;+ ; NAME: ; QTCOMPOSE ; ; 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: ; Convert a rotation angle and axis into quaternion ; ; MAJOR TOPICS: ; Geometry ; ; CALLING SEQUENCE: ; Q = QTCOMPOSE(VAXIS, PHI) ; ; DESCRIPTION: ; ; The function QTCOMPOSE accepts a unit vector rotation axis VAXIS ; and a rotation angle PHI, and returns the corresponding quaternion. ; ; The user must take care to pass the same number of axes as rotation ; angles. ; ; 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: ; ; VAXIS - array of one or more unit vectors specifying the rotation ; axes. For a single rotation, VAXIS should be a 3-vector. ; For N vectors, VAXIS should be a 3xN array. ; ; PHI - one or more rotation angles, in radians. For a single ; rotation, PHI should be a scalar. For N rotations, PHI ; should be an N-vector. ; ; RETURNS: ; ; For a single rotation, returns a quaternion as a 4-vector. For N ; rotations, returns a 4xN vector of quaternions. ; ; ; KEYWORD PARAMETERS: ; ; NONE ; ; EXAMPLE: ; ; IDL> print, qtcompose([0d,1,0], !dpi/4) ; 0.0000000 0.38268343 0.0000000 0.92387953 ; ; Prints 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 ; Allow output to be DOUBLE, 27 Jan 2002, CM ; Allow vector vs scalar arguments, 28 Jan 2002, CM ; Usage message, error checking, 15 Mar 2002, CM ; ; \$Id: qtcompose.pro,v 1.11 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 qtcompose, axis, phi if n_params() EQ 0 then begin info = 1 USAGE: message, 'USAGE:', /info message, 'Q = QTCOMPOSE(AXIS, PHI)', info=1 return, 0 endif nph = n_elements(phi) nv = n_elements(axis)/3 if nph LT 1 OR nv LT 1 then goto, USAGE nq = nv > nph q = make_array(value=axis(0)*phi(0)*0., 4,nq) sph = sin(phi/2) & cph = cos(phi/2) if nph EQ 1 AND nv EQ 1 then return, [ axis(0:2) * sph(0), cph(0) ] if nph GT 1 AND nv EQ 1 then begin ;; Single axis, multiple rotation angles q(0,*) = axis(0)*sph q(1,*) = axis(1)*sph q(2,*) = axis(2)*sph q(3,*) = cph endif else if nph EQ 1 AND nv GT 1 then begin ;; Multiple axis, single rotation q(0:2,*) = axis*sph(0) q(3,*) = cph(0) endif else if nph EQ nv then begin ;; Multiple axes, multiple rotations q(0:2,*) = axis*rebin(reform(temporary(sph),1,nq),3,nq) q(3,*) = temporary(cph) endif else begin message, 'ERROR: number of axes and angles do not match' endelse return, q end