Algorithm for Area of a closed polygon.

Demian M. Nave dnave at
Wed Nov 12 21:23:16 PST 2003

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

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


 Demian M. Nave              | dnave at        | Ph 412 268-4574
 Pgh. Supercomputing Center  |   | Fx 412 268-8200
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 Pittsburgh, PA 15213        |  interrupt." - Kanin

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