Local squaring functions for non-spherical templates

The local squaring functions representing the likelihood that a particular atom type occupies a particular location in the unit cell are generalized so that the likelihood that a multiatom fragment occurs at a given position can be modeled at less than atomic resolution. The orientation space of the fragment is parameterized according to the special unitary 2-group in order to facilitate both interpretation and interpolation. The representation theory of this group is related to the harmonic analysis for functions of rotation. As an example of computer-aided model construction, local squaring functions for several protein backbone fragments are applied to a 2.0 A model electron density. The resulting functions are sufficient to reconstruct the atomic structure from the probable template placements.