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From: turk@Apple.COM (Ken "Turk" Turkowski)
Newsgroups: comp.graphics
Subject: Re: Euler's rotation
Keywords: rotation, quaternion, Euler
Message-ID: <9715@goofy.Apple.COM>
Date: 13 Aug 90 08:30:51 GMT
References: <580@dg.dg.com>
Organization: Advanced Technology Graphics, Apple Computer, Cupertino, CA, USA
Lines: 27

In article <580@dg.dg.com> mpogue@dg.dg.com writes:
>
>   I have read in several papers, books, etc, that Euler 
>proved a famous theorem in 1752 (or whenever), showing that
>for any two orientations of the same object, that there
>was a single rotation about a single axis that would 
>transform one rotation to the other.
>
>   Although the result is mentioned, the actual formula/
>algorithm for calculating the axis of rotation and rotation
>angle is never given!
>
>   Does anybody have this formula handy?

See my paper "The Use of Coordinate Transformations in Computer
Graphics" in Academic Press's new Graphics Gems book.  One of the
examples computes the 3x3 matrix for this transformation.

If you really need the axis and angle, you might be able to do this
by computing the eigenvectors of the matrix.  I believe that Ned
Greene has a paper in Graphics Gems on how to extract rotations
from a matrix.
-- 
Ken Turkowski @ Apple Computer, Inc., Cupertino, CA
Internet: turk@apple.com
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