Path: utzoo!news-server.csri.toronto.edu!cs.utexas.edu!sun-barr!newstop!exodus!deblil.Eng.Sun.COM!stephenj
From: stephenj@deblil.Eng.Sun.COM (Stephen Johnson)
Newsgroups: comp.graphics
Subject: newell plane equation
Keywords: graphics, plane eqation
Message-ID: <9283@exodus.Eng.Sun.COM>
Date: 7 Mar 91 03:50:34 GMT
Sender: news@exodus.Eng.Sun.COM
Lines: 33

I have been using the Newell technique for computing the plane
equation in the form:

Ax + By + Cz + D = 0

and I discovered that the plane defined by the following points is
computing incorrectly:

(2,2,0), (12,2,0), (2,2,3), (12, 2, 3)

From "Procedural Elements for Computer Graphics" bu David F. Rogers,
page 209, the Newell equations are

In the loops: if (i == n) j = 1 else j = i + 1

A = SUM(y[i] - y[j]) * (z[i] + z[j]) for i = 1 to N
B = SUM(z[i] - z[j]) * (x[i] + x[j]) for i = 1 to N
C = SUM(x[i] - x[j]) * (y[i] + y[j]) for i = 1 to N

D = (A * x[0] + B * y[0] + C * z[0])

Unfortunately, with the previously mentioned points:

A = (0 * 0) + (0 * -3) + (0 * 0) + (0 * 3) = 0
B = (0 * 14) + (-3 * 14) + (0 * 14) + (3 * 14) = 0
C = (-10 * 0) + (10 * 0) + (-10 * 0) + (10 * ) = 0

Oops, by inspection we can see that the equation for this plane is
y = -2.  So, what's wrong?  Has someone noticed this before and fixed
it.

Thanks for the Advice,
Stephen Johnson