# Planar Voronoi Diagrams for Sums of Convex Functions, Smoothed Distance and Dilation

@article{Dickerson2010PlanarVD, title={Planar Voronoi Diagrams for Sums of Convex Functions, Smoothed Distance and Dilation}, author={Matthew Dickerson and David Eppstein and Kevin A. Wortman}, journal={2010 International Symposium on Voronoi Diagrams in Science and Engineering}, year={2010}, pages={13-22} }

We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the Voronoi diagram has linear complexity and can be constructed in near-linear randomized expected time. Additionally, the level sets of the distances from the sites form a family of pseudocircles in the plane, all cells in the Voronoi diagram are connected, and…

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