Approximations of 2D and 3D generalized Voronoi diagrams
We propose a new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams. The method supports distinct site shapes (points, line-segments, curved-arc segments, polygons, spheres, lines, polyhedra, etc.), different distance functions (Euclidean distan...
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| Published in: | International journal of computer mathematics Vol. 85; no. 7; pp. 1003 - 1022 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Taylor & Francis
01-07-2008
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| Abstract | We propose a new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams. The method supports distinct site shapes (points, line-segments, curved-arc segments, polygons, spheres, lines, polyhedra, etc.), different distance functions (Euclidean distance, convex distance functions, etc.) and is restricted to diagrams with connected Voronoi regions. The presented approach constructs a tree (a quadtree in 2D/an octree in 3D) which encodes in its nodes and in a compact way all the information required for generating an explicit representation of the boundaries of the Voronoi diagram approximation. Then, by using this hierarchical data structure a reconstruction strategy creates the diagram approximation. We also present the algorithms required for dynamically maintaining under the insertion or deletion of sites the Voronoi diagram approximation. The main features of our approach are its generality, efficiency, robustness and easy implementation. |
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| AbstractList | We propose a new approach for computing in an efficient way polygonal approximations of generalized 2D/3D Voronoi diagrams. The method supports distinct site shapes (points, line-segments, curved-arc segments, polygons, spheres, lines, polyhedra, etc.), different distance functions (Euclidean distance, convex distance functions, etc.) and is restricted to diagrams with connected Voronoi regions. The presented approach constructs a tree (a quadtree in 2D/an octree in 3D) which encodes in its nodes and in a compact way all the information required for generating an explicit representation of the boundaries of the Voronoi diagram approximation. Then, by using this hierarchical data structure a reconstruction strategy creates the diagram approximation. We also present the algorithms required for dynamically maintaining under the insertion or deletion of sites the Voronoi diagram approximation. The main features of our approach are its generality, efficiency, robustness and easy implementation. |
| Author | Madern, Narcís Coll, Narcís Boada, Imma Antoni Sellarès, J. |
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| Cites_doi | 10.1006/gmip.1997.0444 10.1142/S0218195998000114 10.1016/0167-8396(94)90029-9 10.1016/B978-044482537-7/50006-1 10.1016/0146-664X(79)90079-0 10.1109/JRA.1986.1087051 10.1145/116873.116880 10.1109/38.156016 10.1080/13658810110038942 10.1002/9780470317013 10.1145/37402.37422 10.1016/S0010-4485(98)00065-7 10.1007/3-540-44842-X_85 10.1007/978-3-662-03427-9 10.1007/BF01553877 10.1016/S0010-4485(02)00085-4 10.1142/S0218195998000291 10.1109/38.365006 10.1016/S0925-7721(01)00056-6 |
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| Title | Approximations of 2D and 3D generalized Voronoi diagrams |
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