Global Surface Remeshing Using Symmetric Delaunay Triangulation in Uniformization Spaces

W. Zeng, Rui Shi, X. Gu
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引用次数: 2

Abstract

Surface remeshing plays a fundamental role in digital geometry processing. In this paper, we present a novel framework for global surface remeshing based on symmetric Delaunay triangulations on the uniformization spaces. Surfaces with arbitrary topologies can be uniformized to one of three canonical uniformization spaces: the sphere, the Euclidean plane and the hyperbolic plane. The uniformization process induces a symmetry group. A triangulation on the original surface is converted to a triangulation on the uniformization space, which is invariant under the symmetry group, and vice versa. Furthermore, the uniformization process preserves angles, so a symmetric dense Delaunay triangulation on the uniformization space induces a good triangulation on the original surface. We construct the uniformization of surfaces with arbitrary topologies using Ricci flow, and apply orbit insertion technique to the Delaunay refinement algorithm which ensures the symmetry. Experimental results demonstrates that our method is global, intrinsic, general and efficient.
均匀化空间中使用对称Delaunay三角剖分的全局表面网格重划分
曲面网格划分在数字几何处理中起着至关重要的作用。本文提出了一种基于均匀化空间上的对称Delaunay三角剖分的全局曲面网格划分框架。具有任意拓扑结构的曲面可以均匀化为三种标准均匀化空间之一:球面、欧几里得平面和双曲平面。均匀化过程产生对称群。原曲面上的三角剖分转换为均匀化空间上的三角剖分,在对称群下是不变的,反之亦然。此外,均匀化过程保留了角度,因此均匀化空间上的对称密集Delaunay三角剖分可以在原始表面上得到良好的三角剖分。利用Ricci流构造任意拓扑曲面的均匀化,并将轨道插入技术应用于保证对称的Delaunay精化算法中。实验结果表明,该方法具有全局性、内禀性、通用性和高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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