We describe a technique used to locate and classify critical points in 2-D flow fields at the solar photosphere obtained from the evolution of the line-of-sight magnetic field in a region close to the magnetic polarity inversion line of a fully emerged active region. We apply this technique to locate a particular kind of critical point associated to vortex flows, which are considered important, since they can twist and interweave the foot points of flux tubes and generate magnetic reconnection.