Rational S-patches with application to exact sphere representation

A class of multisided Bézier patches, the so-called S-patches, unify triangular and tensor product Bézier patches and at the same time provide their generalization, namely an S-patch can be defined over any convex n-sided polygon, n¿2. It is obtained by first embedding the polygon into the simplex of dimension n-1 and then defining the multivariate Bézier patch of degree d over the simplex. In this talk we shall focus on rational S-patches, i.e. S-patches with rational weights that do not all equal to 1. First, we present their definition, basic properties and connection to Bézier triangles and tensor product patches. Then, we focus on how rational S-patches can be utilised for exact sphere representations. In order to obtain the final results we present a general method that utilizes the stereographic projection.