带边界流形上的单三角带和环

Pablo Diaz-Gutierrez, D. Eppstein, M. Gopi
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引用次数: 4

摘要

Gopi和Eppstein(2004)提出的三角化双流形上的单三角条环路生成算法是基于其对偶图完美匹配的保证存在性。然而,在有边界的三角形的对偶图中,这种完美匹配并不能得到保证。在本文中,我们提出了适当修改对偶图匹配结果的算法,以生成具有边界的流形上的单条环路。此外,Gopi和Eppstein(2004)提出的算法只能产生条形环路,不能产生线性条形环路。我们提出了一种算法,该算法可以在有边界或没有边界的流形上进行拓扑手术来构建具有用户指定的起始和结束三角形的线性条带。本文的主要贡献包括处理不匹配三角形的图算法,减少用于创建条带环路的斯坦纳顶点的数量,以及最后一种生成具有任意起始和结束位置的单个线性条带的新方法
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Single Triangle Strip and Loop on Manifolds with Boundaries
The single triangle-strip loop generation algorithm on a triangulated two-manifold presented by Gopi and Eppstein (2004) is based on the guaranteed existence of a perfect matching in its dual graph. However, such a perfect matching is not guaranteed in the dual graph of triangulated manifolds with boundaries. In this paper, we present algorithms that suitably modify the results of the dual graph matching to generate a single strip loop on manifolds with boundaries. Further, the algorithm presented by Gopi and Eppstein (2004) can produce only strip loops, but not linear strips. We present an algorithm that does topological surgery to construct linear strips, with user-specified start and end triangles, on manifolds with or without boundaries. The main contributions of this paper include graph algorithms to handle unmatched triangles, reduction of the number of Steiner vertices introduced to create strip loops, and finally a novel method to generate single linear strips with arbitrary start and end positions
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