In this paper, we consider rendering color videos using a non-photo-realistic art form technique commonly called stippling. Stippling is the art of rendering images using point sets, possibly with various attributes like sizes, elementary shapes, and colors. Producing nice stippling is attractive not only for the sake of image depiction but also because it yields a compact vectorial format for ...

Voronoi treemaps represent hierarchies as nested polygons. We here show that, contrary to the apparent popular belief, utilization of an algorithm for weighted Voronoi diagrams is not only feasible, but also more efficient than previous low-resolution approximations, even when the latter are implemented on graphics hardware. More precisely, we propose an instantiation of Lloyd’s method for cent...

The Voronoi diagram is a famous structure of computational geometry. We show that there is a straightforward equivalent in graph theory which can be eeciently computed. In particular, we give two algorithms for the computation of graph Voronoi diagrams, prove a lower bound on the problem, and we identify cases where the algorithms presented are optimal. The space requirement of a graph Voronoi ...

Science and mathematics developed with great leaps that affected the world, as a result, new trends concepts appeared based on development of computers. One these is "Voronoi diagram ". The concept emerged an important mathematical principle in field architecture, computer algorithms Voronoi significantly. one most common structural network systems nature, due to its abundance nature through pl...

Voronoi diagrams and Delaunay triangulations have been extensively used to represent and compute geometric features of point configurations. We introduce a generalization to poset diagrams and poset complexes, which contain order-k and degree-k Voronoi diagrams and their duals as special cases. Extending a result of Aurenhammer from 1990, we show how to construct poset diagrams as weighted Voro...

In this paper we present a dynamic algorithm for the construction of the additively weighted Voronoi diagram of a set of weighted points on the plane. The novelty in our approach is that we use the dual of the additively weighted Voronoi diagram to represent it. This permits us to perform both insertions and deletions of sites easily. Given a set B of n sites, among which h sites have non-empty...

This paper gives a survey of static, dynamic, and kinematic Voronoi diagrams as a basic tool for Geographic Information Systems (GIS). We show how the Voronoi diagram with its dual, the Delaunay multigraph, can be used to maintain the topology of the map objects of a GIS. The presented method allows the insertion, deletion, and translation of points and line segments in a Voronoi diagram of n g...

This paper considers a generalization of travel time distances by taking general underlying distance functions into account. We suggest a reasonable set of axioms defining a certain class of distance functions that can be facilitated with transportation networks. It turns out to be able to build an abstract framework for computing shortest path maps and Voronoi diagrams with respect to the indu...