website/content/research/clusteranalysis/notes/lec10-3.md

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---
title: Voronoi Diagram
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---
A Voronoi diagram is a partitioning of a plan into regions based on distance to points in a specific subset of the plane.
The set of points (often called seeds, sites, or generators) is specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than any other.
Different metrics may be used and often result in different Voronoi diagrams
**Euclidean**
![](https://upload.wikimedia.org/wikipedia/commons/thumb/5/54/Euclidean_Voronoi_diagram.svg/382px-Euclidean_Voronoi_diagram.svg.png)
**Manhattan**
![](https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Manhattan_Voronoi_Diagram.svg/382px-Manhattan_Voronoi_Diagram.svg.png)