Alderson, Troy F.Mahdavi-Amiri, AliSamavati, Faramarz2020-10-262020-10-262020-02-11Alderson, T. F., Mahdavi-Amiri, A., & Samavati, F. (2015). RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree. "Journal of latex Class Files", 14(8), August 2015. pp. 1-13. http://dx.doi.org/10.1109/TVCG.2020.2972877http://hdl.handle.net/1880/112705https://doi.org/10.11575/PRISM/46107In this paper, we introduce two local surface averaging operators with local inverses and use them to devise a method for surface multi-resolution (subdivision and reverse subdivision) of arbitrary degree. Similar to previous works by Stam, Zorin, and Schröder that achieved forward subdivision only, our averaging operators involve only direct neighbours of a vertex, and can be configured to generalize B-Spline multi-resolution to arbitrary topology surfaces. Our subdivision surfaces are hence able to exhibit Cd continuity at regular vertices (for arbitrary values of d) and appear to exhibit C1 continuity at extraordinary vertices. Smooth reverse and non-uniform subdivisions are additionally supported.Unless otherwise indicated, this material is protected by copyright and has been made available with authorization from the copyright owner. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.journal articlehttp://dx.doi.org/10.1109/TVCG.2020.2972877