Experimental study on acceleration of an exact-arithmetic geometric algorithm

Proceedings - 1997 International Conference on Shape Modeling and Applications, SMI 1997

Volumn , Issue , 1997, Pages 160-168

  Sugihara, Kokichi ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COSTS; EXACT ARITHMETIC; FLOATING-POINT ARITHMETIC; FLOATING-POINT COMPUTATION; GEOMETRIC ALGORITHM; HYBRID METHOD; NUMERICALLY ROBUST; TOPOLOGICAL STRUCTURE;

ALGORITHMS; COSTS;

DIGITAL ARITHMETIC;

EID: 0001257674     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/SMA.1997.634893     Document Type: Conference Paper

References (27)

1. F. Aurenhammer. Power diagrams: properties, algorithms and applications. SIAM Journal of Computing, 16: 78-96, 1987.
2. M. Benouamer, D. Michelucci and B. Peroche. Error-free boundary evaluation using lazy rational arithmetic - A detailed implementation. Proceedings of the 2nd Symposium on Solid Modeling and Applications, Montreal, 115-126, 1993.
3. B. M. Chand and S. S. Kapur. An algorithm for convex polytopes. Journal of the ACM, 17: 78-86, 1970.
4. D. Dobkin and D. Silver. Recipes for geometric and numerical analysis - Part I, An empirical study. Proceedings of the 4th ACM Annual Symposium on Computational Geometry, Urbana-Champaign, 93-105, 1988.
5. H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, Berlin, 1987.
6. H. Edelsbrunner and E. P. Mücke. Simulation of simplicity - A technique to cope with degenerate cases in geometric algorithms. Proceedings of the 4th ACM Symposium on Computational Geometry, Urbana-Champaign, 118-133, 1988.
7. S. Fortune and C. von Wyk. Efficient exact arithmetic for computational geometry. Proceedings of the 9th ACM Annual Symposium on Computational Geometry, San Diego, 163-172, 1993.
8. L. Guibas, D. Salesin and J. Stolfi. Epsilon geometry - Building robust algorithms from imprecise calculations. Proceedings of the 5th ACM Annual Symposium on Computational Geometry, Saarbrücken, 208-217, 1989.
9. C. M. Hoffmann. The problem of accuracy and robustness in geometric computation. Computer, 22(3): 31-41, 1989.
10. C. M. Hoffmann. Geometric and Solid Modeling - An Introduction. Morgan Kaufmann Publisher, Inc., San Mateo, 1989.
11. H. Imai, M. Iri and K. Murota. Voronoi diagram in the Laguerre geometry and its applications. SIAM Journal of Computing, 14(1): 93-105, 1985.
12. M. Karasick, D. Lieber and L. R. Nakman. Efficient Delaunay triangulation using rational arithmetic. ACM Transactions on Graphics, 10: 71-91, 1991.
13. D. E. Knuth. Axioms and Hulls. Lecture Notes in Computer Science, no. 606, Springer-Verlag, Berlin, 1992.
14. V. Milenkovic. Verifiable implementation of geometric algorithms using finite precision arithmetic. Artificial Intelligence, 37: 377-401, 1988.
15. A. Okabe, B. Boots and K. Sugihara. Spatial Tessellations - Concepts and Applications of Voronoi Diagrams. John Wiley and Sons, Chichester, 1992.
16. T. Ottmann, G. Thiemt and C. Ullrich. Numerical stability of geometric algorithms. Proceedings of the 3rd ACM Annual Symposium on Computational Geometry, Waterloo, 119-125, 1987.
17. F. P. Preparata and M. I. Shamos. Computational Geometry - An Introduction. Springer-Verlag, New York, 1985.
18. M. Segal and C. H. Sequin. Consistent calculations for solid modeling. Proceedings of the ACM Symposium on Computational Geometry, Baltimore, 29-38, 1985.
19. P. Schorn. Robust algorithms in a program library for geometric computation. Dissertation submitted to the Swiss Federal Institute of Technology (ETH) Zürick for the degree of Doctor of Technical Sciences, 1991.
20. K. Sugihara. A simple method for avoiding numerical errors and degeneracy in Voronoi diagram construction. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, E75-A: 468-477, 1992.
21. K. Sugihara. Approximation of generalized Voronoi diagrams by ordinary Voronoi diagrams. CVGIP: Graphical Models and Image Processing, 55(6): 522-531, 1993.
22. K. Sugihara. A robust and consistent algorithm for intersecting convex polyhedra. EUROGRAPIIICS'94, Oslo, C-45-C-54, 1994.
23. K. Sugihara and M. Iri. A solid modelling system free from topological inconsistency. Journal of Information Processing, 12: 380-393, 1989.
24. K. sugihara and M. Iri. Construction of the Voronoi diagram for "one million" generators in single-precision arithmetic. Proceedings of the IEEE, 80: 1471-1488, 1992.
25. C.-K. Yap. A geometric consistency theorem for a symbolic perturbation theorem. Proceedings of the 4th ACM Annual Symposium on Computational Geometry, Urbana-Champaign, 134-142, 1988.
26. C.-K. Yap. Symbolic treatment of geometric degeneracies. Journal of Symbolic Computation, 10: 349-370, 1990.
27. C.-K. Yap. Toward exact geometric computation. Proceedings of the 5th Canadian Conference on Computational Geometry, Waterloo, 405-419, 1993.