  This paper applies a complete parametric set for approximating the geometry
of a quadrilateral element. The approximation basis used is a complete Pascal
polynomial of second order with six free parameters. The interpolation
procedure is a natural interpolation scheme. The six free parameters are
determined using the natural coordinates of the four nodal points (vertices) of
the quadrilateral element and the two intersections points of the lines
crossing every two opposite edges (poles). The presented scheme recovers the
well known Lagrangian interpolation scheme, when every two opposite edges are
parallel. A third order Pascal interpolation scheme is also presented. The four
midpoints of the four edges in addition to the six nodal point from the second
order case are used as significant nodal points. It is expected to reflect the
geometry properties better since the shape functions are complete
