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MathGroup Archive 2004

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Re: Smalest enclosing circle

  • To: mathgroup at smc.vnet.net
  • Subject: [mg50082] Re: Smalest enclosing circle
  • From: kzhang at flashmail.com (Kezhao Zhang)
  • Date: Sat, 14 Aug 2004 01:50:42 -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?
> 	I will be grateful for any tips.
> 
> Steve Gray

Here is one way to do it:
Suppose the equation for the circle is (x-x0)^2+(y-y0)^2==r^2. We want
to minimize r.

Generate some points:
In[]:=points=Partition[Table[Random[NormalDistribution[0,1]],{200}],2];

Constraints that all points are enclosed by the circle:
In[]:= const=(#[[1]]-x0)^2+(#[[2]]-y0)^2<= r^2&/@points;

Numerical minimization with constraints:
In[]:=NMinimize[ Join[{r, r>0},const], {x0,y0, {r,5,10}}]

Please note that it's better to provide some starting values for r 
otherwise NMinimize will complains that a starting value that doesn't satisfy
the constraint is used.

K. Z.


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