An efficient algorithm for construction of the power diagram from the Voronoi diagram in the plane

International Journal of Computer Mathematics

Volumn 61, Issue 1-2, 1996, Pages 49-61

  Gavrilova, Marina ^a   Rokne, Jon ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

Computational complexity; Computational geometry; Delaunay triangulation; Power diagram; Voronoi diagram

Indexed keywords

EID: 0009926351     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169608804499     Document Type: Article

References (18)

1. F. Aurenhammer, "Power Diagrams: Properties, Algorithms and Applications," SIAM Journal of Computing, 16(1) (1987), 78-96.
2. F. Aurenhammer, "Voronoi Diagrams-A Survey of a Fundamental Geometric Data Structure," ACM Computing Surveys, 23(3) (1991), 345-405.
3. S. Fortune, "A Sweepline Algorithm for Voronoi Diagrams," Algorithmica, 2 (1987), 153-174.
4. L. Guibas, J. Stolfi, "Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams," ACM Transactions on Graphics, 4(2) (1985), 74-123.
5. H. Imai, M. Iri and K. Murota, "Voronoi Diagram in the Laguerre Geometry and Its Applications," SIAM Journal of Computing, 14(1) (1985), 93-105.
6. D. Lee and R. Drysdale, "Generalization of Voronoi Diagrams in the Plane," SIAM Journal of Computing, 10(1) (1981), 73-87.
7. D. Lischinski, "Incremental Delaunay Triangulation," Graphics Gems, Academic press, 1994.
8. K. Mulmuley, "Computational geometry: An Introduction Through Randomized Algorithms," Prentice Hall, Inc. A Simon and Schuster Co., Englewood Cliffs, New Jersy, USA (1994), 106-111.
9. J. O'Rourke, "Computational Geometry in C," Cambridge University Press, Cambridge, New York, USA (1994), 182-193.
10. A. Okabe, B. Boots, and K. Sugihara, "Spatial Tessellations: Concepts and Applications of Voronoi Diagrams," John Wiley and Sons, Chichester, West Sussex, England (1992), 205-208.
11. F. P. Preparata and S. Hong, "Convex Hulls of Finite Sets of Points in Two and Three Dimensions," Communications of ACM, 20 (1977), 87-93.
12. F. P. Preparata and M. I. Shamos, "Computational geometry An Introduction," Springer-Verlag New York Inc., New York, USA (1985), 209-211.
13. T. Roos, "Voronoi Diagrams over Dynamic Scenes (Extended Abstract)," In Proceedings of 2nd Canadian Conference on Computational Geometry: (1990), 209-213.
14. H. Rosenberger, "Order-k Voronoi Diagrams of Sites with Additive Weights in the Plane," Algorithmica, 6 (1991), 490-521.
15. R. Seidel, "A Convex Hull Algorithm Optimal for Point Sets in Even Dimensions," Report 81-14, University of British Columbia, Vancouver, 1981, Canada.
16. M. Sharir, "Intersection and Closet-Pair Problems for a Set of Planar Disks," SIAM Journal of Computing, 14(2) (1985), 448-468.
17. W. M. Stewart, "An Algorithm to Find the Facets of the Convex Hull in Higher Dimensions," In Proceedings of the 2nd Canadian Conference in Computational Geometry: (1990), 252-256.
18. G. Voronoi, "Nouvelles applications des parameters continues a la théorie des formes quadratiques, Deuxième Mémoire: Recherches sur les paralléloedres primitifs," J. Reine Angew. Math., 134: 198-287, 36 (1908), 67-181.