Truncated hierarchical Catmull–Clark subdivision with local refinement

In this paper we present a new method termed Truncated Hierarchical Catmull–Clark Subdivision   (THCCS), which generalizes truncated hierarchical B-splines to control grids of arbitrary topology. THCCS basis functions satisfy partition of unity, are linearly independent, and are locally refinable. THCCS also preserves geometry during adaptive hh-refinement and thus inherits the surface continuity of Catmull–Clark subdivision, namely C2C2-continuous everywhere except at the local region surrounding extraordinary nodes, where the surface continuity is C1C1. Adaptive isogeometric analysis is performed with THCCS basis functions on a benchmark problem with extraordinary nodes. Local refinement on complex surfaces is also studied to show potential wide application of the proposed method.