In this paper we propose an efficient algorithm to perform a polynomial approximation of the vector field derived from the usual distance mapping method. The main ingredients consist of minimizing a quadratic functional and transforming this problem in an appropriate setting for implementation. With this approach, we reduce the problem of obtaining an approximating polynomial vector field to the resolution of a not expansive linear algebraic system. By this procedure, we obtain an analytical shape representation that relies only on some coefficients. Fidelity and numerical efficiency of our approach are presented on illustrative examples.