Is it possible to show the delaunay circumcircles in QGIS? I know how to make the Voronoi polygons and Delaunay triangles.

I found a web page that shows the circumcircles at:


It appears that the author did this with QGIS, but he didn't explain how.

Image from Wikipedia:

enter image description here

  • 1
    I think that the image has been borrowed from wikipedia to illustrate the method i.e. it was not created with QGIS. Nov 1, 2013 at 6:28
  • Then is there another program that shows the circumcircles?
    – Jim
    Nov 1, 2013 at 11:54
  • So you just want a way to show the circumcircles of a delaunay triangulation, it doesn't necessarily have to be within QGIS? Is this just for demonstration/teaching purposes?
    – Jake
    Nov 1, 2013 at 14:52
  • Yes, it is for a paper that I'm writing. It doesn't have to be in QGIS.
    – Jim
    Nov 2, 2013 at 17:39

2 Answers 2


You can calculate the Delaunay triangulation and the circumcircles using Matlab (or its open-source counterpart Octave):

% Generate some random points
x = rand(5,1); y = rand(5,1);

% Calculate the Delaunay triangulation
tri = delaunay(x, y);

% Plot the triangulation
hold off
triplot(tri, x, y, 'k')
hold all

% Calculate the circumcircles for all triangles
for row=tri'
    points = [x(row) y(row)];

    % Uses the calcCircle function from http://www.mathworks.de/matlabcentral/fileexchange/19083-calccircle
    [pos, r] = calcCircle(points(1,:), points(2,:), points(3,:));

    % Draw the circle
    rect = rectangle('Position',[pos(1)-r, pos(2)-r,2*r, 2*r], 'Curvature', 1);

    % Change the color of the circle
    set(rect, 'EdgeColor', [0.5 0.5 0.5])

% Make sure circles appear as circles
axis equal
axis off

% Plot the points on top
scatter(x,y, '.r')
  • 1
    Woo hoo! That's what I'm looking for. Thanks so much for your answer.
    – Jim
    Nov 5, 2013 at 3:28

It is possible to delineate the circumcircles of a TIN in QGIS using the Minimum Enclosing Circles tool, entering the TIN as the input vector layer. The Minimum Bounding Geometry tool can also be used in the same way.

enter image description here

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