From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci)
Newsgroups: sci.math,sci.math.num-analysis
Subject: Re: Radius of circle inscribed in an n-sided polygon
Date: 3 Dec 1998 18:16:13 GMT

In article <746ehi$56o$1@nnrp1.dejanews.com>,
 craig@bonsignore.com writes:
|> Anybody know of an algorithm for finding the radius of the largest circle
|> which can be inscribed in an arbitrary n-sided polygon?  The closest I've
|> come is the Mathematica function Inscribed[polytope] ...  I don't have access
|> to Mathematica, and I need to program the algorithm into some source code I'm
|> working on anyway.  Thanks for any suggestions! (please copy reply to
|> craig@bonsignore.com)
if the polygonal bounded domain is convex and described by
     <x,a_i>+\gamma_i <= 0  i=1,...,n
with <a_i,a_i>=1 (the usual Euclidean scalar product), then the solution is found
by  
       max_{r,x01,x02} f(r,x01,x02) = r
under the constraints 
       <x0+r*a_i,a_i> + \gamma_i <= 0 i=1,...,n
where x)=(x01,x02)'. this is a standard LP-problem in dual form.
hope this helps
peter