A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains

Abstract

We introduce a new method for computing the geodesic Voronoi diagram of point sites in a simple polygon and other restricted polygonal domains. Our method combines a sweep of the polygonal domain with the merging step of a usual divide-and-conquer algorithm. The time complexity is O((n+k) log(n+k)) where n is the number of vertices and k is the number of points, improving upon previously known bounds. Space is O(n+k) . Other polygonal domains where our method is applicable include (among others) a polygonal domain of parallel disjoint line segments and a polygonal domain of rectangles in the L 1 metric

Operations on network-based space layouts for modeling multiple space views of buildings

“…Functions in the computational geometry algorithms library (CGAL) are used to generate Euclidean Voronoi diagrams from which volumes of new whole spaces are derived in the decompose operation [51,61]. We use Euclidean rather than geodesic Voronoi diagrams because implementations of the former are currently not available [62].…”

Geodesic-Preserving Polygon Simplification

“…Since then the algorithms have been improved, and the currently best algorithm is due to Papadopoulou and Lee [27]. The furthest-site Voronoi diagram has also been studied in geodesic environments [5].…”

Demand Allocation in Water Distribution Network Modelling – A GIS-Based Approach Using Voronoi Diagrams with Constraints

“…The approach of Aronov (1987) considers nonconvex boundaries but not obstacles within the Voronoi regions. The approach of Papadopoulou and Lee (1998) does consider obstacles as constraints but only if specific conditions are given. None of the known approaches solves the problem satisfactorily for an application in the given context.…”