;+ ; NAME: ; QTAXIS ; ; AUTHOR: ; Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770 ; craigm@lheamail.gsfc.nasa.gov ; UPDATED VERSIONs can be found on my WEB PAGE: ; http://cow.physics.wisc.edu/~craigm/idl/idl.html ; ; PURPOSE: ; Find rotation axis of unit quaternion ; ; MAJOR TOPICS: ; Geometry ; ; CALLING SEQUENCE: ; VAXIS = QTAXIS(Q) ; ; DESCRIPTION: ; ; The function QTAXIS accepts a unit quaternion Q and returns the ; rotation axis VAXIS as a unit vector. ; ; Use QTAXIS and QTANG to extract the properties of an existing ; quaternion. Use QTCOMPOSE to combine a rotation axis and angle ; into a new quaternion. ; ; Conventions for storing quaternions vary in the literature and from ; library to library. This library uses the convention that the ; first three components of each quaternion are the 3-vector axis of ; rotation, and the 4th component is the rotation angle. Expressed ; in formulae, a single quaternion is given by: ; ; Q(0:2) = [VX, VY, VZ]*SIN(PHI/2) ; Q(3) = COS(PHI/2) ; ; where PHI is the rotation angle, and VAXIS = [VX, VY, VZ] is the ; rotation eigen axis expressed as a unit vector. This library ; accepts quaternions of both signs, but by preference returns ; quaternions with a positive 4th component. ; ; INPUTS: ; ; Q - array of one or more unit quaternions. For a single ; quaternion, Q should be a 4-vector. For N quaternions, Q ; should be a 4xN array. ; ; RETURNS: ; ; For a single quaternion, returns the rotation axis unit vector in a ; 3-vector. For N quaternions, returns a 3xN-vector of rotation ; axis unit vectors. ; ; KEYWORD PARAMETERS: ; ; NONE ; ; EXAMPLE: ; ; IDL> print, qaxis(qtcompose([0d,1,0], !dpi/4)) ; 0.0000000 1.0000000 0.0000000 ; ; Prints the axis part of the quaternion composed of a rotation of ; !dpi/4 radians around the axis [0,1,0] ; ; ; SEE ALSO ; QTANG, QTAXIS, QTCOMPOSE, QTERP, QTEXP, QTFIND, QTINV, QTLOG, ; QTMAT, QTMULT, QTPOW, QTVROT ; ; MODIFICATION HISTORY: ; Written, July 2001, CM ; Documented, Dec 2001, CM ; Correct error in normalization, 26 Jan 2002, CM ; Usage message, error checking, 15 Mar 2002, CM ; ; \$Id: qtaxis.pro,v 1.7 2008/12/14 20:00:31 craigm Exp \$ ; ;- ; Copyright (C) 2001, 2002, Craig Markwardt ; This software is provided as is without any warranty whatsoever. ; Permission to use, copy, modify, and distribute modified or ; unmodified copies is granted, provided this copyright and disclaimer ; are included unchanged. ;- function qtaxis, q if n_params() EQ 0 then begin info = 1 USAGE: message, 'USAGE:', /info message, 'AXIS = QTAXIS(Q)', info=info return, 0 endif nq = n_elements(q)/4 if nq LT 1 then goto, USAGE v = q(0:2,*) sinth = sqrt(total(v^2,1)) wh = where(sinth NE 0, ct) if ct GT 0 then v(*,wh) = v(*,wh) / rebin(reform(sinth(wh),1,ct),3,ct) return, v end