In this paper, we construct an algorithm for determining whether a given tessellation on a sphere is a spherical Laguerre Voronoi diagram or not. For spherical Laguerre tessellations, not only the locations of the Voronoi generators, but also their weights are required to recover. However, unlike the ordinary spherical Voronoi diagram, the generator set is not unique, which makes the problem di...

We present novel exploration algorithms and a control law that enables the construction of Voronoi diagrams over unknown areas using a single vehicle equipped with range sensors. The control law uses range measurements to make the vehicle track Voronoi edges between obstacles. The exploration algorithms make decisions at vertices in the Voronoi diagram to expand the explored area until a comple...

In this paper, we propose a novel image steganographic technique based on the Voronoi diagram. The basic idea is to generate a Voronoi diagram of a graph transformed from cover image; that is, the Voronoi points correspond to every two consecutive pixels in the cover image. According to the secret bits to be embedded, every Voronoi point will either be replaced by one of its neighbors or keep i...

Multiresolution representation of high-dimensional scattered data is a fundamental problem in scientific visualization. This paper introduces a data hierarchy of Voronoi diagrams as a versatile solution. Given an arbitrary set of points in the plane, our goal is the construction of an approximation hierarchy using the Voronoi diagram as the essential building block. We have implemented two Voro...

In this paper we study the Voronoi diagram of lines in R. The Voronoi diagram of three lines in general position was studied in [8]. In this paper we complete this work by presenting a complete characterization of the Voronoi diagram of three arbitrary lines in R. As in the general case, we prove that the arcs of trisectors are always monotonic in some direction and we show how to separate the ...

Voronoi diagrams have several important applications in science and engineering. While the properties and algorithms for the ordinary Voronoi diagram of point set have been well-known, their counterparts for a set of spheres have not been sufficiently studied. In this paper, we present the definition, properties and algorithms for the Voronoi diagram of 3D spheres based on the Euclidean distanc...

A set of points in the plane induces a Voronoi diagram, a division of the plane based on proximity to points in the set. Voronoi diagrams have been used extensively in engineering and scientific disciplines, but the possibility of using them for creating abstract ornamental designs is largely unexplored. I present some techniques for creating attractive ornamental designs using Voronoi diagrams...

Sensor networks are unattended deeply distributed systems whose database schema can be conceptualized using the relational model. Aggregation queries on the data sampled at each sensor node are the main means to extract the abstract characteristics of the surrounding environment. However, the non-uniform distribution of the sensor nodes in the environment leads to inaccurate results generated b...

A three-dimensional Voronoi tessellation of folded proteins is used to analyze geometrical and topological properties of a set of proteins. To each amino acid is associated a central point surrounded by a Voronoi cell. Voronoi cells describe the packing of the amino acids. Special attention is given to reproduction of the protein surface. Once the Voronoi cells are built, a lot of tools from ge...

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...