Topology oriented vs. Exact arithmetic experience in implementing the three-dimensional convex hull algorithm

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1350, Issue , 1997, Pages 273-282

  Minakawa, Tsuyoshi ^a   Sugihara, Kokichi ^b  

^a HITACHI LTD   (Japan)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; TOPOLOGY;

COMPUTATIONAL EXPERIMENT; CONVEX HULL; CONVEX HULL ALGORITHM; EXACT ARITHMETIC; FLOATINGPOINT; GEOMETRIC ALGORITHM;

ALGORITHMS;

EID: 84958036292     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-63890-3_30     Document Type: Conference Paper

References (15)

1. M. Benouamer, D. Michelucci and B. Peroche. Error-free boundary evaluation using lazy rational arithmetic -- A detailed implementation. Proc. of the 2nd Syrup. on Solid Modeling and Appl., Montreal, 115-126, 1993
2. A. M. Day. The implementation of an algorithm to find the convex hull of a set of three-dimensional points. ACM Trans. on Graphics, 9: 105-132, 1990
3. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin, 1987
4. H. Edelsbrunner and E. P. Mficke. Simulation of simplicity--A technique to cope with degenerate cases in geometric algorithms. Proc. of the 4th A CM Syrup. on Comput. Geom., Urbana-Champaign, 118-133, 1988
5. S. Fortune and C. von Wyk. Efficient exact arithmetic for computational geometry. Proc. of the 9th A CM Annual Syrup. on Comput. Geom., San Diego, 163-172, 1993
6. L. Guibas, D. Salesin and J. Stolfi. Epsilon geometry -- Building robust algorithms from imprecise calculations. Proc. of the 5th ACM Annual Syrup. on Comput. Geom., Saarbrficken, 208-217, 1989
7. V. Milenkovic. Verifiable implementation of geometric algorithms using finite precision arithmetic. Artif. lntell., 37: 377-401, 1988
8. T. Ono. An eight-way perturbation technique for the three-dimensional convex hull. Proc. of the 6th Canadian Conf. on Comput. Geom., Saskatoon, 159-164, 1994
9. F. P. Preparata and M. I. Shamos. Computational Geometry -- An Introduction. Springer-Verlag, New York, 1985
10. P. Schorn. Robust algorithms in a program library for geometric computation. Dissertation submitted to the Swiss Federal Institute of Technology (ETH) Zfirick for the degree of Doctor of Technical Sciences, 1991
11. E. Steinitz. Polyheder und Raumeinteilungen, Encykloiidie der mathematischen Wissenchaften, Band III, Tell 1, 2. Häilfte, IIIAB12, 1-139, 1916
12. K. Sugihara. A robust and consistent algorithm for intersecting convex polyhedra. EUROGRAPHICS'94, Oslo, C-45-C-54, 1994
13. K. Sugihara and M. Iri. Construction of the Voronoi diagram for "one million" generators in single-precision arithmetic. Proc. of the IEEE, 80: 1471-1488, 1992
14. C.-K. Yap. Symbolic treatment of geometric degeneracies. J. of Symbolic Comput., 10: 349-370, 1990
15. C.-K. Yap. Toward exact geometric computation. Proc. of the 5th Canadian Conf. on Comput. Geom., Waterloo, 405-419, 1993.