;+ ; NAME: ; QTNORMALIZE ; ; 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: ; Normalize a quaternion (unit quaternion and/or sign conventions) ; ; MAJOR TOPICS: ; Geometry ; ; CALLING SEQUENCE: ; QNEW = QTNORMALIZE(QOLD, UNITIZE=1, POS3=1) ; ; DESCRIPTION: ; ; The function QTNORMALIZE performs normalization operations upon a ; quaternion. The two operations are: UNITIZE and POS3. ; ; The UNITIZE operation occurs if /UNITIZE is set (this is the ; default). If set, then the returned quaternion is a unit ; quaternion. Non-unit input quaternions will be adjusted so that ; the components have the same ratios, but unit magnitude. ; ; The POS3 operation occurs if /POS3 is set (this is the default). ; If set, then the returned quaternion is ensured to be positive in ; its third component. In other words, QNEW[3] GE 0. Since the ; same quaternion can have two different representations, differing ; only in the signs of the components, the POS3 operation ensures ; that one sign convention is used for all quaternions. This is ; useful for comparing quaternion component values. ; ; By default /UNITIZE and /POS3 are both set. In order to disable ; them, set UNITIZE=0 or POS3=0 explicitly. ; ; 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 normalized quaternions. For single inputs, returns ; a 4-vector. For N inputs, returns N quaternions as a 4xN array. ; ; ; KEYWORD PARAMETERS: ; ; UNITIZE - if set, then perform UNITIZE operation as described ; above. By default, UNITIZE=1. ; ; POS3 - if set, then perform POS3 operation as described above. By ; default, POS3=1. ; ; ; EXAMPLE: ; ; ; SEE ALSO ; QTANG, QTAXIS, QTCOMPOSE, QTERP, QTEXP, QTFIND, QTINV, QTLOG, ; QTMAT, QTMULT, QTPOW, QTVROT ; ; MODIFICATION HISTORY: ; Written, 2012-08-01, CM ; ; $Id: qtnormalize.pro,v 1.2 2012/10/02 12:29:33 cmarkwar Exp $ ; ;- ; Copyright (C) 2012, 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 qtnormalize, q0, unitize=unitize0, pos3=pos30 if n_elements(unitize0) EQ 0 then unitize = 1 $ else unitize = keyword_set(unitize0) if n_elements(pos30) EQ 0 then pos3 = 1 $ else pos3 = keyword_set(pos30) q = q0 ;; Standardize so that the final element is always non-negative if keyword_set(pos3) then begin wh = where(q(3,*) LT 0, ct) if ct GT 0 then q(*,wh) = -q(*,wh) endif if NOT keyword_set(unitize) then return, q qnorm = sqrt(total(q^2,1)) nu = n_elements(qnorm) if nu EQ 1 then return, q/qnorm(0) return, q / rebin(reform(qnorm,1,nu),4,nu) end