Subdivision surfaces based on point-based splines

We present a new interpolatory subdivision scheme based on PB-splines (point-based B-splines), over triangular meshes. Using the stencil of the interpolatory √3-subdivision scheme, we propose a different refinement strategy by introducing a variable a to each regular vertex (valence = 6). By applying different a (locally or globally), the scheme is suitable for adaptive refinement and can perfectly reach different smoothness conditions (C⁰, C¹ or C²).