NetNews Usenet Archive 1992 #19/NN_1992_19.iso/spool/comp/graphics/9433

Internet Message Format | 1992-09-03 | 1.7 KB

Path: sparky!uunet!cs.utexas.edu!ut-emx!ibmchs!auschs!awdprime.austin.ibm.com!linas
From: [e-mail] (Linas Vepstas)
Newsgroups: comp.graphics
Subject: Re: 3d rotation about an arbitrary axis: how?
Message-ID: <[e-mail]>
Date: 3 Sep 92 22:48:41 GMT
References: <[e-mail]> <[e-mail]>
Sender: [e-mail] (USENET News)
Reply-To: [e-mail]
Organization: IBM Graphics Systems
Lines: 26
Originator: [e-mail]


In article <[e-mail]>, [e-mail] (Jian-Dong Liang) writes:
> >I vaguely remember some kind of matrix formula for which the familiar x-,
> >y-, and z-rotation matrices were but special cases.  Does such a
> >formula exist?  Something about "Euler angles"...
>
> A rotation of magnitude theta around an arbitrary axis (x, y, z)
> corresponds to a unit quaternion q=(q0, q1, q2, q3), where
>

A very similar formula can be dervied from the homomorphism of SU(2)
(the Special (determinant=1) Unitary Group of 2x2 matrices) onto O(3)
(the group of orthogonal (i.e. rotation) 3x3 matrices).  My favorite rep
for the su(2) algebra uses the pauli matrices -- si*si == sj*sj ==
sk*sk == 1, much nicer than the quaternions, where you have that ugly
thing i*i == j*j == k*k == -1. Minus one ??? ehhhugh!

Anyway, if you have access to an IBM RS/6000 with AIX 3.2 or higher,
you can find source code for "rot_about_axis" in /usr/lpp/GL/examples.
--- Linas
[e-mail]
--

                                        Linas Vepstas

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