Drawing triangles from incircles ?

Replies to This Discussion

Permalink Reply by David Rutten on September 25, 2011 at 1:46pm

I can't work it out. If there is a way though I'd love to know.

 

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David Rutten

david@mcneel.com

Poprad, Slovakia

Permalink Reply by Arthur Mamou-Mani on September 25, 2011 at 1:47pm

Hi David,

Sounds like it is very complicated indeed :)

http://math.stackexchange.com/questions/67510/drawing-triangles-fro...

Thanks a lot for trying !

 

Permalink Reply by Caglar on September 25, 2011 at 2:44pm

It sounds like a complex problem. I approached the problem like this but couldn't get any further:

Except the boundary curves, all curves are internal tangents of two neighbouring circles. Delaunay triangles are the set of these tangents trimmed at their intersections. We can find the tangents easily (attached file is my way of doing it). The problem is that each couple of circles have two internal tangents one of which is not usable for the problem and it's probably difficult to know which.

 

This is an interesting theorem but I don't know if it's any useful:

http://en.wikipedia.org/wiki/Japanese_theorem_for_concyclic_polygons

Attachments:

• internal tangent.gh, 7 KB

Permalink Reply by Daniel Piker on September 25, 2011 at 5:07pm

Not quite what you are after, but if you had the circumcircles instead of the incircles then I think you should be able to get the Voronoi diagram and then go back from there to the Delaunay triangulation.

http://www.therightstuff.amatyc.org/voronoidiagrams.pdf

Permalink Reply by Pieter Segeren on September 25, 2011 at 5:23pm

Hi Arthur , First of all I hope I get the mesh-lingo right, because I don't normally work with meshes... Is this a flat mesh? (I hope not) because I tried sth on a (heavily distorted) icosahedron I found pretty hopefull.

Attachments:

• PSG_1stStep2TrianglesFromInCircles...gh, 13 KB