Hi Bernhard
The CCP4/PDBSET/ALMN/AMORE (but NOT X-PLOR ...) convention is:
gamma about z, beta about *fixed* y, alpha about *fixed* z
**** OR ****
alpha about z, beta about *rotated* y, gamma about *rotated* z.
... but NOT any other combination of these!!!
In the equation, the component matrices are written down in order from
right to left, pre-multiplying the co-ordinate vectors.
Although the component matrices are in general completely different in
the fixed & rotated descriptions, the resultant product matrix is
identical, so they both refer to the *same* convention. So as far as
the convention is concerned it is of no consequence whatsoever which way
you describe it or think about it, as long as you don't confuse these 2
alternatives by having first say gamma, then beta, then alpha about
rotated axes: the component matrices are the same as for the correct
rotated axis case, but because they are multiplied in reverse order it
will give you a completely different and incorrect resultant matrix.
My issue with thinking about or working with rotated axes is just that:
it's well nigh impossible to think about them or work with them! Not
only that, it's a pain just to write them down, e.g. for the matrix
describing the component rotation gamma about the rotated z axis, the
direction of the rotated z axis is a function of both alpha & beta, so
the component gamma rotation matrix contains trig functions of all 3
angles! I defy you to write out the complete equation for the rotated
axis case showing all 27 matrix elements (in fact I can't think of a
more pointless exercise!). Contrast that with the fixed axis case where
the component matrices are all functions of a single angle and I can
work them out in 2 secs.
I trust I have convinced you!
Cheers
-- Ian
> -----Original Message-----
> From: Bernhard Rupp [mailto:[EMAIL PROTECTED]
> Sent: 15 August 2007 07:39
> To: Ian Tickle
> Subject: RE: [ccp4bb] CCP4 rotation convention
>
> Ian, my question is actually getting simpler in the process,
> and all I seek is authoritative answer to:
>
> a) What is the "CCP4 convention", if such a convention exists,
> b) and what convention does Amore use.
>
> If it is fixed axes, fine. If it is different
> depending on the program, also ok. Per Navaza ITCF, we can
> all consistently convert the settings - this is not the problem.
>
> (the math is the only thing I can follow. For me this is
> an eigenvalue problem (albeit with a few nasty singularities)
> so I need no conventions to solve the matrix for the Euler axis
> and the principal Euler angle - regardless how the DMC was set up).
>
> I am not sure about the illegality of terms 'new' to indicate
> rotating coordinate system. I think it is legit. As you
> indicate, the math is clear, the descriptions widely and
> wildly divergent.
>
> Thx, BR
>
> -----Original Message-----
> From: Ian Tickle [mailto:[EMAIL PROTECTED]
> Sent: Tuesday, August 14, 2007 7:12 AM
> To: [EMAIL PROTECTED]
> Cc: CCP4BB@JISCMAIL.AC.UK
> Subject: RE: [ccp4bb] CCP4 rotation convention
>
>
> Bernhard -
>
> In case you're still trying to follow the convoluted arguments in my
> previous long answer, here's the short answer (for your summary!):
>
> Replace the word 'new' (twice) in this sentence in Phil's AC
> 2001 article
> with the word 'fixed':
>
> "... rotate by gamma around z, then by beta around the new y,
> then by alpha
> around the new z again.".
>
> Then everything is fine & we all agree!
>
> Your problems with Y1, Z2 etc in Eleanor's description are
> resolved because
> the axes never move. In fact it's not clear to me why we
> need ZO, Y1 & Z2
> at all because Z2 = Z0 = Z and Y1 = Y. So the most concise
> statement is the
> one in my previous email:
>
> R = Rz(a).Ry(b).Rz(g)
>
> ... and please don't mention rotated (or 'new' etc) axes in
> this context
> ever again!
>
> -- Ian
>
> > -----Original Message-----
> > From: [EMAIL PROTECTED]
> > [mailto:[EMAIL PROTECTED] On Behalf Of Bernhard Rupp
> > Sent: 13 August 2007 23:07
> > To: [EMAIL PROTECTED]
> > Cc: CCP4BB@JISCMAIL.AC.UK
> > Subject: RE: [ccp4bb] CCP4 rotation convention
> >
> > Hmmm....this explanation seems to add another discrepancy - I think
> > the connection to the physical process is lost - I cannot
> rotate first
> > about something I don't have yet.
> >
> > Let me try to interpret what E wrote:
> >
> > "I just have to write out matrices:
> > CCP4 rotation matrix:
> > [R11 R12 R13] [x]
> > [R21 R22 R23] [y]
> > [R31 R32 R33] [z]
> > where x y z are orthogonal coordinates relative to fixed axes"
> >
> > I suppose from following this means rotating coordinate
> system, i.e.
> > Euler convention.
> >
> > "represents a rotation of ccordinates by first gamma then beta then
> > alpha as Phil says:"
> >
> > [R11 R12 R13]
> > [R21 R22 R23]
> > [R31 R32 R33]
> > == [R_alpha_about Z0] {R_beta_about_Y1] [ R_gamma_about_Z2]
> >
> > in br alternate notation R = RZ0(al)RY1(be)RZ2(ga)
> >
> > but this means: apply the first physical rotation about z2 (I don't
> > have z2 yet!), then about Y1 and then alpha about zo and
> this is NOT
> > what Phil says:
> >
> > Phil says:
> > "rotate by gamma around z (i.e. zo), then by beta around
> the new y
> > (i.e.
> > y1) ,
> > then by alpha around the new z (i.e. z") again, R =
> > Rz(al)Ry(be)Rz(ga)"
> > i.e., in e/br notation R = Rz"(al)Ry(be)Rzo(ga)
> >
> > So I think "phil" is correct as far as the physical rotations go -
> > first about the old Z axis which I know, then Y1, then
> about new Z2.
> > The sequence of angles in R fits the Euler convention. That is
> > consistent.
> >
> > I'll get back to the roll-pitch-yaw convention about fixed
> X0,Y0, and
> > Z0, their conversion, and the Navaza issue once it is
> sorted out what
> > the interpretation of R in Euler convention truly is - Eleanor
> > R(ZYZ")or Phil R(Z"YZ).
> >
> > I'll tally all in a summary
> >
> > B 'tin man' R
> >
> >
>
>
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