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Subject: Re: medial axis for convex polygons



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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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