A general and efficient implementation of geometric operators and predicates

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

Volumn 1262 LNCS, Issue , 1997, Pages 69-93

  Chan, Edward P F ^a   Ng, Jimmy N H ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

C++ (PROGRAMMING LANGUAGE); DATABASE SYSTEMS;

A-PLANE; EFFICIENT IMPLEMENTATION; GEOMETRIC DATA; INTERSECTION POINTS; SPATIAL DATABASE; SPATIAL DATABASE SYSTEMS; SWEEP LINES; UNIFIED ALGORITHM;

GEOMETRY;

EID: 84885588135     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-63238-7_25     Document Type: Conference Paper

References (24)

1. Benouamer, M.O., Jaillon, P., Michelucci, D. and Moreau, J.M., "A Lazy Solution to Imprecision in Computational Geometry," Proceedings of the Fifth Canadian Conference on Computational Geometry, 1993, pp. 73-78.
2. Bentley, J.L. and Ottmann, T.A., "Algorithms for Reporting and Counting Geometric Intersections," IEEE Transactions on Computer, Vol. c-28 (1979), pp. 643-647.
3. Chan, E.P.F. and Zhu, R., "QL/G: A Query Language for Geometric Databases," Proceedings of the First International Conference on GIS in Urban and Environmental Planning, Island of Samos, Greece, April 1996, pp. 271-286.
4. Chazelle. B. and Edelsbrunner, H., "An Optimal Algorithm for Intersecting Line Segments in the Plane," JACM 39:1, January 1992, pp. 1-54.
5. DeWitt, D., Kabra, N., Luo, J., Patel, J.M., Yu, J.B., "Client-Server Paradise," Proceedings of the 20th International Conference on VLDB, Santiago, Chile, 1994.
6. Fortune, S. and Van Wyk, C. "Efficient Exact Arithmetic for Computational Geometry," Proceedings of the Ninth ACM Symposium on Computational Geometry, San Diego, May 1993, pp. 163-172.
7. Green, D.H. and Yao, F.F., "Finite-resolution Computational Geometry," Proceedings of the 27th Annual Symposium on the Foundation of Computer Science, pp. 143-152, 1986.
8. Guibas, L., Salesin, D., and Stolfi, J., "Epsilon Geometry: Building Robust Algorithms from Imprecise Computations," Proceedings of the Fifth ACM Symposium on Computational Geometry, San Diego, 1989, pp. 208-217.
9. Guting, R.H. and Schneider, M., "Realms-Based Spatial Data Types: The ROSE Algebra," VLDB Journal 4(2), April 1995, pp. 243-286.
10. Guting, R.H., Ridder, T. and Schneider, M., "Implementation of ROSE Algebra: Efficient Algorithms for Realm-Based Spatial Data Types," Proceedings of Advances in Spatial Databases - Fourth International Symposium, SSD '95, pp. 216-239, Portland, Maine, August 1995. Lecture Notes in Computer Science 951. Springer-Verlag.
11. Kriegel, H., Brinkhoff, T. and Schneider, R., "An Efficient Map Overlay Algorithm Based on Spatial Access Methods and Computational Geometry" Proceedings of the International Workshop on DBMS's for Geographic Applications, Capri, May 12-17, 1991.
12. Myers, E.W., "An O(E log E + I) Expected Time Algorithm for the Planar Segment Intersection Problem," SIAM J. of Computing, Vol. 14 (1985), pp. 625-637.
13. Milenkovic, V.J., "Double Precision Geometry: A General Technique for Calculating Line and Segment Intersections Using Rounded Arithmetic," Proceedings of the Thirtieth Annual Symposium on the Foundations of Computer Science, 1989, pp. 500-505.
14. Milenkovic, V.J. and Li, Z., "Constructing Strongly Convex Hulls Using Exact or Rounded Arithmetic," Algorithmica (8), 1992, pp. 345-364.
15. Naher, S., LEDA Manual Version 3.2, TR MPI-I-95-1-002, Max-Planck-Institut fur Informatik, Saarbrucken, 1995.
16. Mehlhorn, K. and Naher, S. "Implementation of a Sweep Line Algorithm for the Straight Line Segment Intersection Problem," TR MPI-I-94-105, Max-Planck-Institut fur Informatik, Saarbrucken, 1993.
17. Mehlhorn, K. and Naher, S. "LEDA, A Platform for Combinatorial and Geometric Computing," CACM (38), Number 1995, pp. 96-102.
18. Nievergelt, J. and Preparata, F.P., "Plane-Sweep Algorithms for Intersecting Geometric Figures," CACM (25), Number 10, 1982, pp. 739-747.
19. Ottmann, G., Thiemt, G. and Ullrich, C., "Numerical Stability of Geometric Algorithms," Proceedings of the Third ACM Symposium on Computational Geometry, 1987, pp. 119-125.
20. Ottmann, T.A., Widmayer, P. and Wood, D. "A Fast Algorithm for the Boolean Masking Problem," Computer Vision, Graphics, and Image Processing (1985), pp. 249-268.
21. Scholl, M. and Voisard, A., "Thematic Map Modelling," Proceedings of the 1st Symposium, SSD 89, Santa Barbara, CA., July 1989, pp. 167-190. Lecture Notes in Computer Science 409, Springer-Verlag, 1989.
22. Shamos, M.I. and Hoey, D., "Geometric Intersection Problems," Proc. 17th ACM Symposium on Foundations of Computer Science (1976), pp. 208-215.
23. Tilove, R.B., "Set Membership Classification: A Unified Approach to Geometric Intersection Problems", IEEE Transaction on Computers, Vol. C-29, No. 10, 1980, pp. 874-883.
24. XYZ GeoBench User Manual, ETH Zurich. Switzerland, 1994.