An extended tuned subdivision scheme with optimal convergence for isogeometric analysis

This paper presents an extended tuned subdivision scheme for quadrilateral meshes that recovers optimal convergence rates in isogeometric analysis while preserving high-quality limit surfaces. Convergence rates can be improved for subdivision surfaces through proper mask tuning with a lower subdominant eigenvalue λ. However, such a tuning might affect the quality of limit surfaces if the tuning parameters are restricted to one-ring refined control vertices only. In this work, we further relax Catmull–Clark subdivision rules for 2-ring refined vertices with additional degrees of freedom in tuning masks with limit surfaces towards curvature continuity at extraordinary positions. Curvatures are bounded near extraordinary positions of valences N ≤ 7, and a relaxation approach is proposed to suppress the local curvature variation for N ≥ 8. We compare the proposed tuned subdivision scheme with several state-of-the-art schemes in terms of both surface qualities and applications in isogeometric analysis. Laplace–Beltrami equations with prescribed test solutions are adopted for verification of analysis results, and the proposed scheme recovers optimal convergence rates in the L²-norm with considerably lower absolute solution error than other schemes. As to surface quality, the proposed scheme has significant improvements compared with other schemes with optimal convergence rates for isogeometric analysis. The proposed scheme produces tighter curvature bounds with comparable reflection lines to the prevalent Catmull–Clark subdivision. © 2023 Elsevier Ltd