A vector-based algorithm to generate and update multiplicatively weighted Voronoi diagrams for points, polylines, and polygons

Authors:
Yongxi Gong;Guicai Li;Yuan Tian;Yaoyu Lin;Yu Liu
Affiliations:
Shenzhen Key Lab of Recycling Economy, Peking University Shenzhen Graduate School, Shenzhen 518055, People's Republic of China and Institute of Remote Sensing & Geographical Information Systems, P ...;Shenzhen Key Lab of Recycling Economy, Peking University Shenzhen Graduate School, Shenzhen 518055, People's Republic of China;Institute of Remote Sensing & Geographical Information Systems, Peking University, Beijing 100871, People's Republic of China;School of Urban Planning and Management, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, People's Republic of China;Institute of Remote Sensing & Geographical Information Systems, Peking University, Beijing 100871, People's Republic of China
Venue:
Computers & Geosciences
Year:
2012

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Generating and updating multiplicatively weighted Voronoi diagrams for point, line and polygon features in GIS

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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.