  This paper presents a complete Pascal interpolation scheme for use in the
plane geometry mapping applied in association with numerical methods. The
geometry of a domain element is approximated by a complete Pascal polynomial.
The interpolation procedure is formulated in a natural coordinate system. It
also presents the methodology of constructing shape functions of Pascal type
and establishing a transformation relation between natural and Cartesian
variables. The performance of the presented approach is investigated firstly by
calculating the geometrical properties of an arbitrary quadrilateral
cross-section like area and moments of inertia and comparing the results with
the exact values and with those provided by the standard linear approach and a
serendipity family approach. Secondly, the assessment of the scheme follows
using a straight-sided, compatible quadrilateral finite element for plate
bending of which geometry is approximated by a complete set of second order
with six free parameters. Triangular and quadrilateral shaped plates with
different boundary conditions are computed and compared with well-known results
in the literature. The presented procedure is of general applicability for
elements with curved edges and not limited to straight-sided edges in the
framework of numerical methods.
