MATLAB Function Reference    

Voronoi diagram



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.


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.


Use one of these methods to plot a Voronoi diagram:


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.

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.


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 For copyright information, see

See Also

convhull, delaunay, LineSpec, plot, voronoin


[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. 469-483. Available in HTML format at pubs/citations/journals/toms/1996-22-4/p469-barber/ and in PostScript format at

[2]  National Science and Technology Research Center for Computation and Visualization of Geometric Structures (The Geometry Center), University of Minnesota. 1993.

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