Compatible intrinsic triangulations
Compatible intrinsic triangulations
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DOI：
10.1145/3528223.3530175
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发表时间：
2022-07
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通讯作者：
Kenshi Takayama
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作者：
Kenshi Takayama
寻找任意亏格表面之间的失真最小化同胚是计算机图形和几何处理中的一项基本任务。我们提出了一种利用固有三角测量的简单方法，直接在原始表面上操作，而不经过任何中间域（例如平面或球体）。给定两个模型 A 和 B 作为三角形网格，我们的算法构建一个兼容的内在三角剖分 (CIT)，即 A 和 B 上的一对内在三角剖分，其顶点、边和面具有完全对应关系。这种细分允许我们通过跟踪 A 和 B 上的分段测地路径，在 B 上建立 A 输入网格的边缘和面的一致图像（反之亦然）。我们构建 CIT 的算法（主要由精心设计的边缘翻转方案组成）本质上是经验性的，没有任何成功保证，但结果证明足够鲁棒，可以在之前文献中使用的类似二阶优化框架中使用。我们的方法的实用性是通过对标准基准数据集的比较和评估来证明的。
Finding distortion-minimizing homeomorphisms between surfaces of arbitrary genus is a fundamental task in computer graphics and geometry processing. We propose a simple method utilizing intrinsic triangulations, operating directly on the original surfaces without going through any intermediate domains such as a plane or a sphere. Given two models A and B as triangle meshes, our algorithm constructs a Compatible Intrinsic Triangulation (CIT), a pair of intrinsic triangulations over A and B with full correspondences in their vertices, edges and faces. Such a tessellation allows us to establish consistent images of edges and faces of A's input mesh over B (and vice versa) by tracing piecewise-geodesic paths over A and B. Our algorithm for constructing CITs, primarily consisting of carefully designed edge flipping schemes, is empirical in nature without any guarantee of success, but turns out to be robust enough to be used within a similar second-order optimization framework as was used previously in the literature. The utility of our method is demonstrated through comparisons and evaluation on a standard benchmark dataset.