Several efficient algorithms are known for constructing Voronoi diagrams, either directly (as the diagram itself) or indirectly by starting with a Delaunay triangulation and then obtaining its dual. Direct algorithms include Fortune's algorithm, an O(n log(n)) algorithm for generating a Voronoi diagram from a set of points in a plane.

In this paper, I describe a simple 3D Voronoi diagram (and Delaunay tetrahedralization) algorithm, and I explain, by giving as many details and insights as possible, how to ensure that it outputs a correct structure, regardless of the spatial distribution of the points in the input. 1. Introduction.

Difference between Voronoi Diagram and Medial Axis. The medial axis is a subset of the Voronoi diagram of the edges and vertices of the polygon. Voronoi edges that meet the reflex vertices are not part of the medial axis.

Jun 10, 2009 · The most effecient algorithm to construct a voronoi diagram is Fortune's algorithm. It runs in O(n log n). Here is a link to his reference implementation in C. Personally I really like the python implementation by Bill Simons and Carson Farmer, since I found it easier to extend.

Voro++ is a software library for carrying out three-dimensional computations of the Voronoi tessellation. A distinguishing feature of the Voro++ library is that it carries out cell-based calculations, computing the Voronoi cell for each particle individually.

We present an e cient algorithm for computing the clipped Voronoi di- agram for a set of sites with respect to a compact 3D volume, assuming that the volume is represented as a tetrahedral mesh.

Feb 1, 2023 · We present a scalable parallel algorithm for constructing 3D Voronoi tessellations based on kd-tree decomposition. The proposed algorithm exploits process-level and thread-level parallelization and can be used in a diverse architectural landscape.

In this paper, I describe a simple 3D Voronoi diagram (and Delaunay tetrahedralization) algorithm, and I explain, by giving as many details and insights as possible, how to ensure that it outputs a correct structure, regardless of the spatial distribution of the points in the input.

algorithm for the movement of points in a three-dimensional VD, and show that it can be relatively easy to implement as it is the extension of a simple two-dimensional algorithm.

The input to the 3D voronoi diagram algorithm is a set of 3D points P = fp 1;p 2;:::;p ng The output is the 3D Delaunay triangulation of the point set P. Input The input points are randomly generated within the unit sphere. Output The Delaunay triangulation is represented as a tetrahedral mesh, using Dart data structure to store.