I just have to write out matrices:
CCP4 rotation matrix:
[R11 R12 R13] [x]
[R21 R22 R23] [y] where x y z are orthogonal coordinates relative
to fixed axes...
[R31 R32 R33] [z]
represents a rotation of ccordinates by first gamma then beta then alpha
as Phil says:
[R11 R12 R13]
[R21 R22 R23] == [R_alpha_about Z0] {R_beta_about_Y1] [
R_gamma_about_Z2]
[R31 R32 R33]
If you consider axes Xo Y0 Z0 :
[X0 Y0 Zo] [R11 R12 R13]
[R21 R22 R23]
[R31 R32 R33]
the matrix rotatates the axes by first alpha, then beta then gamma.
Many programs dont make it clear what they are using the rotation to
describe..
Bernhard Rupp wrote:
> 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
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