Bernhard Sorry, correction, this statement in my last posting is not correct:
"... 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." The component matrices in the case described are not the same as for the correct rotated axis case because for say the 2nd rotation about beta the matrix would be a function of alpha & beta in the correct case, but of beta and gamma in the incorrect case, so the component matrices can't possibly all be the same - but it will still give you a completely different and incorrect resultant matrix, so my point is still valid. You see the kind of confusion that occurs as soon as you start thinking in terms of rotated axes! Otherwise I stand by everything I said! -- Ian > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of Ian Tickle > Sent: 15 August 2007 10:47 > To: [EMAIL PROTECTED] > Cc: CCP4BB@jiscmail.ac.uk > Subject: RE: [ccp4bb] CCP4 rotation convention > > 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 > > > > > > > > > > > > Disclaimer > > This communication is confidential and may contain privileged > > information > > intended solely for the named addressee(s). It may not be > > used or disclosed > > except for the purpose for which it has been sent. If you > are not the > > intended recipient you must not review, use, disclose, copy, > > distribute or > > take any action in reliance upon it. 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