       RE: Point inside a plygon?

• To: mathgroup at smc.vnet.net
• Subject: [mg25398] RE: [mg25239] Point inside a plygon?
• From: torres <torres at morgon.lmt.ens-cachan.fr>
• Date: Fri, 29 Sep 2000 01:06:34 -0400 (EDT)
• Organization: ENS Cachan, France
• References: <8qhmln\$ivh@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```   Hi, we can know if a point is inside a polygon using the following
calculation...  It works for right or left ordered polygons (it changes
the sign of I)

Denoting by P the point and V_i the set of N vertex of the polygon, we
can calculate the following

I = Sum( angle(V_(i+1)-P, V_i-P), i=1..N-1) + angle(V_N-P,V_1-P)

if I != 0 then P is inside the polygon.  If P == 0 the P is outside.

with angle returning a value in ]-Pi,Pi] or ]-180,180].

This is a discrete form of a Gauss integral (from complex calculus)

I hope this helps....

Rafa

Rafael Torres Carot
rtorres at onera.fr	torres at lmt.ens-cachan.fr
Spanish PhD Student en el extranjero

```

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