# Minimum length inside the voronoi

Hi everyone, I have built a voronoi diagram but I have too short lines and I would like to fix the minimum length inside the voronoi.
Can anyone help me? i think something can be done with galapagos or kangaroo however i can’t find anything like that on the web.

I tried to use Loyds but then I lose information about the density of points that I had set on some areas of my surface. I don’t want everything to become regular.

You would really help me.
Thank you for your time.

.voronoi.gh (13.8 KB)

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I’m assuming it is not actually a Voronoi diagram specifically that you are after, but rather an organic looking distribution of polygonal cells.
The vertices of the Voronoi diagram can be seen as the centres of the circumcircles of the triangles of the Delaunay mesh of the points (https://en.wikipedia.org/wiki/Delaunay_triangulation).
For a general distribution there is no guarantee that these circumcentres are anywhere near the centre of, or even inside the triangles, so they can end up very close to the circumcentres of adjacent faces, giving you short edges in the Voronoi, as you found.

(note the pair of almost overlapping circles near the bottom, and the resulting short edge)

If instead of the circumcentric dual (ie the Voronoi), we take the centre of the incircle of each triangle, we get much better bounds on the shortest edge length. There is an output for the incentric dual on the ‘TangentCircles’ component under the Kangaroo>Mesh tab.
We can also improve the shapes of this incentric dual further by optimising for the tangent incircles energy. This gives us a dual which like the Voronoi has its edges perpendicular to those of the primal triangulation.
cells_indual.gh (14.5 KB)

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Thanks Daniel, you are really strong.

HI Daniel Piker,
excuse me if I reopen this discussion after a long time but I am interested in the subject. I would like to ask If you think it is possible to apply the same method on voronoi 3d.