The Farthest-Point Geodesic Voronoi Diagram of Points on the Boundary of a Simple Polygon
نویسندگان
چکیده
Given a set of sites (points) in a simple polygon, the farthest-point geodesic Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O((n + m) log logn)time algorithm to compute the farthest-point geodesic Voronoi diagram for m sites lying on the boundary of a simple n-gon. 1998 ACM Subject Classification I.3.5 Computational Geometry and Object Modeling
منابع مشابه
The Geodesic Farthest-point Voronoi Diagram in a Simple Polygon
Given a set of point sites in a simple polygon, the geodesic farthest-point Voronoi diagram partitions the polygon into cells, at most one cell per site, such that every point in a cell has the same farthest site with respect to the geodesic metric. We present an O(n log log n+m logm)time algorithm to compute the geodesic farthest-point Voronoi diagram of m point sites in a simple n-gon. This i...
متن کاملVoronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon
Given a set of sites in a simple polygon, a geodesic Voronoi diagram partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones form ≤ n/polylogn. Moreover, the algorithms for the ne...
متن کاملL_1 Geodesic Farthest Neighbors in a Simple Polygon and Related Problems
In this paper, we investigate the L1 geodesic farthest neighbors in a simple polygon P , and address several fundamental problems related to farthest neighbors. Given a subset S ⊆ P , an L1 geodesic farthest neighbor of p ∈ P from S is one that maximizes the length of L1 shortest path from p in P . Our list of problems include: computing the diameter, radius, center, farthestneighbor Voronoi di...
متن کاملHigher-Order Geodesic Voronoi Diagrams in a Polygonal Domain with Holes
We investigate the higher-order Voronoi diagrams of n point sites with respect to the geodesic distance in a simple polygon with h > 0 polygonal holes and c corners. Given a set of n point sites, the korder Voronoi diagram partitions the plane into several regions such that all points in a region share the same k nearest sites. The nearest-site (first-order) geodesic Voronoi diagram has already...
متن کاملVoronoi Diagram for Convex Polygonal Sites with Convex Polygon-Offset Distance Function
The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...
متن کامل