MATLAB: Voronoi Diagram with Delaunay Triangulation overlay

circlesdelaunay triangulationMATLABvoronoi

If I have some Voronoi Diagram:
clc
clear all
close all
n=5
x=10*rand(1,n)
y=10*rand(1,n)
voronoi(x,y)
[vx vy] =voronoi(x,y)
close all
plot(x,y,'r+',vx,vy,'b-'); axis equal
figure(2)
for j=1:length(vx(1,:))
  line([vx(1,j) vx(2,j)],[vy(1,j) vy(2,j)])
end
axis equal
How can I use the Delaunay Triangulation Matlab program (DelaunayTri) from the points created by the Voronoi Diagram, and to have the circles appear as in the attached link (most left image), or more like the interactions on the top of page 3 from the linked paper Animating Bubble Interactions in a Liquid Foam ? Delaunay Triangulation Image

Best Answer

Try this:
clc; clear all; close all;
n=5;
x = 10*rand(1, n);
y = 10*rand(1, n);
voronoi(x,y,'--k');
DT = DelaunayTri(x', y');
% use this in newer versions of matlab
% DT = delaunayTriangulation (x, y);
hold all;
triplot(DT,'k-');
[centers, radii] = DT.circumcenters();
theta = -pi:pi/20:pi;
for iCircle=1:size(centers,1)
  xCircle = centers(iCircle,1) + radii(iCircle)*cos(theta);
  yCircle = centers(iCircle,2) + radii(iCircle)*sin(theta);
  plot(xCircle, yCircle, 'b-');
end
plot(x,y,'+k', 'MarkerSize', 12)
axis equal;
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