RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree

In this paper, we introduce two local surface averaging operators with local inverses and use them to devise a method for surface multiresolution (subdivision and reverse subdivision) of arbitrary degree. Similar to previous works by Stam, Zorin, and Schroder that achieved forward subdivision only, our averaging operators involve only direct neighbours of a vertex, and can be configured to generalize B-Spline multiresolution to arbitrary topology surfaces. Our subdivision surfaces are hence able to exhibit C(d) continuity at regular vertices (for arbitrary values of d) and appear to exhibit C(1) continuity at extraordinary vertices. Smooth reverse and non-uniform subdivisions are additionally supported.