The complexity of bisectors and Voronoi diagrams on realistic terrains

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

Volumn 5193 LNCS, Issue , 2008, Pages 100-111

  Aronov, Boris ^a   De Berg, Mark ^b   Thite, Shripad ^c  

^a Polytechnic University   (United States)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASPECT RATIO; COMPUTATIONAL GEOMETRY; LANDFORMS;

GEODESIC DISTANCES; LOW DENSITY; NUMBER OF TRIANGLES; REALISTIC TERRAINS; TIGHT BOUND; VORONOI DIAGRAMS; WORST-CASE COMPLEXITY;

GRAPHIC METHODS;

EID: 57749176352     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-87744-8_9     Document Type: Conference Paper

References (13)

1. Aurenhammer, F.: Voronoi diagrams: A survey of a fundamental geometric data structure. ACM Comput. Surv. 23, 345-405 (1991)
2. Aurenhammer, F., Klein, R.: Voronoi diagrams. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry, ch. 5. Elsevier, Amsterdam (1999)
3. de Berg, M.: Improved bounds for the union complexity of fat objects. Discr. Comput. Geom. (in print, 2008)
4. de Berg, M., van der Stappen, A.F., Vleugels, J., Katz, M.J.: Realistic input models for geometric algorithms. Algorithmica 34, 81-97 (2002)
5. Chen, J., Han, Y.: Shortest paths on a polyhedron. Int. J. Comput. Geom. Appl. 6, 127-144 (1996)
6. Fortune, S.: Voronoi diagrams and Delaunay triangulations. In: Goodman, J.E., O'Rourke, J. (eds.) Handbook of Discrete and Computational Geometry, ch. 23. CRC Press, Boca Raton (2004)
7. Moet, E.: Computation and complexity of visibility in geometric environments. PhD thesis, Utrecht University (2008)
8. Moet, E., van Kreveld, M., van der Stappen, A.F.: On realistic terrains. In: Proc. 22nd ACM Sympos. Comput. Geom., pp. 177-186 (2006)
9. Okabe, A., Boots, B., Sugihara, K.: Spatial tesselations: Concepts and applications of Voronoi diagrams. John Wiley & Sons, Chichester (1992)
10. Mitchell, J.S.B., Mount, D.M., Papadimitriou, C.H.: The discrete geodesic problem. SIAM J. Comput. 16, 647-668 (1987)
11. Schreiber, Y.: Shortest paths on realistic polyhedra. In: Proc. 23rd ACM Sympos. Comput. Geom., pp. 74-83 (2007)
12. Schreiber, Y.: Personal communication (April 2008)
13. van der Stappen, A.F.: Motion planning amidst fat obstacles. Ph.D. thesis, Utrecht University (1994)