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# listochkin/gist:1200393 Created Sep 7, 2011

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Algorithm for Area of a closed polygon.

# Re: Algorithm for Area of a closed polygon.

``````To: Ted Hill <thill@tomotherapy.com>
Subject: Re: Algorithm for Area of a closed polygon.
From: "Demian M. Nave" <dnave@psc.edu>
Date: Wed, 12 Nov 2003 21:23:16 -0500 (EST)
Cc: <compgeom-discuss@research.bell-labs.com>
References: <1E2E66102E75104D8C740340EBCD98671BC279@tomoex.tomotherapy.com>
``````

Hi Ted,

I want to be able to calculate the area inside a closed many-sided polygon.

As long as your polygon has no self-crossings or internal holes, this algorithm is probably the simplest. It will return twice the signed area of your polygon:

``````Let 'vertices' be an array of N pairs (x,y), indexed from 0
Let 'area' = 0.0
for i = 0 to N-1, do
Let j = (i+1) mod N
Let area = area + vertices[i].x * vertices[j].y
Let area = area - vertices[i].y * vertices[j].x
end for
Return 'area'
``````

If the vertices of your polygon are specified in counter-clockwise order (i.e. by the right-hand rule), then the area will be positive. Otherwise, the area will be negative, assuming the polygon has non-zero area to begin with.

Hope this helps. Send another note to the mailing list if not. :-)

Cheers, Demian

``````Demian M. Nave              | dnave@psc.edu        | Ph 412 268-4574
Pgh. Supercomputing Center  | www.psc.edu/~dnave   | Fx 412 268-8200-
4400 Fifth Avenue           | "When your work speaks for itself, don't
Pittsburgh, PA 15213        |  interrupt." - Kanin
``````

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