Quickest Paths, Straight Skeletons, and the City Voronoi Diagram

Constructing the city Voronoi diagram faster

Given a set P of n point sites in the plane, the city Voronoi diagram subdivides the plane into the Voronoi regions of the sites, with respect to the city metric. This metric is induced by quickest paths according to the Manhattan metric and an accelerating transportation network that consists of c non-intersecting axis-parallel line segments. We describe an algorithm that constructs the city V...

Hierarchic Voronoi skeletons

Robust and time-efficient skeletonization of a (planar) shape, which is connectivity preserving and based on Euclidean metrics, can be achieved by first regularizing the Voronoi diagram (VD) of a shape’s boundary points, i.e., by removal of noise-sensitive parts of the tessellation and then by establishing a hierarchic organization of skeleton constituents . Each component of the VD is attribut...

Quickest paths: parallelization and dynamization

Let N = (V, E, c, /) be a network, where G = (V, E), (VI = n and (El = m, is a directed graph, c(e) > 0 is the capacity and I(e) 2 0 is the lead time for each edge e E E. The transmission time to send u units of data from a given source s to a destination t using path p is T(a,p) = I(p) + &, where 1(p) is the sum of the lead times of the edges in p, and c(p) is the minimum capacity of the edges...

Polytope Skeletons and Paths

Straight Skeletons by Means of Voronoi Diagrams Under Polyhedral Distance Functions

We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary conditions for input shapes in order to obtain identical straight skeletons and Voronoi diagrams with respec...