Hi Bernhard
Yes you are right, these descriptions cannot be talking about the same
overall rotation, assuming the angles are defined in the same way of
course (i.e. assuming that alpha & gamma have not been switched round in
the J.Appl.Cryst. paper you refer to). The 'Crowther' convention (used
consistently by all CCP4 progs) is as you say:
gamma about z, beta about *rotated* y (call it y'), alpha about
*rotated* z (z'):
R = Rz'(a).Ry'(b).Rz(g)
whereas clearly
alpha about z, beta about *rotated* y (presumably?), gamma about
*rotated* z is:
R = Rz'(g).Ry'(b).Rz(a)
which is not the same at all!
Personally I find it very confusing & counter-intuitive having to think
about bodies which are rotating around axes and at the same time the
axes are themselves rotating w.r.t. to the laboratory frame (OK if
you're thinking about things moving around inside a tumbling space
shuttle maybe ...).
Fortunately there's an simple equivalence with rotations about *fixed*
axes:
alpha about z, beta about *fixed* y, gamma about *fixed* z, which also
gives the Crowther convention result:
R = Rz(a).Ry(b).Rz(g)
Possibly this is the source of confusion in the paper.
-- Ian
> -----Original Message-----
> From: [EMAIL PROTECTED]
> [mailto:[EMAIL PROTECTED] On Behalf Of Bernhard Rupp
> Sent: 12 August 2007 20:37
> To: CCP4BB@JISCMAIL.AC.UK
> 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
> [EMAIL PROTECTED]
> [EMAIL PROTECTED]
> 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
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>
>
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