Three-dimensional bead models of proteins in solution are routinely determined from one-dimensional Small Angle X-ray Scattering (SAXS) data. The Situs software provides a novel set of visualization and registration procedures to facilitate the localization of protein structures in low-resolution SAXS bead models. The docking algorithm takes advantage of a reduced representation of the input data sets by means of topology-representing neural networks to expedite the rigid-body search. The precision of the docking was tested on ten different simulated bead models: For > 100 beads typically arising in SAXS models, a docking precision on the order of an Angstrom can be achieved. The shape-matching score captured the correct solutions in all ten trial cases and was sufficiently stringent to yield unique matches in seven systems. A size-invariant shape descriptor of `sphericity' is proposed to assess the onset of ambiguity in the matching of globular molecules. The software, a tutorial, and supplementary data are available at URL http://situs.scripps.edu/saxs.