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MathGroup Archive 2001

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Re: Point order

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30362] Re: [mg30347] Point order
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 12 Aug 2001 02:29:51 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I assume that you what you man is this. You are given an ordered set of 
points (in two dimensions) which describe a simple polygon, that is one 
without self intersections (otherwise the question does not make sense). 
You want to know whether your ordering corresponds to moving clockwise 
or counter-clockwise along the polygon.

One way to do this (which may not be the fastest) is to make use of the 
function ConvexHull of the ComputationslGeometry package. Given a set 
of  coordinates of points in 2 dimensions it returns a sublist of those 
points which generate the convex hull of the original set, arranged in 
counterclockwise order. So all we need to check is if these points 
appear in the original list in the same order. The following function 
should do this:

<< DiscreteMath`ComputationalGeometry`

clockwiseQ[l_List] :=
   Module[{ch = l[[ConvexHull[l]]]},
     Signature[
         Flatten[Position[Select[l, MemberQ[ch, #] &], #] & /@ ch]] == -1]

for example:

poly = {{4.4, 14}, {6.7, 15.25}, {6.9, 12.8}, {9.5, 14.9}, {13.2,
         11.9}, {10.3, 12.3}, {6.8, 9.5}, {13.3, 7.7}, {0.6, 1.1}, {1.3,
         2.4}, {2.45, 4.7}};

In[4]:=
clockwiseQ[poly]

Out[4]=
False

In[5]:=
clockwiseQ[Reverse[poly]]

Out[5]=
True

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/

On Saturday, August 11, 2001, at 04:40  PM, Rafael Sanchez wrote:

> Hello all,
> If I draw a polygone of n sides, how do I know if the points are drawn
> in clockwise order or not?
> Thanks
> Rafael
>
>
>



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