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
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Bernhard Rupp
001 (925) 209-7429
+43 (676) 571-0536
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