A new ray-based approach for converting multicomponent normal moveout uncorrected offset domain prestack seismic data into angles is presented. From any two-way zero-offset time sample and a given angle of incidence, the exact ray and a few neighboring rays that contribute to the given angle of incidence are traced through the medium to their corresponding source and receiver locations to compute their raypath lengths, traveltimes, and offsets. A polynomial then is fitted locally between these computed offsets and their corresponding traveltimes. Next the traveltimes for the actual offsets on data that lie within these traced rays are computed from this local polynomial fit, and their corresponding time samples are partially stacked and moved to their two-way zero-offset times. Repetition of this procedure for all zero-offset time samples and for all desired angles produces an angle gather. The procedure allows computation of both primary (P-P) and mode-converted (P-SV) angle gathers. Also, by calculating the exact raypath length, an accurate geometric spreading compensation can be computed and applied to these gathers. By using the methodology for a horizontally stratified transversely isotopic medium with a vertical symmetry axis (a VTI medium), it is possible to extract a much more accurate angle-domain response from the ray-based method than is possible from a traditional NMO-based method. Accuracy out to large angles for both primary and mode-converted reflection suggests that this ray-based transform potentially could be used in a multicomponent prestack waveform inversion scheme.