, Oct. 24-27), 387-395.
 
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Dus~, T~ AND YAP, C.K. 1994. A basis for implementing exact geometric algorithms. Manuscript.
 
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FORTUNE, S. 1993. Progress in computational geometry, Ch. 3. In Directions in Geometric Computing, R. Martin, Ed., Information Geometers Ltd, 81-128.
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FORTt'NE, S. AND VAN WYK, C. 1993. LN users manual. Manuscript, AT&T Bell Laboratories.
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FORTUNE, S. 1995b. Numerical stability of algorithms for 2D Delaunay triangulations, Int. J. Comput. Geom. Appl. 5, l, 2, 193-213.
 
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GREENE, D. AND YAO, F. 1986. Finite-resolution computational geometry. In Proceedings of the 27th Annual Symposium on the Foundations of Computer Science, (Toronto, Ontario, Oct. 27-29), 143-152.
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HoBsY, J. 1993. Practical segment intersection with finite precision output. Submitted.
 
20
 
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JAILLON, P. 1993. Proposition d'une arithm~tique rationnelle paresseuse et d'un outil d'aide la saisie d'objets en synth~se d'images, Thbse, Ecole Nationale Superieure des Mines de Saint-Etienne. URL: http://www.emse.fr/pub/papers/LAZY/thesePJ.ps.Z.
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23
 
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MEHLHORN, K. AND NAHER, S. 1994. Implementation of a sweepline algorithm for the straight line segment intersection problem. Manuscript.
 
25
MILENKOVIC, V. 1989. Rounding face lattices in the plane. In First Canadian Conference on Computational Geometry (Montreal, Quebec, Aug. 21-25).
 
26
NAHER, S. 1995. The LEDA User Manual. Ver. 3.1, Jan. 16, LEDA is available by anonymous FTP from ftp.mpi-sb.mpg.de in directory/pub/LEDA.
 
27
 
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SERPETTE, B., VUILLEMIN, J., AND HERVE, J.C. 1989. BigNum: a portable and efficient package for arbitrary-precision arithmetic. Res. Rep. 2, Digital Paris Research Laboratory, May.
 
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SHEWCHUK, J.g. 1995. Adaptive precision floating-point arithmetic and fast robust geometric predicates in C. Res. Rep., Carnegie-Mellon Univ., Dec.
 
30
SUGII~mA, K. AND IRI, M. 1989. Construction of the Voronoi diagram for one million generators in single precision arithmetic. In First Canadian Conference on Computational Geometry (Montreal, Quebec, Aug. 21-25).
 
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VAN WYE, C. 1994. Plane sweep with efficient exact arithmetic. Manuscript.
 
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VAN WYK, C. 1995. Missing real numbers. Am. Math. Monthly 105, 260-265.
 
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YAP, C. 1993. Towards exact geometric computation. In Proceedings of the Fifth Canadian Conference on Computational Geometry (Waterloo, Ontario, Aug. 5-9), 405-419.
 
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YAP, C. AND DUBS T. 1995. The exact computation paradigm. In Computing in Euclidean Geometry. D. Z. Du, F. Hwang, Eds, World Scientific, 2nd ed., 452-492.

CITED BY  19

Collaborative Colleagues:
Steven Fortune: colleagues
Christopher J. Van Wyk: colleagues