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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Bibliographic Details
Published in:Computers & geosciences Vol. 42; pp. 118 - 125
Main Authors: Gong, Yongxi, Li, Guicai, Tian, Yuan, Lin, Yaoyu, Liu, Yu
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.05.2012
Subjects:
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
Multiplicatively weighted Voronoi diagrams
Vector-based algorithm
Boolean operations on conic polygons
ISSN:0098-3004, 1873-7803
Online Access:Get full text
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Summary: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.
Bibliography:http://dx.doi.org/10.1016/j.cageo.2011.09.003
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ISSN:0098-3004
1873-7803
DOI:10.1016/j.cageo.2011.09.003