Path: utzoo!utgpu!news-server.csri.toronto.edu!rutgers!apple!netcom!rodent
From: rodent@netcom.UUCP (Ben Discoe)
Newsgroups: comp.graphics
Subject: how do i rotate around an arbitrary vector in 3D?
Message-ID: <18733@netcom.UUCP>
Date: 14 Dec 90 00:44:23 GMT
Distribution: usa
Organization: Netcom- The Bay Area's Public Access Unix System {408 241-9760 guest}
Lines: 24

i need to rotate a large set of points around an arbitrary axis,
specified as a vector.  i know how to rotate around any base axis
(since it's just 2D rotation).  If i had Mathematica around, i'd
just multiply the five rotation matrices involved, but i left
that behind when i left academia.

i figure you take the vector, find it's spherical coordinates theta phi,
then:	rotate -theta around z
	rotate -phi around y
	(original vector now lies along z^)
	rotate desired amount around z
	(then reverse the first two steps)
	rotate phi around y
	rotate theta around z

If these transformations simplify into a nice simple matrix, great!
The above assumes right-handed coords.  If someone knows the final
matrix, please specify which handedness you used.

In case anyone is interested, it's for a cartographic application.

Thanks!
---------
Ben Discoe, frustrated visionary at large.