Re: [ccp4bb] difference between polar angle and eulerian angle

On 1 April 2014 00:12, Edward A. Berry wrote: > Yes of course, but if you start from the left you are not (at least not > obviously) > "first rotating the coordinates by alpha about z"; you are rotating the > columns > of the second matrix. And in the second multiplication you are not > rotating

Re: [ccp4bb] difference between polar angle and eulerian angle

On 1 April 2014 00:12, Edward A. Berry wrote: > I need to work on something else now, but when i get time I will go > through Ian's derivation and see how it is in fact tractable. > I should point out that it's not my derivation. This proof was given to me by Tilman Shirmer. For the original

Re: [ccp4bb] difference between polar angle and eulerian angle

__ De : CCP4 bulletin board [CCP4BB@JISCMAIL.AC.UK] de la part de Edward A. Berry [ber...@upstate.edu] Envoyé : mardi 1 avril 2014 01:12 À : CCP4BB@JISCMAIL.AC.UK Objet : Re: [ccp4bb] difference between polar angle and eulerian angle Dear Tim, Ian, Tim Gruene wrote: > [...] > Actually it does

Re: [ccp4bb] difference between polar angle and eulerian angle

Dear Tim, Ian, Tim Gruene wrote: [...] Actually it does not depend - the rotation matrices are a representation of the group SO(3) and hence the matrix multiplication is associative. It does not matter whether you start left or right or in the middle - that is not the same as not being commutativ

Re: [ccp4bb] difference between polar angle and eulerian angle

Dear Ed, On 03/31/2014 08:55 PM, Edward A. Berry wrote: [...] > > Looking at the math, it depends whether you multiply from right to left > or left to right > > >x' = Rz(a) Ry(b) Rz(g) x > or >x' = Rz(a) (Ry(b) (Rz(g) x)) > [...] Actually it does not depend - the rotation matrices are

Re: [ccp4bb] difference between polar angle and eulerian angle

Ed, > I think we are saying the same thing here. When I say the axes are kept fixed, I mean they are the screen axes. When you say "new axis" you do not mean that the axis has been rotated, but that it passes through the molecule differently. Or maybe not . . . No I mean exactly that. What I'm s

Re: [ccp4bb] difference between polar angle and eulerian angle

I think I can agree with all of that. Thanks for helping me work this out! Ian Tickle wrote: We come up with the same conclusions with our different ways of thinking about it: for one, deriving the concatenated simple operators to represent a general rotation, and the commutativit

Re: [ccp4bb] difference between polar angle and eulerian angle

Ed, OK, I need to think about this more when I have time, but at this point > I think it is a semantic difference- For me the first and last rotation are > about the same Z axis because as you say they are both around the screen Z > axis > and both operators look like cos,sin, 0, -sin, cos, 0, 0

Re: [ccp4bb] difference between polar angle and eulerian angle

Ian Tickle wrote: Ed, the screen z axis is not the same axis in the molecule for the first and last rotations, except in the special case beta = 0 or 180. The fallacy in your argument is that you're implicitly assuming that rotations commute, whereas of course they don't i.e. Rz.Ry.Rz is not

Re: [ccp4bb] difference between polar angle and eulerian angle

The main reason for using Eulerian (or polar) angles is speed (not for nothing is Crowther's implementation called the "Fast Rotation Function"). Expression of the rotation in terms of Eulerian or polar angles makes it possible to express the Patterson functions in terms of orthogonal spherical har

Re: [ccp4bb] difference between polar angle and eulerian angle

Ed, the screen z axis is not the same axis in the molecule for the first and last rotations, except in the special case beta = 0 or 180. The fallacy in your argument is that you're implicitly assuming that rotations commute, whereas of course they don't i.e. Rz.Ry.Rz is not the same as Rz.Rz.Ry un

Re: [ccp4bb] difference between polar angle and eulerian angle

>>> Edward Berry 03/29/14 5:22 PM >>> Thanks, Ian! I agree it may have to do with being used to computer graphics, where x,y,z are fixed and the coordinates rotate. But it still doesn't make sense: -My mistake- in computer graphics x,y,z rotates with the atomic coordinates relative to screen coor

Re: [ccp4bb] difference between polar angle and eulerian angle

There are good arguiments for using quaternions rather than Eulerian (or other) angles anyway, this is very well explained in the paper "*Quaternions *in *molecular modeling*

Re: [ccp4bb] difference between polar angle and eulerian angle

Thanks, Ian! I agree it may have to do with being used to computer graphics, where x,y,z are fixed and the coordinates rotate. But it still doesn't make sense: If the axes rotate along with the molecule, in the catenated operators of the polar angles, after the first two operators the z axis would

Re: [ccp4bb] difference between polar angle and eulerian angle

Hi Edward As far as Eulerian rotations go, in the 'Crowther' description the 2nd rotation can occur either about the new (rotated) Y axis or about the old (unrotated) Y axis, and similarly for the 3rd rotation about the new or old Z. Obviously the same thing applies to polar angles since they can

Re: [ccp4bb] difference between polar angle and eulerian angle

According to the html-side the 'visualisation' includes two back-rotations in addition to what you copied here, so there is at least one difference to the visualisation of the Eulerian angles. Right- it says: "This can also be visualised as rotation ϕ about Z, rotation ω about the new Y, rotati

Re: [ccp4bb] difference between polar angle and eulerian angle

-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 Dear Qixu Cai, maybe the confusion is due to that your quote seems incomplete. According to the html-side the 'visualisation' includes two back-rotations in addition to what you copied here, so there is at least one difference to the visualisation of

Re: [ccp4bb] difference between polar angle and eulerian angle

Message- From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Phil Evans Sent: Donnerstag, 27. März 2014 11:11 To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] difference between polar angle and eulerian angle The polar angles ?, ? define the direction of an axis about which a

Re: [ccp4bb] difference between polar angle and eulerian angle

This is a helpful introductory paper on the topic: http://journals.iucr.org/d/issues/2001/10/00/ba5006/ba5006.pdf -- David On 27 March 2014 06:11, Qixu Cai wrote: > Dear all, > > From the definition of CCP4 (http://www.ccp4.ac.uk/html/ > rotationmatrices.html), the polar angle (ϕ, ω, κ) can be

Re: [ccp4bb] difference between polar angle and eulerian angle

The polar angles ϕ, ω define the direction of an axis about which a rotation by angle κ occurs, i.e. a single rotation around a defined axis. This is different from Eulerian angles which define 3 successive rotations around principal axes On 27 Mar 2014, at 06:11, Qixu Cai wrote: > Dear all, >

[ccp4bb] difference between polar angle and eulerian angle

Dear all, From the definition of CCP4 (http://www.ccp4.ac.uk/html/rotationmatrices.html), the polar angle (ϕ, ω, κ) can be visualised as rotation ϕ about Z, rotation ω about the new Y, rotation κ about the new Z. It seems the same as the ZXZ convention of eulerian angle definition. What's the