  This article focuses on gradient vector fields of unit Euclidean norm in
$\mathbb{R}^N$ . The stream functions associated to such vector fields solve
the eikonal equation and the prototype is given by the distance function to a
closed set. We introduce a kinetic formulation that characterizes stream
functions whose level sets are either spheres or hyperplanes in dimension $N
\geq 3$. Our main result proves that the kinetic formulation is a selection
principle for the vortex vector field whose stream function is the distance
function to a point.
