I want to grow circles centered at a set of $n$ points simultaneously and uniformly until a circle packing is created.
Is there a way I can solve for the radii of the circles in the packing analytically?
2026-03-28 06:08:24.1774678104
Obtaining a circle packing from a set of circle centers?
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An essential technique for what you want to do is "Delaunay triangulation" of your set of points. This will provide you the "closest neighbour" of a given point
Indeed, being given a certain point $V_1$; it is among the vertices of the Delaunay triangles having $V_1$ as one of their vertices that one finds another vertex $V_2$ which is at the shortest distance from $V_1$, a result that dramatically decreases the search time
Just a pitfall to avoid: "A has B for its closest neighbour" is not at all reversible: B can have another C as its closest neighbour.
I don't enter more into other details for the moment, but I can give more precisions (tomorrow: it's late now in Europe...).