Extended Truncated Hierarchical Catmull–Clark Subdivision

• eTHCCS builds basis functions over arbitrary quadrilateral meshes and applies them to THCCS.
• eTHCCS significantly improves the efficiency of local refinement in THCCS by refining only one-ring neighboring elements rather than two-ring.
• eTHCCS inherits the properties of THCCS, such as partition of unity, convex hull, global linear independence, geometry preservation, and nested spaces.

In this paper we present an extended Truncated Hierarchical Catmull–Clark Subdivision (eTHCCS) method, which improves the efficiency of local refinement in Truncated Hierarchical Catmull–Clark Subdivision (THCCS). Based on the Stam’s method, we first build a set of basis functions over arbitrary quadrilateral meshes and apply them to THCCS. Then, a new basis-function-insertion scheme is developed with the aid of the truncation mechanism, which refines one-ring neighboring elements rather than two-ring neighborhoods. Therefore, eTHCCS significantly improves the efficiency of local refinement compared with THCCS, as demonstrated by one benchmark problem and several complex models. Moreover, eTHCCS is also proved to preserve the input geometry and produce nested spaces.