A Theoretical Study of Parallel Voronoi Diagram

Voronoi Diagrams for Parallel Halflines in 3D

We consider the Euclidean Voronoi diagram for a set of n parallel halflines in R. A relation of this diagram to planar power diagrams is shown, and is used to analyze its geometric and topological properties. Moreover, a simple plane-sweep algorithm is given that computes the Voronoi diagram for parallel halflines at logarithmic cost per face.

Parallel and Network Algorithms and Applications for Steiner Trees and Voronoi Diagram

Variational Anisotropic Surface Meshing with Voronoi Parallel Linear Enumeration

This paper introduces a new method for anisotropic surface meshing. From an input polygonal mesh and a specified number of vertices, the method generates a curvature-adapted mesh. The main idea consists in transforming the 3d anisotropic space into a higher dimensional isotropic space (typically 6d or larger). In this high dimensional space, the mesh is optimized by computing a Centroidal Voron...

On the possibility of simple parallel computing of Voronoi diagrams and Delaunay graphs

The Voronoi diagram is a widely used data structure. The theory of algorithms for computing Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. However, this theory has been quite steady during the last few decades in the sense that new algorithms have not entered the game. In addition, most of the known algorithms are sequential in nat...

Dynamic Spatial Data Structures - the Voronoi Approach

Voronoi diagrams have recently received attention as data structures containing significant information about the spatial adjacency of map objects. Despite their theoretical efficiency, batch construction techniques require complete rebuilding after each modification. Incremental Voronoi creation methods use processes such as insert, delete and move for points, and from these derive insertion a...