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Original Articles

Approximations of 2D and 3D generalized Voronoi diagrams

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Pages 1003-1022 | Received 26 Sep 2006, Accepted 03 May 2007, Published online: 04 Mar 2011

References

  • Alani , H. , Jones , C. B. and Tudhope , D. 2001 . Voronoi-based region approximation for geographical information retrieval with gazetteers . Int. J. Geogr. Inf. Sci. , 15 ( 4 ) : 287 – 306 .
  • Aurenhammer , F. 1991 . Voronoi diagrams: a survey of a fundamental geometric data structure . ACM Computer Surveys , 23 ( 3 ) : 686 – 695 .
  • Aurenhammer , F. and Klein , R. 2000 . “ Voronoi diagrams ” . In Handbook of Computational Geometry , Edited by: Sack , J. R. and Urrutia , J. 201 – 290 . Elsevier .
  • Behnke , S. Local Multiresolution path planning . Proceedings of 7th RoboCup International Symposium ,
  • de Berg , M. , van Kreveld , M. , Overmars , M. and Schwarzkopf , O. 1997 . Computational Geometry: Algorithms and applications , Springer-Verlag .
  • Boada , I. , Coll , N. and Sellarès , J. A. 2002 . The Voronoi-Quadtree: construction and visualization . Eurographics 2002 Short Presentation , : 349 – 355 .
  • Boada , I. , Coll , N. and Sellarès , J. A. 2003 . Dynamically Maintaining a Hierarchical Planar Voronoi Diagram Approximation , 836 – 846 . Springer-Verlag . ICCSA 2003, Lecture Notes on Computer Science 2669
  • Boada , I. , Coll , N. , Madern , N. and Sellarès , J. A. Approximations of 3D Generalized Voronoi Diagrams . Proceedings of 21th European Workshop on Computational Geometry , pp. 163 – 166 .
  • Chiang , Y. J. and Tamassia , R. 1992 . Dynamic algorithms in computational geometry . Proceedings of IEEE, Special Issue on Computational Geometry , 80 ( 9 ) : 362 – 381 .
  • Choi , H. I. , Choi , S. W. and Moon , H. P. 1997 . New algorithm for medial axis transform of plane domain . Graph. Mod. and Image Process , 59 ( 6 ) : 463 – 483 .
  • Chou , J. J. 1995 . Voronoi diagrams for planar shapes . IEEE Comput. Graph. Appl. , : 52 – 59 .
  • Coll , N. , Hurtado , F. and Sellarès , J. A. Approximating planar subdivisions and generalized Voronoi diagrams from random sections . Proceedings of 19th European Workshop on Computational Geometry , pp. 27 – 30 .
  • Coll , N. 2004 . “ Approximation and visualization methods for bidimensional geometric objects ” . In Universitat Politècnica de Catalunya PhD Thesis
  • Dobkin , D. P. and Laszlo , M. J. 1989 . Primitives for the manipulation of three-dimensional subdivisions . Algorithmica , 4 : 3 – 12 .
  • Elber , G. and Kim , M. 1998 . Bisector curves for planar rational curves . Comput. Aided Design , 30 ( 14 ) : 1089 – 1096 .
  • Etzion , M. and Rappoport , A. 2002 . Computing Voronoi skeletons of a 3-D polyhedron by space subdivision . Computat. Geomet. , 21 : 87 – 120 .
  • Farouki , R. and Johnstone , J. 1994 . The bisector of a point and a plane parametric curve . Comput. Aided Geomet. Design , 11 ( 2 ) : 117 – 151 .
  • Farouki , R. and Ramamurthy , R. 1998 . Specified-precision computations of curve/curve bisectors . Int. J. Comput. Geomet. appl. , 8 ( 5–6 ) : 599 – 617 .
  • Gold , C. The Voronoi Web Site http://www.voronoi.com/
  • Herman , G. T. and Liu , K. H. 1979 . Three dimensional display of human organs from computed tomograms . Comput. Graph. Image Process , 9 ( 1 ) : 1 – 21 .
  • Hoff , K. , Culver , T. , Keyser , J. , Lin , M. and Manocha , D. Proceedings of SIGGRAPH’99 . Fast computation of generalized Voronoi diagrams using graphics hardware , pp. 277 – 286 . ACM Press .
  • Kambhampati , S. and Davis , L. S. 1986 . Multiresolution path planning for mobile robots . IEEE J. Robot. Automat. , RA-2 ( 3 ) : 135 – 145 .
  • Lavender , D. , Bowyer , A. , Davenport , J. , Wallis , A. and Woodwark , J. 1992 . Voronoi diagrams of set-thoretic solid models . IEEE Comput. Graph. Appl. , 12 ( 5 ) : 69 – 77 .
  • Lorensen , W. and Cline , H. E. International Conference on Computer Graphics and Interactive Techniques . Marching cubes: a high resolution 3D surface construction algorithm , pp. 163 – 169 . ACM Press .
  • Okabe , A. , Boots , B. , Sugihara , K. and Chiu , S. N. 2000 . Spatial Tessellations: Concepts and Application of Voronoi Diagrams , John Wiley & Sons .
  • Ramanathan , M. and Gurumoorthy , B. 2002 . Constructing medial axis transform of planar domains with curves boundaries . Comput. Aided Design , 35 : 619 – 632 .
  • Ramamurthy , R. 1998 . Voronoi diagrams and medial axes of planar domains with curved boundaries , Michigan . Phd Thesis
  • Samet , H. 1993 . Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS , Addison-Wesley .
  • Santaló , L. A. 1976 . Integral Geometry and Geometric Probability , Addison-Wesley .
  • Teichmann , M. and Teller , S. 1997 . Polygonal approximation of Voronoi diagrams of a set of triangles in three dimensions , Laboratory of Computer science, MIT . Technical Report 766
  • Vleugels , J. and Overmars , M. 1998 . Approximating generalized Voronoi diagrams in any dimension . Int. J. Comput. Geomet. Appl. , 8 : 201 – 221 .

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