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Re: point in convex hull

  • To: mathgroup at
  • Subject: [mg55471] Re: point in convex hull
  • From: Peter Pein <petsie at>
  • Date: Fri, 25 Mar 2005 05:48:13 -0500 (EST)
  • References: <d1tvc0$rli$>
  • Sender: owner-wri-mathgroup at

steve fisk wrote:
> 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?
If you integrate 1/(x-w) along the boundary of the convex hull you get
2Pi*I if w lies inside, 0 else.

Off[NIntegrate::ploss, General::spell1];
inConvexHull[pt_, set_, tol_:10^(-3)] := Module[{path, x},
 path = Prepend[
   Complex @@@ set[[(Append[#1, First[#1]] & )[ConvexHull[set]]]], x];
 Abs[NIntegrate[1/(x - Complex @@ pt), Evaluate[path]] - 2*Pi*I] < tol]

data = Table[Random[], {10}, {2}];

inConvexHull[{1/2, 1/2}, data]

inConvexHull[{1/2, -1/2}, data]

Peter Pein

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