Wednesday, October 30, 2013

Understanding Voronoi Diagrams.

Recently I have been trying to study methods for triangulations. I want to triangulate random 3D points for surface generation. While researching the problem, I stumbled upon an interesting diagram called Voronoi Diagram.

The Voronoi Diagram of a collection of geometric objects is a partition of space into cells, each of those cells consists of the set to points closer to one particular object that to any other.

In Mathematical terms, given a set S of n distinct points in a plane, Voronoi Diagram is the partition of plane into n polyhedral region V(p) (p belongs to S). Each region V(p) is called the Voronoi cell of p and is defined as the set of points in plane which are closer to p than any other points ( - p) in S. The closeness of one point to other is calculated using the Euclidean Distance Formulation, which is just the length of line segment connecting two points.

You can refer to this post on Wolfram for more information : Voroni Diagram --from Wolfram.

I will soon try to implement this Diagram and see it in life. I will keep you updated :D


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