Wachspress type rational complex planar splines of degree (3,1)

We study the existence, uniqueness and approximation properties of rational complex planar spline interpolants of order (3, 1). We also find sufficient conditions for such interpolants to be quasiregular and quasiconformal. Examples are given. This work was carried out with the aid of MACSYMA, a large symbolic manipulation program developed at the MIT Laboratory for Computer Science and supported from 1975 to 1983 by the National Aeronautics and Space Administration under grant NSG 1323, by the Office of Naval Research under grant N00014-77C-0641, by the U.S. Department of Energy under grant ET-78-C-024687, and by the U.S. Air Force under grant F49620-79-C-020, and since 1982 by Symbolics, Inc. of Burlington, MA.