       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=(#[]-x0)^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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