Exact Computation of Delaunay and Power Triangulations

Reliable Computing

Volumn 6, Issue 1, 2000, Pages 39-60

  Gavrilova, Marina ^a   Ratschek, Helmut ^b   Rokne, Jon G ^a  

^a UNIVERSITY OF CALGARY   (Canada)

^b HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0004542279     PISSN: 13853139     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009934225596     Document Type: Article

References (29)

1. Aurenhammer, F.: Power Diagrams: Properties, Algorithms, and Applications, SIAM Journal of Computing 16 (1987), pp. 78-96.
2. Dwyer, R.: A Fast Divide and Conquer Algorithm for Constructing Delaunay Triangulations, Algorithmica 2 (1987), pp. 137-151.
3. Dwyer, R.: Higher-Dimensional Voronoi Diagrams in Linear Expected Time, Discrete and Computational Geometry 6 (1991), pp. 343-367.
4. Edelsbrunner, H. and Mücke, E.: Simulation of Simplicity: A Technique to Cope with Degenerate Cases in Geometric Algorithms, in: Proceedings of the 4th Annual ACM Symposium on Computational Geometry, 1988, pp. 118-133.
5. Farouki, R.: Numerical Stability in Geometric Algorithms and Representations, in: Hanscomb, D. C. (ed.), Proceedings Mathematics of Surfaces III, Oxford University Press, New York, 1989, pp. 83-113.
6. Fortune, S.: Numerical Stability of Algorithms for 2D Delaunay Triangulations, International Journal of Computational Geometry and Applications 6 (1995), pp. 193-213.
7. Fortune, S.: Stable Maintenance of Point Set Triangulations in Two Dimensions, in: 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 494-499.
8. Fortune, S. and Wyk, C.: Efficient Exact Arithmetic for Computational Geometry, in: Proceedings of the 4th Annual ACM Symposium on Computational Geometry, 1993, pp. 163-172.
9. Gavrilova, M. and Rokne, J.: An Efficient Algorithm for Construction of the Power Diagram from the Voronoi Diagram in the Plane, International Journal of Computer Mathematics 11 (1996), pp. 3-4.
10. Guibas, L. and Stolfi, J.: Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagram, ACM Transactions on Graphics 4 (2) (1985), pp. 75-123.
11. Guibas, L., Knuth, D., and Sharir, M.: Randomized Incremental Construction of Delaunay and Voronoi Diagram, Algorithmica 7 (1992), pp. 381-413.
12. Hoffmann, C.: Geometric and Solid Modeling, Morgan Kaufmann, San Mateo, CA, 1989.
13. Hoffmann, C.: The Problem of Accuracy and Robustness in Geometric Computation, IEEE Computing 22 (1989), pp. 31-42.
14. Jünger, K., Reinelt, G., and Zepf, D.: Computing Correct Delaunay Triangulations, Computing 47 (1991), pp. 43-49.
15. Kao, T. and Knott, G.: An Efficient and Numerically Correct Algorithm for the 2D Convex Hull Problem, BIT 30 (1990), pp. 311-331.
16. Karasick, M., Lieber, D., and Nackman, L.: Efficient Delaunay Triangulation Using Rational Arithmetic, ACM Transactions of Graphics 10 (1991), pp. 71-91.
17. Katajainen, J. and Koppinen, M.: Constructing Delaunay Triangulations by Merging Buckets in Quadtree Order, Annales Sociatatis Mathematicae Polonae, Series IV, Fundamenta Informaticae 11 (1988), pp. 275-288.
18. Li, Z. and Milenkovic, V.: Constructing Strongly Convex Hulls Using Exact or Rounded Arithmetic, in: Proceedings of the 6th Annual ACM Symposium on Computational Geometry, 1990, pp. 235-243.
19. Maus, A.: Delaunay Triangulation and the Convex Hull of n Points in Expected Linear Time, BIT 24 (1984), pp. 151-163.
20. Milenkovic, V.: Double Precision Geometry: A General Technique for Calculating Line and Segment Intersections in Rounded Arithmetic, in: Proceedings of 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 500-505.
21. Milenkovic, V.: Verifiable Implementations of Geometric Algorithms Using Finite-Precision Arithmetic, Artificial Intelligence 37 (1988), pp. 377-401.
22. Oishi, Y. and Sugihara, K.: Topology-Oriented Divide-and-Conquer Algorithm for Voronoi Diagrams, Graphics Models and Image Processing 57 (1995), pp. 303-314.
23. Okabe, A., Boots, B., and Sugihara, K.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, John Wiley & Sons, Chichester, West Sussex, England, 1992, pp. 205-208.
24. Ratschek, H. and Rokne, J.: Determination of the Exact Sign of a Sum, Applied Maths. and Comp. 99 (1999), pp. 99-127.
25. Salesin, D.: Epsilon Geometry: Building Robust Algorithms for Imprecise Computations, Ph.D. Thesis, Stanford University, 1991.
26. Su, P. and Drysdale, R.: A Comparison of Sequential Delaunay Triangulation Algorithms, in: Proceedings of the 11 th Annual Symposium on Computational Geometry, 1995, pp. 61-70.
27. Sugihara, K.: A Simple Method for Avoiding Numerical Errors and Degeneracy in Voronoi Diagram Construction, IEICE Trans. Fundamentals E75-A (1992), pp. 468-477.
28. Sugihara, K. and Iri, M.: A Robust Topology-Oriented Incremental Algorithm for Voronoi Diagrams, International Journal of Computational Geometry and Applications 4 (1994), pp. 179-228.
29. Yap, C.: A Geometric Consistency Theorem for a Symbolic Perturbation Theorem, in: Proceedings of the 4th Annual ACM Symposium on Computational Geometry, 1988, pp. 134-142.