MATLAB Function Reference 
Syntax
Definition
Consider a set of coplanar points . For each point in the set , you can draw a boundary enclosing all the intermediate points lying closer to than to other points in the set . Such a boundary is called a Voronoi polygon, and the set of all Voronoi polygons for a given point set is called a Voronoi diagram.
Description
voronoi(x,y)
plots the bounded cells of the Voronoi diagram for the points x
,y
. Cells that contain a point at infinity are unbounded and are not plotted.
voronoi(x,y,TRI)
uses the triangulation TRI
instead of computing it via delaunay
.
voronoi(...,'LineSpec')
plots the diagram with color and line style specified.
h = voronoi(...)
returns, in h
, handles to the line objects created.
[vx,vy] = voronoi(...)
returns the finite vertices of the Voronoi edges in vx
and vy
so that plot(vx,vy,'',x,y,'.')
creates the Voronoi diagram.
Note
For the topology of the Voronoi diagram, i.e., the vertices for each Voronoi cell, use voronoin . [v,c] = voronoin([x(:) y(:)])

Visualization
Use one of these methods to plot a Voronoi diagram:
voronoi
plots the diagram. See Example 1.
[vx,vy] = voronoi(...)
. This syntax returns the vertices of the finite Voronoi edges, which you can then plot with the plot
function. See Example 2.
voronoin
with n = 2
to get the indices of each cell, and then use patch
and other plot functions to generate the figure. Note that patch
does not fill unbounded cells with color. See Example 3.
Examples
Example 1. This code uses the voronoi
function to plot the Voronoi diagram for 10 randomly generated points.
Example 2. This code uses the vertices of the finiteVoronoi edges to plot the Voronoi diagram for the same 10 points.
rand('state',5); x = rand(1,10); y = rand(1,10); [vx, vy] = voronoi(x,y); plot(x,y,'r+',vx,vy,'b'); axis equal
Note that you can add this code to get the figure shown in Example 1.
Example 3. This code uses voronoin
and patch
to fill the bounded cells of the same Voronoi diagram with color.
rand('state',5); x=rand(10,2); [v,c]=voronoin(x); for i = 1:length(c) if all(c{i}~=1) % If at least one of the indices is 1, % then it is an open region and we can't % patch that. patch(v(c{i},1),v(c{i},2),i); % use color i. end end axis equal
Algorithm
If you supply no triangulation TRI
, the voronoi
function performs a Delaunay triangulation of the data that uses Qhull [2]. This triangulation uses the Qhull joggle option ('QJ'
). For information about Qhull, see http://www.geom.umn.edu/software/qhull/. For copyright information, see http://www.geom.umn.edu/software/download/COPYING.html.
See Also
convhull
, delaunay
, LineSpec
, plot
, voronoin
Reference
[1] Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Transactions on Mathematical Software, Vol. 22, No. 4, Dec. 1996, p. 469483. Available in HTML format at http://www.acm.org/ pubs/citations/journals/toms/1996224/p469barber/ and in PostScript format at ftp://geom.umn.edu/pub/software/qhull96.ps.
[2] National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center), University of Minnesota. 1993.
volumebounds  voronoin 