**comp.graphics.algorithms**

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

news:1146579646.744634.15610@j73g2000cwa.googlegroups.com...

> I am a bit confused on the basics properties of the medial axis of

> convex polygons : why the arcs of the medial axis of a CONVEX polygon

> are ONLY straight lines ? why there are no parabolics arcs ? I'm agree

> with this result (!) but I don't manage to prove it ...

Parabolic arcs are generated by reflex vertices. Convex

polygons have only convex vertices. The arc generated

by a reflex vertex and an edge is thought of as the set

of points equidistant from a point (the vertex) and a

line (containing the edge). This is the classic definition

for a parabola.

--

Dave Eberly

http://www.geometrictools.com

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