Voronoi diagram


Qhull-specific options are no longer supported. Remove the OPTIONS argument from all instances in your code that pass it to voronoi.


The behavior of h = voronoi(...) has changed. The new behavior returns a vector of two chart line handles; one representing the points and the other representing the Voronoi edges.


h = voronoi(...)
[vx,vy] = voronoi(...)


voronoi(x,y) plots the bounded cells of the Voronoi diagram for the points x,y. Lines-to-infinity are approximated with an arbitrarily distant endpoint.

voronoi(x,y,TRI) uses the triangulation TRI instead of computing internally.

voronoi(dt) uses the Delaunay triangulation dt instead of computing it.

voronoi(AX,...) plots into AX instead of gca.

voronoi(...,'LineSpec') plots the diagram with color and line style specified.

h = voronoi(...) returns h, which is a vector of two chart line handles. One represents the points and the other represents the Voronoi edges.

[vx,vy] = voronoi(...) returns the finite vertices of the Voronoi edges in vx and vy.


For the topology of the Voronoi diagram, i.e., the vertices for each Voronoi cell, use voronoin.

[v,c] = voronoin([x(:) y(:)])


Use one of these methods to plot a Voronoi diagram:

  • If you provide no output argument, voronoi plots the diagram.

  • To gain more control over color, line style, and other figure properties, use the syntax [vx,vy] = voronoi(...). This syntax returns the vertices of the finite Voronoi edges, which you can then plot with the plot function.

  • To fill the cells with color, use 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.


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This code uses the voronoi function to plot the Voronoi diagram for 10 randomly generated points.

x = gallery('uniformdata',[1 10],0);
y = gallery('uniformdata',[1 10],1);

This code uses the vertices of the finite Voronoi edges to plot the Voronoi diagram for the same 10 points used in the previous example.

x = gallery('uniformdata',[1 10],0);
y = gallery('uniformdata',[1 10],1); 
[vx,vy] = voronoi(x,y);
axis equal

Note that you can add the following code to get the figure shown in the previous example.

xlim([min(x) max(x)])
ylim([min(y) max(y)])

This code uses voronoin and patch to fill the bounded cells of the same Voronoi diagram with color.

x = gallery('uniformdata',[10 2],5);
[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.

More About

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Voronoi Polygon

Consider a set of coplanar points P. For each point Px in the set P, you can draw a boundary enclosing all the intermediate points lying closer to Px than to other points in the set P. Such a boundary is called a Voronoi polygon.

Voronoi Diagram

The set of all Voronoi polygons for a given point set is called a Voronoi diagram.

Extended Capabilities

Introduced before R2006a