From NURBS to NURPS geometries

Quadratic Powell–Sabin splines and their rational extension, the so-called NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a B-spline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic NURBS representation into a NURPS representation, suitable for the analysis.