Voronoi网壳结构
Voronoi Grid-Shell Structures
摘要：
我们介绍了一个框架，用于生成网格壳结构，是基于沃罗诺伊图，并允许我们设计镶嵌，实现出色的静态性能。我们从分析输入曲面上的应力入手，利用得到的张量场在其上诱导出各向异性的非欧度量，然后在相同的度量下计算一个质心Voronoi Tessellation。生成的网格是六边形主导的，由具有可变密度的单元组成，密度取决于应力的大小，而各向异性形状取决于最大应力的方向。考虑到细胞的对称性和规则性，该网格被进一步优化以改善美观性。我们证明，我们的网格壳实现了更好的静态性能与四为基础的网格壳，同时提供了一个创新和美观的外观。
英文摘要：
We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input surface and we use the resulting tensor field to induce an anisotropic non-Euclidean metric over it. Then we compute a Centroidal Voronoi Tessellation under the same metric. The resulting mesh is hex-dominant and made of cells with a variable density, which depends on the amount of stress, and anisotropic shape, which depends on the direction of maximum stress. This mesh is further optimized taking into account symmetry and regularity of cells to improve aesthetics. We demonstrate that our grid-shells achieve better static performances with respect to quad-based grid shells, while offering an innovative and aesthetically pleasing look.
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