The Transform Class in SPARX and EMAN2.

We describe the Transform Class in SPARX/EMAN2 that is designed to handle rigid body motions of two- and three-dimensional data. We describe relationships between Eulerian angles conventions used in different electron microscopy software packages, as well as give examples of the simple scripts that execute conversions of Eulerian angles between these packages and handle other related tasks. The Transform Class is also responsible for generating point-group symmetry operations as well as generating quasi-evenly distributed points on the sphere (which is used in creating reference projections for structure refinement procedures in single particle reconstruction). We discuss how this is carried out internally in the code, and how symmetry operations are accessed through the SPARX interactive interface. We present a comprehensive description of symmetry operations for all point-group symmetries, as implemented in the class. Finally, we provide solutions to a number of typical problems associated with rotation operations-alignment of markers for dual-axis tomography, delineations of asymmetric subunits, quasi-uniform distribution of projection directions and such, and provide examples how these problems are solved using operations in the Transform Class.