Fitting Voronoi Diagrams to Planar Tesselations
Greg Aloupis, Hebert P\'erez-Ros\'es, Guillermo Pineda-Villavicencio,, Perouz Taslakian, Dannier Trinchet

TL;DR
This paper presents an algorithm to find a minimal set of points whose Voronoi diagram matches a given planar tessellation, with a linear number of points relative to the tessellation size under certain angle constraints.
Contribution
The paper introduces a new algorithm for the Generalized Inverse Voronoi Problem that efficiently constructs fitting Voronoi diagrams with a linear number of points.
Findings
Algorithm solves GIVP with linear point count
Works under constant smallest angle assumption
Efficiently fits Voronoi diagrams to planar tessellations
Abstract
Given a tesselation of the plane, defined by a planar straight-line graph , we want to find a minimal set of points in the plane, such that the Voronoi diagram associated with "fits" \ . This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of , assuming that the smallest angle in is constant.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Remote Sensing and LiDAR Applications · 3D Modeling in Geospatial Applications
