RIAS: Repeated Invertible Averaging for Surface Multiresolution of Arbitrary Degree

Abstract

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 Schröder 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 nonuniform subdivisions are additionally supported.

A Subdivision-Based Combined Shape and Topology Optimization in Acoustics

“…Subdivision curves/surfaces provide graceful isogeometric, bidirectional mapping between geometric and analytical models [6]. Subdivision uses a coarse mesh and a restricted process of duplicated refinement to describe geometric shapes [7][8][9][10]. Multiresolution subdivision surfaces have the following advantages: (1) Having the ability to represent topologically arbitrary geometries; (2) wavelet-like multiresolution representation of geometries; (3) Subdivision-friendly integration with CAD packages.…”