The theory behind a new, three-dimensional analysis technique for the measurement of time-integral, perturbed angular correlation (IPAC) functions is presented. The new technique is described in relation to existing methods and in terms of its specific application to a large, Ge-detector array. The effective application of the new technique is demonstrated with results from an experiment where the g factors of excited states in 252Cf, secondary fission fragments were determined. A 252Cf source, sandwiched between two iron foils and placed in a saturated magnetic field at the centre of the Gammasphere detector array, was used to make IPAC measurements of prompt γ rays in order to deduce Larmor precession angles of stopped fragments in iron. The g factor of the Iπ = 2+ state in 104Mo was thus measured to be g = +0.248(22). This new measurement shows a factor-of-5 improvement to the precision which has previously been attained in more conventional experiments.