Approximate Cr- Blending with Tensor Product Polynomials

An algorithm is presented which generates a 4-sided C r surface. The surface is piecewise polynomial of degree 2r + 1 and interpolates arbitrary C k boundary data within a given tolerance. The number of polynomial pieces depends on the subdivision strategy used. Therefore it can be controlled. The method developed in this paper has the advantage over known solutions that it generates no singularities and generates a non-rational surface versus a rational one.