On Wachspress quadrilateral patches Original Research Article

Wachspress initiated the study of rational basis functions for finite element construction over quadrilaterals and more general polygonal and curved elements. Later Apprato et al. (1979) and Gout (1979, 1985) studied the interpolatory and convergence properties of lower degree rational finite elements and their applications in solving second order boundary value problems. In the present paper we introduce higher degree Wachspress functions by an iterative technique and study their properties from the point of view of applications to surface fitting problems. It is indeed remarkable to note that these functions possess properties similar to tensor product Bernstein polynomials and hence could be effectively used to generate quadrilateral patches.