A model developed primarily for the analysis of drifter data is discussed. The model is based on a parametric representation of the drifter velocity in terms of Monge potentials, two of which are constants following the motion of the fluid. In the application presented here, one of the potentials is taken as the frequency of rotation about a ring by a parcel. A more restricted intepretations of the velocity gradient invariant for horizontal flow is also discussed. The other potential is taken as the streamline of a parcel that is locally approximated as a conic section. For the restricted interpretation, solutions to the model equations are critically dependent on the relative sizes of the squares of the vertical vorticity and the total deformation rate. This model differs from drifter cluster models in that each drifter provides independent estimates of the vorticity and deformation rates. Application is made to path data from three drifters that were seeded in a warm core ring in the Gulf of Mexico in November 1980. The model provided estimates of the ring translation and swirl velocities along with the ring geometry. The analysis showed that the ring was persistently elliptical with the major axis aligned in the east-west direction. A satellite infrared photo on January 21, 1981, confirmed this orientation.