JiscMail Logo
Email discussion lists for the UK Education and Research communities

Help for CCP4BB Archives


CCP4BB Archives

CCP4BB Archives


CCP4BB@JISCMAIL.AC.UK


View:

Message:

[

First

|

Previous

|

Next

|

Last

]

By Topic:

[

First

|

Previous

|

Next

|

Last

]

By Author:

[

First

|

Previous

|

Next

|

Last

]

Font:

Proportional Font

LISTSERV Archives

LISTSERV Archives

CCP4BB Home

CCP4BB Home

CCP4BB  August 2007

CCP4BB August 2007

Options

Subscribe or Unsubscribe

Subscribe or Unsubscribe

Log In

Log In

Get Password

Get Password

Subject:

Re: CCP4 rotation convention

From:

Ian Tickle <[log in to unmask]>

Reply-To:

Ian Tickle <[log in to unmask]>

Date:

Mon, 13 Aug 2007 19:10:46 +0100

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (117 lines)

 
Hi folks

I hate to say this but I think everyone here has got it wrong to some
degree (including myself - and I hereby retract my previous e-mail and
issue the correction below!).  If you don't believe me then read &
digest Jorge Navaza's article "Rotation functions" in Int. Tab. Vol. F
(sect 13.2, p. 269), particularly sections 13.2.2 and Appendix
A13.2.1.1.

Phil's article in Acta D57 1355-1359 (2001), i.e. the 2001 S/W
proceedings, states:

"... 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'(a).Ry'(b).Rz(g)"

Compare this with Jorge's equation 13.2.2.3 which he explicitly states
applies to rotations about fixed axes, not rotated axes (but using my
notation):

	R = Rz(a).Ry(b).Rz(g)

i.e. first by gamma about z, then by beta about the *fixed* y axis, then
by alpha about the *fixed* z axis.

The same formula cannot apply to both rotations about fixed and rotated
axes at the same time!

Looking at Jorge's equation 13.2.2.1 it's plain that the correct version
involving rotated axes is (again substituting my own notation which
should be obvious):

	R = Rz'(g).Ry'(b).Rz(a)

i.e. the correct statement is that the rotation is generated by rotating
first by alpha about z, then by beta about the rotated y axis (y'), then
by gamma about the rotated z axis (z').

Of course it may well be that Phil's equation is based on an older
version of Jorge's analysis perhaps using a different convention in his
Acta Cryst. (1994), A50, 157-163 paper, but unfortunately I don't have
online access to AC(A) to check it out, maybe someone who has access
could do so.

In fact it's quite obvious looking at the individual matrices Rz(a) &
Ry(b) at the bottom of page 1358 in Phil's paper that they must apply to
fixed not rotating axes, because if say the Ry(b) matrix were for
rotation about the rotated y axis, it would have to be a function of
gamma: applying the Rz(g) matrix as given in the paper first to the
y-axis vector (0,1,0) gives the rotated y-axis vector
(-sin(g),cos(g),0).  Similarly if the Rz(a) matrix represented rotation
about the rotated z axis it would have to be a function of both beta &
gamma and plainly it's not.

This all goes to show that a) even the experts sometimes get it wrong
particularly where matrix algebra is concerned, and b) you should avoid
the concept of rotating about rotated axes like the plague!

-- Ian


> -----Original Message-----
> From: [log in to unmask] 
> [mailto:[log in to unmask]] On Behalf Of Bernhard Rupp
> Sent: 12 August 2007 20:37
> To: [log in to unmask]
> Subject: CCP4 rotation convention
> 
> 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
> 001 (925) 209-7429
> +43 (676) 571-0536
> [log in to unmask]
> [log in to unmask] 
> http://www.ruppweb.org/                 
> -----------------------------------------------------------------
> People can be divided in three classes:
> The few who make things happen
> The many who watch things happen
> And the overwhelming majority 
> who have no idea what is happening.
> -----------------------------------------------------------------
> 
> 


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. If you have received this communication in error, please notify Astex Therapeutics Ltd by emailing [log in to unmask] and destroy all copies of the message and any attached documents. 
Astex Therapeutics Ltd monitors, controls and protects all its messaging traffic in compliance with its corporate email policy. The Company accepts no liability or responsibility for any onward transmission or use of emails and attachments having left the Astex Therapeutics domain.  Unless expressly stated, opinions in this message are those of the individual sender and not of Astex Therapeutics Ltd. The recipient should check this email and any attachments for the presence of computer viruses. Astex Therapeutics Ltd accepts no liability for damage caused by any virus transmitted by this email. E-mail is susceptible to data corruption, interception, unauthorized amendment, and tampering, Astex Therapeutics Ltd only send and receive e-mails on the basis that the Company is not liable for any such alteration or any consequences thereof.
Astex Therapeutics Ltd., Registered in England at 436 Cambridge Science Park, Cambridge CB4 0QA under number 3751674

Top of Message | Previous Page | Permalink

JISCMail Tools


RSS Feeds and Sharing


Advanced Options


Archives

April 2014
March 2014
February 2014
January 2014
December 2013
November 2013
October 2013
September 2013
August 2013
July 2013
June 2013
May 2013
April 2013
March 2013
February 2013
January 2013
December 2012
November 2012
October 2012
September 2012
August 2012
July 2012
June 2012
May 2012
April 2012
March 2012
February 2012
January 2012
December 2011
November 2011
October 2011
September 2011
August 2011
July 2011
June 2011
May 2011
April 2011
March 2011
February 2011
January 2011
December 2010
November 2010
October 2010
September 2010
August 2010
July 2010
June 2010
May 2010
April 2010
March 2010
February 2010
January 2010
December 2009
November 2009
October 2009
September 2009
August 2009
July 2009
June 2009
May 2009
April 2009
March 2009
February 2009
January 2009
December 2008
November 2008
October 2008
September 2008
August 2008
July 2008
June 2008
May 2008
April 2008
March 2008
February 2008
January 2008
December 2007
November 2007
October 2007
September 2007
August 2007
July 2007
June 2007
May 2007
April 2007
March 2007
February 2007
January 2007


WWW.JISCMAIL.AC.UK

Secured by F-Secure Anti-Virus CataList Email List Search Powered by the LISTSERV Email List Manager