Hybrid non-uniform recursive subdivision with improved convergence rates

This paper introduces a new non-uniform subdivision surface representation, called hybrid non-uniform subdivision surface (for short, HNUSS). The subdivision scheme is constructed through two steps. The first step inserts a set of edges and converts a valence-n extraordinary point into a valence-n face. The second step combines both primal and dual subdivision schemes to define the subdivision rules. The developed subdivision scheme generalizes bi-cubic NURBS to arbitrary topology and is proved to be G(1)-continuous for any valence extraordinary points and any non-negative knot intervals. The HNUSS limit surface has comparable shape quality as non-uniform subdivision via eigen-polyhedron (Li et al., 2016) and has better shape quality than all the other subdivision schemes. In addition, numerical experiments show that HNUSS based isogeometric analysis yields improved convergence rates compared to any existing non-uniform subdivision schemes. (C) 2019 Elsevier B.V. All rights reserved.