;+ ; NAME: ; QTINV ; ; 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: ; Compute inverse of QUATERNION ; ; MAJOR TOPICS: ; Geometry ; ; CALLING SEQUENCE: ; QINV = QTINV(Q) ; ; DESCRIPTION: ; ; The function QTINV computes the inverse of the quaternion Q. The ; inverse of a quaternion is equivalent to a rotation about the same ; axis but the opposite direction. ; ; The inverse is also defined mathematically such that ; ; QTMULT( Q, QTINV(Q) ) ; ; becomes [0, 0, 0, 1], which is the identity 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: ; ; The resulting inverse unit quaternions. For a single input ; quaternion, returns a 4-vector. For N input quaternions, returns ; N quaternions as a 4xN array. ; ; ; KEYWORD PARAMETERS: ; ; NONE ; ; EXAMPLE: ; ; IDL> print, qtcompose([0d,1,0], !dpi/4) ; 0.0000000 0.38268343 0.0000000 0.92387953 ; IDL> print, qtinv(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], then the inverse of the same quaternion. ; ; ; SEE ALSO ; QTANG, QTAXIS, QTCOMPOSE, QTERP, QTEXP, QTFIND, QTINV, QTLOG, ; QTMAT, QTMULT, QTPOW, QTVROT ; ; MODIFICATION HISTORY: ; Written, July 2001, CM ; Documented, Dec 2001, CM ; Usage message, error checking, 15 Mar 2002, CM ; ; \$Id: qtinv.pro,v 1.6 2002/05/09 23:03:27 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 qtinv, q if n_params() EQ 0 then begin info = 1 USAGE: message, 'USAGE:', /info message, 'QNEW = QTINV(Q)', info=info return, 0 endif nq = n_elements(q)/4 if nq LT 1 then goto, USAGE return, [-q(0:2,*), q(3,*)] end