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We are developing an electronically-collimated gamma-ray detector for safety and security applications; localization is achieved using Compton-scatter coincidence detection. Electronic collimation allows the device to operate without physical collimation, providing high sensitivity while also allowing directional information to be determined. We report on the directional algorithm implemented for this system. Two approaches to direction reconstruction were evaluated; the first is filtered backprojection on a sphere using stereographic projection to implement filtering (Gunter, NSS-MIC2005). The second technique also backprojects events onto the sphere, then determines source location by the intersection of circumscribed rectangles for the backprojected cones. Algorithm performance was evaluated using randomly generated ideal Compton-scatter events from point sources for our detector geometry, as well as data from concurrent Monte Carlo simulations of a prototype system. Direction angles are calculated within 5% accuracy for source positions up to 45deg off-axis for the filtering approach and ~30deg for the circumscription approach. Error in calculated direction angles depends on the arbitrary diameter of the sphere; optimally, the sphere should intersect the source. The circumscription technique converges to an estimate of direction angles in ~50 events; the filtering approach requires ~1000 events. The two methods complement each other in speed and field-of-view.