There are several further references at the end of the Web page that Miguel mentions. A comprehensive book on the subject is S. L. Altmann, "Rotations, Quaternions and Double Groups", Oxford University Press. Altmann explains why the RxRyRz or yaw-pitch-roll form is unsatisfactory for arbitrary rotations. (It's fine for small rotations, and natural for controlling aeroplanes.)
There are numerous pitfalls for the unwary in this area. For Euler angles, the rotations are about z,y,z (Whitaker convention) or z,x,z (Goldstein convention). An Euler rotation (phi,theta,psi) may be achieved by rotating first through phi about z, then through theta about the _rotated_ y (or x), and then through psi about the _rotated_ z. Alternatively, and with exactly the same result, one may rotate through psi about z, then through theta about the _original_ y axis, then through phi about the _original_ z axis. For many purposes, the angle-axis formulation, which is closely related to the quaternion approach, is the simplest and most convenient. The matrix describing a rotation through psi about an axis described by the unit vector (nx,ny,nz) is 1-2*(ny^2+nz^2)*s^2 -nz*S+2*nx*ny*s^2 ny*S+2*nz*nx*s^2 nz*S+2nx*ny*s^2 1-2*(nz^2+nx^2)*s^2 -nx*S+2+ny*nz*s^2 -ny*S+2nz*nx*s^2 nx*S+2*ny*nz*s^2 1-2*(nx^2+ny^2)*s^2 where S=sin psi and s=sin(psi/2). Anthony At 07:19 on 5 October, Miguel wrote: > Egon wrote: > > > >> I suggest that Jmol should use one of these standard, well-documented, > >> approaches rather than introducing something different. > > > > Can you send us some pointers to such documentation? > > Egon, > > I found the following reference by using goole for 'euler angle rotation' > > http://mathworld.wolfram.com/EulerAngles.html > > other googling for 'euler angle rotation x convention' generated other > references. > > > Miguel > > -- Anthony Stone http://www-stone.ch.cam.ac.uk/ University Chemical Laboratory, Email: [EMAIL PROTECTED] Lensfield Road, Phone: +44 1223 336375 Cambridge CB2 1EW Fax: +44 1223 336362 ------------------------------------------------------- This SF.net email is sponsored by: IT Product Guide on ITManagersJournal Use IT products in your business? Tell us what you think of them. Give us Your Opinions, Get Free ThinkGeek Gift Certificates! Click to find out more http://productguide.itmanagersjournal.com/guidepromo.tmpl _______________________________________________ Jmol-developers mailing list [EMAIL PROTECTED] https://lists.sourceforge.net/lists/listinfo/jmol-developers
