柔性离散平移曲面
Flexible discrete translational surfaces
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中文总结 AI 辅助
本文通过将分类问题归结为球面柔性完全二部框架，完整列出了可弯曲的平移网，并发现了与Bottema球面16杆机构及恒定对角角框架相关的两个新类别，同时讨论了柔性平移管和环面。
中文摘要 AI 辅助
我们给出了平移网在其离散平移曲面类中可弯曲的完整列表，通过将分类问题归结为球面上柔性完全二部框架的分类问题（该问题的解已知）。我们还获得了两个新类别，分别对应于Bottema球面16杆机构和恒定对角角框架。基于构造所有柔性平移网的算法，我们还讨论了柔性平移管和环面。此外，我们展示了由Bottema球面16杆机构所隐含的两种拓扑的新结果。
英文摘要
We give a full list of translational nets which flex within their class of discrete surfaces of translation, by reducing the classification problem to the one of flexible complete bipartite frameworks on the sphere, for which the solution is known. We also obtained two novel classes which correspond to Bottema's spherical 16-bar mechanisms and the constant diagonal angle frameworks. Based on an algorithm for the construction of all flexible translational nets, we also discuss flexible translational tubes and toroids. Furthermore, we present novel results for both topologies which are implied by Bottema's spherical 16-bar mechanisms.
发表机构
- Institute of Discrete Mathematics and Geometry & Center for Geometry and Computational Design, TU Wien（离散数学与几何研究所及几何与计算设计中心，维也纳工业大学）
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