The biomedical application of maxillo-facial morphometric analysis can be cited as an important application of the present methodology. The idea is now being utilized for general three-dimensional cases. For the unconventional concave quadrilateral finite element, the proposed formulation made it possible to generate all shape functions starting from the one which pertains to the concave node.

To our knowledge there is neither any published work nor any hint that the shape functions for elements can be generated from a single one by satisfying (desirable) interpolation conditions. Perhaps no investigator other than Wachspress could conceive the shape functions in the x-y frame. In fact, except for Taig's isoparametric formulation in the computational domain of a unit square, there exists no other original idea, to our knowledge, of generating shape functions. For the quadrilateral example presented here, it has been shown that if the first shape function is generated by isoparametric formulation, then the three remaining functions can be constructed according to the proposed scheme, automatically satisfying the patch test.