comp.graphics.algorithms

Subject: Re: medial axis for convex polygons

wrote in message
news:1146641655.570415.71430@y43g2000cwc.googlegroups.com...

> I have read in an article that if a convex polygon P has n edges, the
> Medial Axis has n faces, n-2 vertices and 2n-3 edges. It's easy to see
> that it has n faces, but for the other things, do you know where I can
> see that ? thank you !

Be aware that the number of "vertices" (branch points)
and number of edges are upper bounds. For example,
a square has n = 4. Its medial axis has 1 branch point,
not 2, and 4 edges, not 5. You also see such bounds
for the "straight skeleton". Medial axes for simple
polygons have bounds of n+r-2 branch points and
2n+r-3 edges (line segments or parabolic arcs), where
r is the number of reflex vertices.

I am aware of the bounds but have never searched for
or thought about a proof. Sorry.

--
Dave Eberly
http://www.geometrictools.com

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medial axis for convex polygons =>Re: medial axis for convex polygons =>Re: medial axis for convex polygons =>Re: medial axis for convex polygons =>Re: medial axis for convex polygons =>Re: medial axis for convex polygons =>

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