Abstract
Every region in a 2-dimensional Voronoi diagram consists of all points for which the corresponding site minimizes the Euclidean distance.
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For this to be true, we have to assume that both weights are positive. A similar but geometrically not quite as compelling interpretation can also be found for the case in which one of the weights is non-positive.
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Edelsbrunner, H. (2014). Weighted Diagrams. In: A Short Course in Computational Geometry and Topology. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-05957-0_3
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DOI: https://doi.org/10.1007/978-3-319-05957-0_3
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