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From: baer@cs.mcgill.ca (Lawrence BAER)
Newsgroups: comp.graphics
Subject: Plane Equation using Newell's method
Message-ID: <1991Jan3.163452.27481@cs.mcgill.ca>
Date: 3 Jan 91 16:34:52 GMT
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Organization: SOCS, McGill University, Montreal, Canada
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Originator: baer@homer

Given n not quite planar points meant to define a plane in 3-D, Newman and
Sproull (2nd ed., Appendix II, p.499 I believe) define Newell's method for 
calculating the plane equation coefficients (ax +by +cz +d = 0):

   Let the coordinates of the ith point be stored in X[i],Y[i],Z[i]. Then
   a=sum[1..n]{(Y[i]-Y[(i+1)mod n])(Z[i]+Z[(i+1)mod n])}
   b=sum[1..n]{(Z[i]-Z[(i+1)mod n])(X[i]+X[(i+1)mod n])}
   c=sum[1..n]{(X[i]-Z[(i+1)mod n])(Y[i]+Y[(i+1)mod n])}

   and d is obtained by requiring one of the points to lie on the plane.

I am looking for an explanation or proof of reasonableness of Newell's
method i.e. where does it come from.  A reference would be great.

Thanks in advance,

Larry Baer
School of Computer Science
McGill University
e-mail: baer@cs.mcgill.ca