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Interpolants within Convex Polygons: Wachspress' Shape Functions

During the 1970s, Wachspress developed shape functions for convex n-gons as polynomials of n-2 degree divided by the one of n-3. Originated from projective geometry these interpolants are linear on the sides and can exactly reproduce arbitrary linear fields. Here an alternative derivation is presented. The wide availability of computer algebra programs makes these high accuracy elements accessible. Associated C++ codes are particularly suited for large scale finite element analysis employed in the aerospace industry.