Higher-order Voronoi diagrams on triangulated surfaces

Information Processing Letters

Volumn 109, Issue 9, 2009, Pages 440-445

  Cabello, S ^a   Fort, M ^b   Sellares J A ^b  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

^b UNIVERSITY OF GIRONA   (Spain)

Author keywords

Combinatorial complexity; Computational geometry; Triangulated surface; Triangulated terrain; Voronoi diagram

Indexed keywords

COMPUTATIONAL COMPLEXITY; GRAPHIC METHODS;

COMBINATORIAL COMPLEXITY; GEODESIC DISTANCES; HIGHER ORDERS; POLYGONAL DOMAINS; TRIANGULATED SURFACE; TRIANGULATED TERRAIN; VORONOI DIAGRAM; WORST CASE;

COMPUTATIONAL GEOMETRY;

EID: 61649097698     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ipl.2009.01.001     Document Type: Article

References (13)

1. Aronov B., van Kreveld M., van Oostrum R.W., and Varadarajan K. Facility location on terrains. Discrete Comput. Geom. 30 (2003) 257-372
2. Aronov B., de Berg M., and Thite S. The complexity of bisectors and Voronoi diagrams on realistic terrains. Algorithms-ESA 2008, 16th Annual European Symposium on Algorithms. LNCS vol. 5193 (2008) 100-111
3. Aurenhammer F. Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Comput. Surv. 23 (1991) 345-405
4. Aurenhammer F., and Klein R. Voronoi diagrams. In: Sack J.R., and Urrutia J. (Eds). Handbook of Computational Geometry (2000), Elsevier 201-290
5. Clarkson K.L., and Shor P.W. Application of random sampling in computational geometry, II. Discrete Comput. Geom. 4 (1989) 387-421
6. M. Fort, J.A. Sellarès, Generalized higher-order Voronoi diagrams on polyhedral terrains, in: 4th International Symposium on Voronoi Diagrams in Science an Engineering, 2007, pp. 74-84
7. Lee D.T. On k-nearest neighbor Voronoi diagrams in the plane. IEEE Trans. Comput. 31 (1982) 478-787
8. Mitchell J.S.B., Mount D.M., and Paparimitriou C.H. The discrete geodesic problem. SIAM J. Comput. 16 (1987) 647-668
9. Moet E., van Kreveld M., and van der Stappen F. On realistic terrains. SCG '06: Proceedings of the 22nd Symposium on Computational Geometry (2006) 177-186
10. D.M. Mount, Voronoi diagrams on the surface of a polyhedron, Technical report, No. 1496, University of Maryland, 1985
11. Okabe A., Boots B., Sugihara K., and Chiu S.N. Spatial Tessellation: Concepts and Application of Voronoi Diagrams (2000), John Wiley and Sons
12. Schmitt D., and Spehner J.C. Order-k Voronoi diagrams, k-sections, and k-sets. JCDCG '98: Japanese Conference on Discrete and Computational Geometry. LNCS vol. 1763 (1998) 290-304
13. Sharir M. The Clarkson-Shor technique revisited and extended. Combinatorics, Probab. Comput. 12 (2003) 191-201