Topology-preserving simplification of 2D nonmanifold meshes with embedded structures
Topology-preserving simplification of 2D nonmanifold meshes with embedded structures
复制标题
具有嵌入结构的二维非流形网格的拓扑保持简化
DOI：
10.1007/s00371-005-0334-y
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
P. Texier
中科院分区：
文献类型：
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作者：
F. Vivodtzev;Georges;P. Texier
网格简化多年来受到了极大的关注。在这一领域中，以前的大部分工作都涉及正确选择误差度量来指导简化。保留网格的拓扑特征以及可能附加到网格上的数据是一个较新的主题，也是本文的主题。我们引入了一种新的拓扑保持简化算法，用于三角形网格，可能是非流形的，嵌入了折线。在这种情况下，嵌入意味着折线的边缘也是网格的边缘。本文介绍了一种鲁棒性测试，用于检测网格中边缘的崩溃是否改变了网格的拓扑结构或嵌入的折线的拓扑结构。该有效性检验是利用组合拓扑结果推导出来的。更准确地说，我们从输入网格和嵌入的折线中定义了一个所谓的扩展复合体。我们表明，如果网格的边缘塌陷保留了这个扩展复合体的拓扑结构，那么它也保留了网格的拓扑结构和嵌入的折线。我们的有效性测试可以用于任何2-complex网格，包括非流形三角形网格，并且可以与任何先前引入的误差测量相结合。描述了该效度检验的实现方法。我们用来自神经科学、地质学和机械工程CAD/CAM模型的科学数据集展示了我们方法的强大功能和多功能性。
Mesh simplification has received tremendous attention over the years. Most of the previous work in this area deals with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic and the subject of this paper. We introduce a new topology-preserving simplification algorithm for triangular meshes, possibly nonmanifold, with embedded polylines. In this context, embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely, we define a so-calledextended complexfrom the input mesh and the embedded polylines. We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including nonmanifold triangular meshes, and can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology, and CAD/CAM models from mechanical engineering.