In this study the problem of modeling a family of curves is addressed. The need of such modeling appears frequently in many aspects of image processing where many linear structures keep spatial relationships during their evolution. We come up with a modeling tool well suited to the spatial modeling of a family of curves, and which can be very useful for motion tracking and curve evolution as well. The family of curves is represented as the line paths (orbits) of a `` spline vector field '', i.e. a vector field interpolating data using a framework similar to the theory of spline curves. The model is exemplified with oceanic satellite data. Its usefullness for curve evolution modeling is also presented.