메뉴 건너뛰기




Volumn , Issue , 2009, Pages 43-52

Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space

Author keywords

Envelopes; Minimum width annulus; Randomization; Voronoi diagrams

Indexed keywords

COMPUTATIONAL GEOMETRY ALGORITHMS; DISTANCE FUNCTIONS; DIVIDE AND CONQUER; DIVIDE-AND-CONQUER APPROACH; EXACT RESULTS; PARAMETRIC SURFACES; RUNNING TIME; VORONOI DIAGRAMS; WORST CASE;

EID: 77951461522     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISVD.2009.20     Document Type: Conference Paper
Times cited : (5)

References (45)
  • 3
    • 0001781555 scopus 로고    scopus 로고
    • Voronoi diagrams
    • J.-R. Sack and J. B. Urrutia, Eds. Elsevier, ch. 5
    • F. Aurenhammer and R. Klein, "Voronoi diagrams," in Handb. Comput. Geom., J.-R. Sack and J. B. Urrutia, Eds. Elsevier, 2000, ch. 5, pp. 201-290.
    • (2000) Handb. Comput. Geom. , pp. 201-290
    • Aurenhammer, F.1    Klein, R.2
  • 7
    • 0010268561 scopus 로고
    • Randomized incremental construction of abstract voronoi diagrams
    • August
    • R. Klein, K. Mehlhorn, and S. Meiser, "Randomized incremental construction of abstract Voronoi diagrams," Comput. Geom. Theory Appl., vol. 3, no. 3, pp. 157-184, August 1993.
    • (1993) Comput. Geom. Theory Appl. , vol.3 , Issue.3 , pp. 157-184
    • Klein, R.1    Mehlhorn, K.2    Meiser, S.3
  • 8
    • 52449147685 scopus 로고
    • A sweepline algorithm for voronoi diagrams
    • November
    • S. J. Fortune, "A sweepline algorithm for Voronoi diagrams," Algorithmica, vol. 2, no. 1-4, pp. 153-174, November 1987.
    • (1987) Algorithmica , vol.2 , Issue.1-4 , pp. 153-174
    • Fortune, S.J.1
  • 9
    • 52449149247 scopus 로고
    • Randomized incremental construction of delaunay and voronoi diagrams
    • June
    • L. J. Guibas, D. E. Knuth, and M. Sharir, "Randomized incremental construction of Delaunay and Voronoi diagrams," Algorithmica, vol. 7, no. 1-6, pp. 381-413, June 1992.
    • (1992) Algorithmica , vol.7 , Issue.1-6 , pp. 381-413
    • Guibas, L.J.1    Knuth, D.E.2    Sharir, M.3
  • 13
    • 84867952068 scopus 로고    scopus 로고
    • The predicates of the apollonius diagram: Algorithmic analysis and implementation
    • January
    • I. Z. Emiris and M. I. Karavelas, "The predicates of the Apollonius diagram: Algorithmic analysis and implementation," Comput. Geom. Theory Appl., vol. 33, no. 1-2, pp. 18-57, January 2006.
    • (2006) Comput. Geom. Theory Appl. , vol.33 , Issue.1-2 , pp. 18-57
    • Emiris, I.Z.1    Karavelas, M.I.2
  • 16
    • 85012242791 scopus 로고
    • How to compute the voronoi diagram of line segments: Theoretical and experimental results
    • ser. LNCS, Springer
    • C. Burnikel, K. Mehlhorn, and S. Schirra, "How to compute the Voronoi diagram of line segments: Theoretical and experimental results," in Proc. 2nd Annu. Eur. Symp. Alg., ser. LNCS, vol. 855. Springer, 1994, pp. 227-239.
    • (1994) Proc. 2nd Annu. Eur. Symp. Alg. , vol.855 , pp. 227-239
    • Burnikel, C.1    Mehlhorn, K.2    Schirra, S.3
  • 18
    • 0035276713 scopus 로고    scopus 로고
    • VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments
    • March
    • M. Held, "VRONI: An engineering approach to the reliable and efficient computation of Voronoi diagrams of points and line segments," Comput. Geom. Theory Appl., vol. 18, no. 2, pp. 95-123, March 2001.
    • (2001) Comput. Geom. Theory Appl. , vol.18 , Issue.2 , pp. 95-123
    • Held, M.1
  • 21
    • 34250131231 scopus 로고
    • Voronoi diagrams and arrangements
    • December
    • H. Edelsbrunner and R. Seidel, "Voronoi diagrams and arrangements," Disc. Comput. Geom., vol. 1, no. 1, pp. 25-44, December 1986.
    • (1986) Disc. Comput. Geom. , vol.1 , Issue.1 , pp. 25-44
    • Edelsbrunner, H.1    Seidel, R.2
  • 22
    • 45849096563 scopus 로고    scopus 로고
    • Laguerre voronoi diagram on the sphere
    • K. Sugihara, "Laguerre Voronoi diagram on the sphere," J. for Geom. Graphics, vol. 6, no. 1, pp. 69-81, 2002.
    • (2002) J. for Geom. Graphics , vol.6 , Issue.1 , pp. 69-81
    • Sugihara, K.1
  • 23
    • 33750724734 scopus 로고    scopus 로고
    • Robust, generic and efficient construction of envelopes of surfaces in three-dimensional space
    • M. Meyerovitch, "Robust, generic and efficient construction of envelopes of surfaces in three-dimensional space," in Proc. 14th Annu. Eur. Symp. Alg., 2006, pp. 792-803.
    • (2006) Proc. 14th Annu. Eur. Symp. Alg. , pp. 792-803
    • Meyerovitch, M.1
  • 26
    • 77951435769 scopus 로고    scopus 로고
    • M.Sc. Thesis, The Blavatnik School of Computer Science, Tel-Aviv University, Tel-Aviv, Israel, Forthcoming, draft version can be found at
    • O. Setter, "Constructing two-dimensional Voronoi diagrams via divide-and-conquer of envelopes in space," M.Sc. Thesis, The Blavatnik School of Computer Science, Tel-Aviv University, Tel-Aviv, Israel, Forthcoming, draft version can be found at: http://acg.cs.tau.ac.il/projects/internal- projects/ vd-via-dc-of-envelopes/thesis.pdf.
    • Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space
    • Setter, O.1
  • 27
    • 38049077509 scopus 로고    scopus 로고
    • Sweeping and maintaining two-dimensional arrangements on surfaces: A first step
    • ser. LNCS, Springer
    • E. Berberich, E. Fogel, D. Halperin, K. Mehlhorn, and R. Wein, "Sweeping and maintaining two-dimensional arrangements on surfaces: A first step," in Proc. 15th Annu. Eur. Symp. Alg., ser. LNCS, vol. 4698. Springer, 2007, pp. 645-656.
    • (2007) Proc. 15th Annu. Eur. Symp. Alg. , vol.4698 , pp. 645-656
    • Berberich, E.1    Fogel, E.2    Halperin, D.3    Mehlhorn, K.4    Wein, R.5
  • 29
    • 57349191885 scopus 로고    scopus 로고
    • Exact and efficient 2darrangements of arbitrary algebraic curves
    • Philadelphia, PA, USA: Soc. for Industrial and Applied Math. (SIAM)
    • A. Eigenwillig and M. Kerber, "Exact and efficient 2Darrangements of arbitrary algebraic curves," in Proc. 19th Annu. ACM-SIAM Symp. Disc. Alg. Philadelphia, PA, USA: Soc. for Industrial and Applied Math. (SIAM), 2008, pp. 122- 131.
    • (2008) Proc. 19th Annu. ACM-SIAM Symp. Disc. Alg. , pp. 122-131
    • Eigenwillig, A.1    Kerber, M.2
  • 31
    • 0021358006 scopus 로고
    • An optimal algorithm for constructing the weighted voronoi diagram in the plane
    • F. Aurenhammer and H. Edelsbrunner, "An optimal algorithm for constructing the weighted Voronoi diagram in the plane," Pattern Recognition, vol. 17, no. 2, pp. 251-257, 1984.
    • (1984) Pattern Recognition , vol.17 , Issue.2 , pp. 251-257
    • Aurenhammer, F.1    Edelsbrunner, H.2
  • 33
    • 0001119219 scopus 로고
    • The exact computation paradigm
    • 2nd ed., ser. LNCS, D.-Z. Du and F. K. Hwang, Eds. Singapore: World Scientific
    • C.-K. Yap and T. Dube, "The exact computation paradigm," in Computing in Euclidean Geometry, 2nd ed., ser. LNCS, D.- Z. Du and F. K. Hwang, Eds. Singapore: World Scientific, 1995, vol. 1, pp. 452-492.
    • (1995) Computing in Euclidean Geometry , vol.1 , pp. 452-492
    • Yap, C.-K.1    Dube, T.2
  • 36
    • 0038672621 scopus 로고    scopus 로고
    • The clarkson-Shor technique revisited and extended
    • M. Sharir, "The Clarkson-Shor technique revisited and extended," Combinatorics, Probability & Computing, vol. 12, no. 2, 2003.
    • (2003) Combinatorics, Probability & Computing , vol.12 , Issue.2
    • Sharir, M.1
  • 37
    • 0001160943 scopus 로고
    • Computing convolutions by reciprocal search
    • December
    • L. J. Guibas and R. Seidel, "Computing convolutions by reciprocal search," Disc. Comput. Geom., vol. 2, no. 1, pp. 175-193, December 1987.
    • (1987) Disc. Comput. Geom. , vol.2 , Issue.1 , pp. 175-193
    • Guibas, L.J.1    Seidel, R.2
  • 38
    • 77949843371 scopus 로고    scopus 로고
    • Exact implementation of arrangements of geodesic arcs on the sphere with applications
    • E. Fogel, O. Setter, and D. Halperin, "Exact implementation of arrangements of geodesic arcs on the sphere with applications," in Abstracts of 24th Eur. Workshop Comput. Geom., 2008, pp. 83-86.
    • (2008) Abstracts of 24th Eur. Workshop Comput. Geom. , pp. 83-86
    • Fogel, E.1    Setter, O.2    Halperin, D.3
  • 39
    • 57349104993 scopus 로고    scopus 로고
    • Movie: Arrangements of geodesic arcs on the sphere
    • New York, NY, USA: ACM Press
    • "Movie: Arrangements of geodesic arcs on the sphere," in Proc. 24th Annu. ACM Symp. Comput. Geom. New York, NY, USA: ACM Press, 2008, pp. 218-219.
    • (2008) Proc. 24th Annu. ACM Symp. Comput. Geom. , pp. 218-219
  • 41
    • 0002545504 scopus 로고
    • Approximating by circles
    • T. J. Rivlin, "Approximating by circles," Computing, vol. 21, pp. 93-104, 1979.
    • (1979) Computing , vol.21 , pp. 93-104
    • Rivlin, T.J.1
  • 42
    • 0005422426 scopus 로고    scopus 로고
    • Intersections with random geometric objects
    • June
    • P. Bose and L. Devroye, "Intersections with random geometric objects," Comput. Geom. Theory Appl., vol. 10, no. 3, pp. 139-154, June 1998.
    • (1998) Comput. Geom. Theory Appl. , vol.10 , Issue.3 , pp. 139-154
    • Bose, P.1    Devroye, L.2
  • 43
    • 84969213993 scopus 로고    scopus 로고
    • On bregman voronoi diagrams
    • Philadelphia, PA, USA: Soc. for Industrial and Applied Math. (SIAM)
    • F. Nielsen, J.-D. Boissonnat, and R. Nock, "On Bregman Voronoi diagrams," in Proc. 18th Annu. ACM-SIAM Symp. Disc. Alg. Philadelphia, PA, USA: Soc. for Industrial and Applied Math. (SIAM), 2007, pp. 746-755.
    • (2007) Proc. 18th Annu. ACM-SIAM Symp. Disc. Alg. , pp. 746-755
    • Nielsen, F.1    Boissonnat, J.-D.2    Nock, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.