A vector-based algorithm to generate and update multiplicatively weighted Voronoi diagrams for points, polylines, and polygons
A Voronoi diagram is a basic data structure in geometry with many applications. Existing research studies have focused on ordinary Voronoi diagrams, and some vector-based algorithms have been developed to generate multiplicatively weighted Voronoi diagrams (MWVDs) for points. An algorithm to constru...
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| Published in: | Computers & geosciences Vol. 42; pp. 118 - 125 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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01.05.2012
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| ISSN: | 0098-3004, 1873-7803 |
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| Abstract | A Voronoi diagram is a basic data structure in geometry with many applications. Existing research studies have focused on ordinary Voronoi diagrams, and some vector-based algorithms have been developed to generate multiplicatively weighted Voronoi diagrams (MWVDs) for points. An algorithm to construct MWVDs for points, polylines, and polygons is raster-based and has drawbacks. We propose a vector-based algorithm to generate and update MWVDs for points, polylines, and polygons. The MWVDs of two sites characterize the geometric features of multiplicatively weighted Voronoi regions, and the algorithm for Boolean operations on conic polygons is the computational preliminary to the MWVDs of N sites. The proposed algorithm is vector-based and can deal with sites with mixed spatial extents and various weights. We implement the algorithm in C# and present several examples of generating and updating MWVDs.
► We develop an algorithm to generate MWVDs for sites with mixed spatial extents. ► The method is vector-based and can explore the shape characteristic of the MWVDs. ► The method can generate both MWVDs and OVDs, and degeneration cases are considered. ► The method is accurate than raster-based method and is efficient for GIS applications. |
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| AbstractList | A Voronoi diagram is a basic data structure in geometry with many applications. Existing research studies have focused on ordinary Voronoi diagrams, and some vector-based algorithms have been developed to generate multiplicatively weighted Voronoi diagrams (MWVDs) for points. An algorithm to construct MWVDs for points, polylines, and polygons is raster-based and has drawbacks. We propose a vector-based algorithm to generate and update MWVDs for points, polylines, and polygons. The MWVDs of two sites characterize the geometric features of multiplicatively weighted Voronoi regions, and the algorithm for Boolean operations on conic polygons is the computational preliminary to the MWVDs of N sites. The proposed algorithm is vector-based and can deal with sites with mixed spatial extents and various weights. We implement the algorithm in C# and present several examples of generating and updating MWVDs. A Voronoi diagram is a basic data structure in geometry with many applications. Existing research studies have focused on ordinary Voronoi diagrams, and some vector-based algorithms have been developed to generate multiplicatively weighted Voronoi diagrams (MWVDs) for points. An algorithm to construct MWVDs for points, polylines, and polygons is raster-based and has drawbacks. We propose a vector-based algorithm to generate and update MWVDs for points, polylines, and polygons. The MWVDs of two sites characterize the geometric features of multiplicatively weighted Voronoi regions, and the algorithm for Boolean operations on conic polygons is the computational preliminary to the MWVDs of N sites. The proposed algorithm is vector-based and can deal with sites with mixed spatial extents and various weights. We implement the algorithm in C# and present several examples of generating and updating MWVDs. ► We develop an algorithm to generate MWVDs for sites with mixed spatial extents. ► The method is vector-based and can explore the shape characteristic of the MWVDs. ► The method can generate both MWVDs and OVDs, and degeneration cases are considered. ► The method is accurate than raster-based method and is efficient for GIS applications. |
| Author | Gong, Yongxi Tian, Yuan Liu, Yu Li, Guicai Lin, Yaoyu |
| Author_xml | – sequence: 1 givenname: Yongxi surname: Gong fullname: Gong, Yongxi organization: Shenzhen Key Lab of Recycling Economy, Peking University Shenzhen Graduate School, Shenzhen 518055, People's Republic of China – sequence: 2 givenname: Guicai surname: Li fullname: Li, Guicai organization: Shenzhen Key Lab of Recycling Economy, Peking University Shenzhen Graduate School, Shenzhen 518055, People's Republic of China – sequence: 3 givenname: Yuan surname: Tian fullname: Tian, Yuan organization: Institute of Remote Sensing & Geographical Information Systems, Peking University, Beijing 100871, People's Republic of China – sequence: 4 givenname: Yaoyu surname: Lin fullname: Lin, Yaoyu organization: School of Urban Planning and Management, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China – sequence: 5 givenname: Yu surname: Liu fullname: Liu, Yu email: liuyu@urban.pku.edu.cn organization: Institute of Remote Sensing & Geographical Information Systems, Peking University, Beijing 100871, People's Republic of China |
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| Cites_doi | 10.1111/j.0033-0124.1975.00426.x 10.1016/S0097-8493(00)00090-X 10.1111/j.1538-4632.1979.tb00695.x 10.2307/142991 10.1016/S0198-9715(00)00007-7 10.1016/S0925-7721(01)00003-7 10.1145/116873.116880 10.1007/3-540-45749-6_19 10.1016/j.cageo.2007.04.005 10.1515/crll.1850.40.209 10.1016/0031-3203(84)90064-5 10.1080/136588197242176 10.1016/S0377-2217(97)80001-X 10.2307/142716 10.1111/j.0033-0124.2004.05602007.x 10.1016/j.cor.2004.07.001 10.1007/s11390-009-9246-z 10.1016/j.jlap.2004.07.006 10.1145/1138127.1138131 10.1109/SFCS.1975.8 10.1007/BF01840357 10.1524/zkri.1927.65.1.391 10.1103/PhysRev.43.804 |
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| Snippet | A Voronoi diagram is a basic data structure in geometry with many applications. Existing research studies have focused on ordinary Voronoi diagrams, and some... |
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| SubjectTerms | Algorithms Boolean algebra Boolean operations on conic polygons C (programming language) Computation computers Conics Construction data analysis Data structures Multiplicatively weighted Voronoi diagrams Polygons shape Vector-based algorithm |
| Title | A vector-based algorithm to generate and update multiplicatively weighted Voronoi diagrams for points, polylines, and polygons |
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