Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!iuvax!watmath!watcgl!ksbooth
From: ksbooth@watcgl.waterloo.edu (Kelly Booth)
Newsgroups: comp.graphics
Subject: Re: Need an algorithm to calculate area of polygons
Keywords: Polygon, algorithm
Message-ID: <11780@watcgl.waterloo.edu>
Date: 5 Oct 89 18:56:55 GMT
References: <484@ctycal.UUCP> <619@cditi.UUCP> <6059@tekgvs.LABS.TEK.COM>
Reply-To: ksbooth@watcgl.waterloo.edu (Kelly Booth)
Organization: U. of Waterloo, Ontario
Lines: 11

In article <6059@tekgvs.LABS.TEK.COM> jackg@tekirl.LABS.TEK.COM (Jack Gjovaag) writes:
>
>A = abs(sum (i=1 to n) (x(i+1)-x(i))*(y(i+1)+y(i))/2)
>

This is Newell's formula (with the abs and the /2 added).  The general form
works in 3-D and computes three terms which are the components of a vector
whose magnitude (abs again) is the area.

The formula does have meaning if the edges cross in the sense that it
subtracts out areas.