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From: wjh@wayback.UUCP (Bill Hery)
Newsgroups: sci.math
Subject: Re: point inside a triangle
Message-ID: <991@wayback.UUCP>
Date: Fri, 24-Oct-86 17:41:00 EDT
Article-I.D.: wayback.991
Posted: Fri Oct 24 17:41:00 1986
Date-Received: Sat, 25-Oct-86 05:53:52 EDT
References: <8900031@osiris>
Organization: AT&T Bell Labs, Whippany, NJ
Lines: 13

> 		Can we generalise to determine whether (p1,p2) is
> 		inside a polygon? Use the VECTOR approach, ONLY, as
> 		it is clearly the most superior, elegant and non-
> 		paleozoic approach to the problem. I will not even
> 		scan any other precambrian attempts.
> 

For a convex polygon with vertices at x(i) (i=1,n, x(i) vectors), the
set of points inside the polygon is the convex hull of the these points.
The convex hull of a finite set of points is precisely those points which
can be represented in the form x=sum{x(i)*a(i)}, with sum{a(i)}=1.

Bill Hery