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:
http://www.scribd.com/doc/147332295/A-Gentle-Introduction-to-Gis
It appears that the author did this with QGIS, but he didn't explain how.
Image from Wikipedia:
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])
end
% Make sure circles appear as circles
axis equal
axis off
% Plot the points on top
scatter(x,y, '.r')
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.
