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MathGroup Archive 2005

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Re: point in convex hull

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55477] Re: point in convex hull
  • From: "Carl K. Woll" <carlw at u.washington.edu>
  • Date: Fri, 25 Mar 2005 05:48:18 -0500 (EST)
  • Organization: University of Washington
  • References: <d1tvc0$rli$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"steve fisk" <fisk at bowdoin.edu> wrote in message 
news:d1tvc0$rli$1 at smc.vnet.net...
> If pts is a set of points, and w is a point I can use ConvexHull[pts] to
> find the convex hull of the points in pts. Is there a function to
> determine if w lies in the convex hull?
>

Steve,

Why don't you find out if the ConvexHull of w added to the old ConvexHull 
includes the point w. Something like

Needs["DiscreteMath`"]

pts=Table[{Random[],Random[]},{1000}];
ch=pts[[ConvexHull[pts]]];

inside[w_, ch_] := ! MemberQ[ConvexHull[Join[ch, {w}]], Length[ch] + 1]

Carl Woll




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