In this article, 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 non-uniform subdivisions are additionally supported.

中文翻译：

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RIAS：任意度表面多分辨率的重复可逆平均

在本文中，我们介绍了两个具有局部逆的局部表面平均算子，并使用它们来设计一种任意度的表面多分辨率（细分和反向细分）方法。与 Stam、Zorin 和 Schröder 之前仅实现前向细分的工作类似，我们的平均算子仅涉及顶点的直接邻居，并且可以配置为将 B-Spline 多分辨率推广到任意拓扑表面。因此，我们的细分表面能够展示$C^d$ 规则顶点的连续性（对于任意值 $d$ ) 并且似乎表现出 $C^1$非凡顶点的连续性。另外还支持平滑反向和非均匀细分。