Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!wuarchive!cs.utexas.edu!rice!uw-beaver!ubc-cs!alberta!calgary!ctycal!ingoldsb
From: ingoldsb@ctycal.UUCP (Terry Ingoldsby)
Newsgroups: comp.graphics
Subject: Area of Polygons (with Arcs)
Keywords: Thanks to all, here's the method we used
Message-ID: <498@ctycal.UUCP>
Date: 19 Oct 89 15:00:10 GMT
Organization: The City of Calgary, Ab
Lines: 22

Thanks to all who posted/mailed suggestions.  They were most
helpful, and I can see where each technique proposed would be
useful in a given circumstance.

The method we are using is Newell's formula (suggested by many)
to calculate the area of the straight sided polygon.  To handle
the arcs, we use Ken Shiriff's suggestion of determining
whether to add or subtract a chorded arc area
based on the sign of the vector cross product.  Once the chorded
areas are added or subtracted, the absolute value of the total is
the correct area in all cases.

By the way, the reason we got into this is because some 3rd party
software we purchased was getting the wrong answer.  Not only
does the technique outlined above give the right answer, it is
20 times faster than the 3rd party stuff.  Moral of the story:
if you want it done right, do it yourself!

-- 
  Terry Ingoldsby                       ctycal!ingoldsb@calgary.UUCP
  Land Information Systems                           or
  The City of Calgary         ...{alberta,ubc-cs,utai}!calgary!ctycal!ingoldsb