Path: utzoo!utgpu!news-server.csri.toronto.edu!rutgers!mcnc!thorin!proline!banks
From: banks@proline.cs.unc.edu (David Banks)
Newsgroups: comp.graphics
Subject: Re: Euler's rotation
Keywords: rotation, quaternion, Euler
Message-ID: <14982@thorin.cs.unc.edu>
Date: 4 Jul 90 06:18:19 GMT
References: <580@dg.dg.com>
Sender: news@thorin.cs.unc.edu
Reply-To: banks@proline.cs.unc.edu (David Banks)
Organization: University Of North Carolina, Chapel Hill
Lines: 18

mpogue@dg.dg.com writes:
>
>  ... Euler proved ... that for any two orientations ... 
>  a single rotation ... would transform one rotation to the other.
>
>  ... Does anybody have this formula handy?


Mike Pique's paper, "Semantics of Interactive Rotations"
(Proceedings, 1986 Chapel Hill Workshop on Interactive 3D Graphics, 
p. 268) offers a formula which, given a rotation matrix R, 
computes a direction vector V and a rotation angle theta:

cos(theta) = (R11 + R22 + R33 - 1)/2

Vx = (R32 - R23)/(2 sin(theta) )
Vy = (R13 - R31)/(2 sin(theta) )
Vz = (R21 - R12)/(2 sin(theta) )