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Data Visualization Using Weighted Voronoi Diagrams
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Author(s): Raghuveer Devulapalli (University of Minnesota, USA), Neil Peterson (University of Minnesota, USA)and John Gunnar Carlsson (University of Southern California, USA)
Copyright: 2015
Pages: 24
Source title:
Geo-Intelligence and Visualization through Big Data Trends
Source Author(s)/Editor(s): Burçin Bozkaya (Sabanci University School of Management, Turkey)and Vivek Kumar Singh (Rutgers, The State University of New Jersey, USA & Massachusetts Institute of Technology, USA)
DOI: 10.4018/978-1-4666-8465-2.ch007
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Abstract
A Voronoi diagram is a standard spatial tessellation that partitions a domain into sub-regions based on proximity to a fixed set of landmark points. In order to maintain control over the size and shape of these sub-regions, a weighting scheme is often used, in which each landmark has a scalar value associated with it. This suggests a natural “inverse” problem: given a fixed set of landmark points in a given planar region and a set of “desired” areas, is it possible to calculate a set of weights so that each sub-region has a particular area? In this chapter, the authors give a fast scheme for determining these weights based on theory from convex optimization, which is then applied to a variety of problems in data visualization.
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