Date: Wed, 18 Jun 2003 13:00:54 +0200
From: Manuel Martin <m m a r t i n @ c e y d . e s>
To: efg2@efg2.com
Subject: Polygon area accuracy

Hi
I read then comments from Frank van het Veld about managing
formulas for polygon area and centroid

It's true that if you do A*B where A,B are big (say 1.0E7)
the result will lose accuracy because of size of numbers in
any computer.

Same is said for any other formula, such as SQR(A*B-B*C)

When working with geometry, a simple method can be applied
to improve (not solve) accuracy:

   work with relative coordinates

So, calling:
    X = A - A,  Y = B - A,  Z = C - A
(this is, substract a medium/origin Xo value to all Xi values
and a medium/origin Yo value to all Yi values)
we get:
    X*Y instead of A*B

Area is _not_changed.
Centroid coordinates must be changed to real, not relative.
So:
  Xc (world) = Xc (relative) + Xo
  Yc (world) = Yc (relative) + Yo

And that's all.

Hope this help
Regards,
Manuel