**comp.graphics.algorithms**

## Subject: **Re: medial axis for convex polygons**

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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