Hi Eleanor
We seem to agree completely, i.e. the relevant statement from my second
(corrected) e-mail in this thread (the one you replied to) was:
R = Rz(a).Ry(b).Rz(g)
i.e. first by gamma about z, then by beta about the *fixed* y axis, then
by alpha about the *fixed* z axis, which seems to be precisely what
you're now saying - previously you seemed to be saying that what Phil
said in the AC 2001 S/W proceedings was correct?. The issue is that in
Phil's article he refers to *rotated* ('new') axes not *fixed* ('old')
axes. His equation is perfectly correct (it's just inconsistent with
his description), so of course you won't find any inconsistency by
comparing the equation with the PDBSET code.
So if the literature agrees exactly with what you are saying, I'm a bit
puzzled as to why I would be foolish to believe it? If you read the
IT(F) article, Jorge presents formal proofs so it seems extremely
unlikely that he got it wrong (and it would be very unlike Jorge!), or
indeed that the convention that he's using is in any way different from
the CCP4 one.
Best wishes
-- Ian
> -----Original Message-----
> From: Eleanor Dodson [mailto:[log in to unmask]]
> Sent: 14 August 2007 10:01
> To: Ian Tickle
> Subject: Re: [ccp4bb] CCP4 rotation convention
>
> I think you are foolish to believe the literature!
> The only information I trust is the rotation matrix to be applied to
> coordinates, which is listed by program PDBSET when you apply a Amore
> solution.
>
> This certainly takes Amore output alpha beta gamma, and
> calculates a matrix
> Rot_alpha Rot_beta Rot_gamma to pre-multiply a set of
> coordinates
> and shift them relative to fixed axes.
> (This is an older version of Amore but I doubt if Jorge changed
> conventions..)
> This assumes anti-clockwise rotation - ie for +Alpha moving a
> point on
> the X0 axis towards the Y0 axis etc
>
> Eleanor
>
>
> Ian Tickle wrote:
> >
> > Hi folks
> >
> > I hate to say this but I think everyone here has got it
> wrong to some
> > degree (including myself - and I hereby retract my previous
> e-mail and
> > issue the correction below!). If you don't believe me then read &
> > digest Jorge Navaza's article "Rotation functions" in Int.
> Tab. Vol. F
> > (sect 13.2, p. 269), particularly sections 13.2.2 and Appendix
> > A13.2.1.1.
> >
> > Phil's article in Acta D57 1355-1359 (2001), i.e. the 2001 S/W
> > proceedings, states:
> >
> > "... the convention used in AMoRe (Navaza, 1994) and other
> CCP4 programs
> > (Collaborative Computational Project, Number 4, 1994) is to
> rotate by
> > gamma around z, then by beta around the new y, then by
> alpha around the
> > new z again, R = Rz'(a).Ry'(b).Rz(g)"
> >
> > Compare this with Jorge's equation 13.2.2.3 which he
> explicitly states
> > applies to rotations about fixed axes, not rotated axes
> (but using my
> > notation):
> >
> > R = Rz(a).Ry(b).Rz(g)
> >
> > i.e. first by gamma about z, then by beta about the *fixed*
> y axis, then
> > by alpha about the *fixed* z axis.
> >
> > The same formula cannot apply to both rotations about fixed
> and rotated
> > axes at the same time!
> >
> > Looking at Jorge's equation 13.2.2.1 it's plain that the
> correct version
> > involving rotated axes is (again substituting my own notation which
> > should be obvious):
> >
> > R = Rz'(g).Ry'(b).Rz(a)
> >
> > i.e. the correct statement is that the rotation is
> generated by rotating
> > first by alpha about z, then by beta about the rotated y
> axis (y'), then
> > by gamma about the rotated z axis (z').
> >
> > Of course it may well be that Phil's equation is based on an older
> > version of Jorge's analysis perhaps using a different
> convention in his
> > Acta Cryst. (1994), A50, 157-163 paper, but unfortunately I
> don't have
> > online access to AC(A) to check it out, maybe someone who has access
> > could do so.
> >
> > In fact it's quite obvious looking at the individual
> matrices Rz(a) &
> > Ry(b) at the bottom of page 1358 in Phil's paper that they
> must apply to
> > fixed not rotating axes, because if say the Ry(b) matrix were for
> > rotation about the rotated y axis, it would have to be a function of
> > gamma: applying the Rz(g) matrix as given in the paper first to the
> > y-axis vector (0,1,0) gives the rotated y-axis vector
> > (-sin(g),cos(g),0). Similarly if the Rz(a) matrix
> represented rotation
> > about the rotated z axis it would have to be a function of
> both beta &
> > gamma and plainly it's not.
> >
> > This all goes to show that a) even the experts sometimes
> get it wrong
> > particularly where matrix algebra is concerned, and b) you
> should avoid
> > the concept of rotating about rotated axes like the plague!
> >
> > -- Ian
> >
> >
> >
> >> -----Original Message-----
> >> From: [log in to unmask]
> >> [mailto:[log in to unmask]] On Behalf Of Bernhard Rupp
> >> Sent: 12 August 2007 20:37
> >> To: [log in to unmask]
> >> Subject: CCP4 rotation convention
> >>
> >> Dear programmers -
> >>
> >> Phil Evans writes in acta D57 1355 (2001) on p 1358 section 5.2:
> >>
> >> "....the convention used in AMoRe (Navaza, 1994)
> >> and other CCP4 programs (Collaborative Computational
> >> Project, Number 4, 1994) is to rotate by gamma around z, then by >
>
> >>
> > beta
> >
> >> around the new y, then by alpha around the new z again,
> >> R = Rz(al)Ry(be)Rz(ga)"
> >>
> >> This seems correct, as the first rotation is applied first to
> >> vector x, then the second to the new one, etc, thus
> >> x' = (Rz(al)(Ry(be)(Rz(ga)x)))
> >>
> >> In J.Appl.Cryst. 30 402-410 (1977) in the convrot description,
> >> Sascha Uzhumtsev lists in table one for (Navaza 1994):
> >>
> >> alpha about Z, beta about Y and gamma about new Z
> >> and gives the *same* resulting rotation
> >> Rz(al)Ry(be)Rz(ga)
> >>
> >> This seems to be a contradiction I cannot resolve?
> >>
> >> Thx, br
> >> -----------------------------------------------------------------
> >> Bernhard Rupp
> >> 001 (925) 209-7429
> >> +43 (676) 571-0536
> >> [log in to unmask]
> >> [log in to unmask]
> >> http://www.ruppweb.org/
> >> -----------------------------------------------------------------
> >> People can be divided in three classes:
> >> The few who make things happen
> >> The many who watch things happen
> >> And the overwhelming majority
> >> who have no idea what is happening.
> >> -----------------------------------------------------------------
> >>
> >>
> >>
> >
> >
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