Exact geometric computation using cascading

International Journal of Computational Geometry and Applications

Volumn 11, Issue 3, 2001, Pages 245-266

  Burnikel, Christoph ^a   Funke, Stefan ^a   Seel, Michael ^a  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

Author keywords

Exact arithmetic; Expression compiler; Floating point filter

Indexed keywords

EID: 0035591185     PISSN: 02181959     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218195901000493     Document Type: Article

References (16)

1. F. Avnaim et al.: Evaluating signs of determinants using single-precision arithmetic, ( INRIA, 1995)
2. D. H. Bailey: A Portable High Performance Multiprecision Package, (Technical Report RNR-90-022, NASA Ames Research Center, May 1993)
3. H. Brönnimann, C. Burnikel, S. Pion: Interval Analysis Yields Efficient Arithmetic Filters for Computational Geometry, (Proceedings of the 14th Symposium on CG 1998, ACM Press)
4. C. Burnikel: Exact Computation of Voronoi Diagrams and Line Segment Intersections, (PhD thesis, Max-Planck-Institut für Informatik, 1996)
5. Christoph Burnikel, Kurt Mehlhorn, Stefan Schirra: The LEDA class real number, (Research report MPI-I-96-1-001, Max-Planck-Institut für Informatik, 1996)
6. O. Devillers, P. Preparata: A Probabilistic Analysis of the Power of Arithmetic Filters, (Technical Report CS 96-27, Center for Geometric Computing, Dept. Computer Science, Brown Univ.)
7. Steven Fortune, Christopher J. Van Wyk: Efficient Exact Arithmetic for Computational Geometry, (Proceedings of the 9th Annual Symposium on CG 1993, ACM Press)
8. S. Funke: Exact Arithmetic using Cascaded Computation, (Master-Thesis, Max-Planck-Institut für Informatik, 1997)
9. David Goldberg: What Every Computer Scientist Should Know About Floating-Point Arithmetic, (ACM Computing Surveys 23(1):5-48, March1991)
10. IEEE standard 754-1985 for binary floating-point arithmetic, reprinted in SIGPLAN 22, 2:9-25, 1987
11. K. Mehlhorn, S. Näher, C. Uhrig: The LEDA User Manual (Version R 3.4) (Max-Planck-Institut für Informatik, 1996)
12. K. Mehlhorn, S. Näher: The Implementation of Geometric Algorithms, Proc. 13th World Computer Congress IFIP94, vol.1, 223-231
13. M. Seel: Eine Implementierung abstrakter Voronoidiagramme, (Master Thesis, Universität des Saarlandes 1994)
14. R. Seidel: A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, (Computational Geometry: Theory and Applications 1 (1991) 51-64)
15. B. Serpette, J. Vuillemin, J.C. Herve: BigNum: a portable and efficient package for arbitrary-precision arithmetic, (INRIA)
16. K. Sugihara, M. Iri: A robust Topology-Oriented Incremental Algorithm for Voronoi diagrams, (Internat. J. Comput. Geom. Appl. 4 (1994) 179-228)