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From: davis@bedlam.esd.sgi.com (Tom Davis)
Newsgroups: comp.sys.sgi
Subject: Re: Area of a Polygon
Summary: Formula for polygonal area
Keywords: area,polygon,arbitrary,overlay
Message-ID: <83906@sgi.sgi.com>
Date: 4 Feb 91 16:01:34 GMT
References: <Feb.3.19.12.39.1991.10354@pilot.njin.net>
Sender: guest@sgi.sgi.com
Distribution: usa
Organization: Silicon Graphics, Inc., Mountain View, CA
Lines: 19



There's a simple formula to find the (signed) area of a polygon.  The
sign will be positive or negative depending on whether the points
describe a counter-clockwise or clockwise polygon, respectively.

Assume the polygon has n points: (x[0], y[0]), (x[1], y[1]), ... (x[n-1], y[n-1]).
For notational convenience, define x[n] = x[0] and y[n] = y[0].  Then the area
is given by:

           n-1
           __
A =       \     (x[i]*(y[i+1] - y[i]) - y[i]*(x[i+1] - x[i]))/2
          /__
          i = 0

I hope this helps.  If you can't remember the formula (I usually can't),
it's just a trivial application of Stokes Theorem, where the surface is
just the x-y plane.