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MathGroup Archive 2004

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Re: Smalest enclosing circle

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50083] Re: Smalest enclosing circle
  • From: koopman at sfu.ca (Ray Koopman)
  • Date: Sat, 14 Aug 2004 01:50:46 -0400 (EDT)
  • References: <cfi8tm$4p6$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Steve Gray <stevebg at adelphia.net> wrote in message 
news:<cfi8tm$4p6$1 at smc.vnet.net>...
> Given n points in the  plane, I want to find the smallest
> enclosing circle. Does anyone have Mathematica code to do this?

In[1]:= xy = Table[Random[],{n=10},{2}]
Out[1]= {{0.638751, 0.871865}, {0.0864434, 0.329484},
         {0.187036, 0.881106}, {0.319298, 0.317072},
         {0.438137, 0.531929}, {0.917911, 0.661329},
         {0.734183, 0.883059}, {0.983413, 0.700878},
         {0.196696, 0.611701}, {0.103151, 0.0506141}}

In[2]:= Clear[z]; FindMinimum[Max[Norm[#-z]&/@xy],
                              {z,Mean[xy],Median[xy]}]
Out[2]= {0.560158, {z -> {0.472102, 0.472102}}}


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