Acoustic Doppler current profiler (ADCP) measurements from moving vessels have recently been used to obtain detailed observations of the spatial patterns of tidal flows, as well as patterns of vorticity and dynamical terms. Developments in radial basis function (RBF) interpolation theory are demonstrated to significantly improve the quality of the tidal velocity field extracted from the measurements using thin plate splines. These include placing centers at data locations, enforcing "side conditions" on the solution, and using higher-order splines. For tidal flows with a scale less than a few kilometers the differentiability of RBFs can be exploited to fit the stream function directly to the measurements. This ensures the observed tidal velocity field satisfies mass continuity. Enforcing mass continuity is demonstrated to significantly improve the ability of the splines to interpolate across wide gaps between vessel tracks. Extraordinarily detailed ADCP measurements of the tidal stream function within Bluff Harbour, New Zealand, reveal the stagnation streamline that separates a 200 m wide flood tidal jet from an associated 400 m diameter eddy. The stagnation streamline clearly shows that the eddy gains its fluid and vorticity from inshore of the jet's vorticity maximum. The eddy forms at 04:45 hours before high tide, grows in spiral fashion, and becomes isolated from the jet 02:30 hours before high tide; after which its vorticity rapidly decays.