On Wachspress quadrilateral patches

Wachspress initiated the study of rational basis functions for finite eleme nt construction over quadrilaterals and more general polygonal and curved e lements. Later Apprato et al. (1979) and Gout (1979, 1985) studied the inte rpolatory and convergence properties of lower degree rational finite elemen ts 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 ap plications to surface fitting problems. It is indeed remarkable to note tha t these functions possess properties similar to tensor product Bernstein po lynomials and hence could be effectively used to generate quadrilateral pat ches.