C2 free-form surfaces of degree (3,5) Original Research Article

This paper introduces new techniques for modeling low degree, smooth free-form surfaces of unrestricted patch layout. In particular, surfaces that are C2 after reparametrization can be built from tensor-product Bézier or spline patches of degree (3,3) and (3,d+2); at extraordinary points, these surfaces have the flexibility of C2 splines of total degree d>0. The particular choice, d=3, yields more than n+5 vector-valued degree of freedom where n patches join. The techniques generalize to Gk constructions of free-form surfaces of degree (k+1,d+2k−2).