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From: jroth@allvax.enet.dec.com (Jim Roth)
Newsgroups: comp.graphics
Subject: Re: How to determine 4 points in a 3D plane??
Message-ID: <3299@ryn.esg.dec.com>
Date: 24 Oct 90 23:00:21 GMT
Sender: guest@ryn.esg.dec.com
Organization: Digital Equipment Corporation
Lines: 26


In article <31644@netnews.upenn.edu>, sichen@grasp.cis.upenn.edu (the S T R A N G E R ???!!!) writes...

>  I am looking for the algorithm (pseudocode is fine) to determine any 4 given
>abitrary points p(x,y,z) that lie in the same plane...e.g. The algorithm should
>work for the following points ..

>	a)	p1=[1,1,0] p2=[0,2,1] p3=[1,0,2] p4=[3,-1,2]

>	b)	p1=[4, 2, 1] p2=[0, -3, 4] p3=[2, 0, 3] p4=[1, 4, 1]

It's unclear what you want - in both of your cases, the points aren't coplanar.

If you need a predicate that tests if points lie on a plane or not, try
evaluating the determinant

	| x1 y1 z1 1 |
	| x2 y2 z2 1 |
	| x3 y3 z3 1 |
	| x4 y4 z4 1 |

This is zero, or nearly so, if the points lie on the same plane.  In fact,
it is 6 times the volume of a tetrahedron with the given 4 vertices (in
homogenous coordinates.)

- Jim