# voronoiDiagram

Class: DelaunayTri

(Will be removed) Voronoi diagram

 Note:   `voronoiDiagram(DelaunayTri)` will be removed in a future release. Use `voronoiDiagram(delaunayTriangulation)` instead.`DelaunayTri` will be removed in a future release. Use `delaunayTriangulation` instead.

## Syntax

`[V, R] = voronoiDiagram(DT)`

## Description

`[V, R] = voronoiDiagram(DT)` returns the vertices `V` and regions `R` of the Voronoi diagram of the points `DT.X`. The region `R{i}` is a cell array of indices into `V` that represents the Voronoi vertices bounding the region. The Voronoi region associated with the `i`'th point, `DT.X(i)` is `R{i}`. For 2-D, vertices in `R{i}` are listed in adjacent order, i.e. connecting them will generate a closed polygon (Voronoi diagram). For 3-D the vertices in `R{i}` are listed in ascending order.

The Voronoi regions associated with points that lie on the convex hull of `DT.X` are unbounded. Bounding edges of these regions radiate to infinity. The vertex at infinity is represented by the first vertex in `V`.

## Input Arguments

 `DT` Delaunay triangulation.

## Output Arguments

 `V` `numv`-by-`ndim` matrix representing the coordinates of the Voronoi vertices, where `numv` is the number of vertices and `ndim` is the dimension of the space where the points reside. `R` Vector cell array of `length(DR.X)`, representing the Voronoi cell associated with each point.

## Definitions

The Voronoi diagram of a discrete set of points `X` decomposes the space around each point `X(i)` into a region of influence `R{i}`. Locations within the region are closer to point `i` than any other point. The region of influence is called the Voronoi region. The collection of all the Voronoi regions is the Voronoi diagram.

The convex hull of a set of points `X` is the smallest convex polygon (or polyhedron in higher dimensions) containing all of the points of `X`.

## Examples

Compute the Voronoi Diagram of a set of points:

```X = [ 0.5 0 0 0.5 -0.5 -0.5 -0.2 -0.1 -0.1 0.1 0.1 -0.1 0.1 0.1 ] dt = DelaunayTri(X) [V,R] = voronoiDiagram(dt) ```

## See Also

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