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MathGroup Archive 2006

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Re: Fit rectangle to set of points

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69354] Re: Fit rectangle to set of points
  • From: john2 <john2 at 8889.fsnet.co.uk>
  • Date: Thu, 7 Sep 2006 23:58:55 -0400 (EDT)
  • References: <edom0n$hu2$1@smc.vnet.net>

buttgereit at biomediclab.de wrote:
> Dear Group,
> 
> I have a set of 2D points given for which I would like to find the
> smallest rectangle circumscribing all the points.
> 
> Doing this with a circle instead of a rectangle was easy --- for the
> rectangle I don't see the trick.


I would guess you would first find the convex hull of the points, then 
discard all the interior points.
"Smallest" is undefined.  Smallest Area? smallest perimeter? Smallest 
maximum side?
Rotate the convex hull through theta by an orthogonal rotation and find 
the minimum of the chosen definition of "smallest".

john2


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