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From: "Marcin " <mb1234@gazeta.pl>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Rotate 3D object to align with x-y plane
Date: Thu, 20 May 2010 21:21:04 +0000 (UTC)
Organization: Bournemouth University
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> You must face facts, Marcin!  What you are asking for, you simply cannot accomplish without more information to go on.  You state that you have a set of points which "describe" a three-dimensional object, but how is anyone to tell how these points were originally oriented in space when the object was, as you say, "horizontal"?  Even if the points are known to have been originally lying in a horizontal plane, (which would mean that the points are also currently colinear) that still isn't enough information to determine what rotation has been performed.  Infinitely many are still possible as I have already pointed out to you at some length.
> 
> Roger Stafford

That's the catch. Nobody knows that, so it must be some kind of guess. I think that PCA might do in this case. Anyway, I still don't know how to plot it though. The data is an output of a 3D scan, so I should be able to use mesh/surf or similar function.