# 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.