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From: root@fstc-chville.army.mil (Operator)
Newsgroups: comp.graphics
Subject: Re: Problem: Best plane fitting 3D points ?
Message-ID: <1990Dec14.125326.28339@fstc-chville.army.mil>
Date: 14 Dec 90 12:53:26 GMT
References: <5110.276634ff@cc.curtin.edu.au>
Organization: US Army Foreign Science & Technology Center
Lines: 25

Kessells_SR@cc.curtin.edu.au writes:
>Problem :
>	Given a set of 3D points what is the best plane of fit to them.

Mike...

From Ballard and Brown page 476 or
Foley and VanDam page 512:

given three points (x,y,z), form the equation
 _             _   _ _     _ _
| x1  y1  z1  1 | | A |   | 0 |
| x2  y2  z2  1 | | B |   | 0 |
| x3  y3  z3  1 | | C | = | 0 |
| 0   0   0   1 | | D |   | 1 |
 _             _   _ _     _ _

Invert the first matrix, solve for [ABCD].

The equation of the plane is Ax+By+Cz+D=0.

See the references for cases when the large matrix doesn't invert.

Brian
boyter@fstc-chville.army.mil