Algorithm for Area of a closed polygon.
Demian M. Nave
dnave at psc.edu
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
with.
Hope this helps. Send another note to the mailing list if not. :-)
Cheers,
Demian
--
Demian M. Nave | dnave at psc.edu | Ph 412 268-4574
Pgh. Supercomputing Center | www.psc.edu/~dnave | Fx 412 268-8200
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Pittsburgh, PA 15213 | interrupt." - Kanin
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