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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