Name

even_angles - generate a list of quasi-uniformly distributed Eulerian angles

Usage

angles = even_angles(delta, [ theta1, theta2, phi1, phi2, method, phiEqpsi, symmetry])

• Note: angles are in SPIDER convention.

Input

delta

angular spacing of Eulerian angles

theta1

lower range of theta (optional, default = 0.0)

theta2

upper range of theta (optional, default = 90.0)

phi1

lower range of phi (optional, default = 0.0)

phi2

upper range of phi (optional, default = 359.99)

method

method of quasi-uniformly distributing Eulerian angles: 'P' Penczek '94 algorithm, theta angle is changing in steps of delta (default) or 'S' Saff hellical method

phiEqpsi

If this string is set to 'Minus' (default) then each of the Eulerian angles psi will be set to -phi. This results in neighboring projections having similar in-plane orientations. Otherwise, ('Zero') psi is set to zero.

symmetry

point group symmetry - the program will return angles for asymmetric unit, possibilities are cn, dn, tet, oct, ico (default c1). Currently, for icosahedral symmetry, the angles correspond to 5-fold symmetry axis placed on z-axis. Use list_syms to see the available symmetries.

Output

angles:: - a list of Eulerian angles stored as:

• angles[0] - first triplet of angles, where
• angles[0][0] is phi,
• angles[0][1] is theta,
• angles[0][2] is psi (set to zero or -phi).
• angles[1] - second triplet of angles

...

• Note - len(angles) will yield number of triplets generated. This number depends on the parameters.

Reference

• Penczek, P., Grassucci, R. A. and Frank, J.: The ribosome at improved resolution: new techniques for merging and orientation refinement in 3D cryo electron microscopy of biological particles. Ultramicroscopy 53:251-270, 1994.
• Saff, E. B., Kuijlaars, A. B. J., 1997. Distributing many points on a sphere. Mathematical Intelligencer 19:5-11, 1997.
• Baldwin, P.R., Penczek, P.A.: The transform class in SPARX and EMAN2. J. Struct. Biol., 2007.

Author / Maintainer

Pawel A. Penczek and P. R. Baldwin

Keywords

category 1

UTILITIES

Files

utilities.py

Maturity

stable

works for most people, has been tested; test cases/examples available.

PRB checked (8/22/06) the Saff algorithm pretty carefully for large solid angles, but not for very small ones.

Bugs

None. It is perfect.