Design of self-supporting surfaces
Design of self-supporting surfaces
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DOI：
10.1145/2185520.2185583
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
E. Vouga;Mathias Höbinger;J. Wallner;H. Pottmann
中科院分区：
文献类型：
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作者：
E. Vouga;Mathias Höbinger;J. Wallner;H. Pottmann
自支撑砌体是建造曲线形状的最古老和最优雅的技术之一。由于其破坏的几何性质，分析和建模这样的结构是一个几何处理问题比经典连续介质力学之一。本文采用推力网络分析方法，提出了一种迭代非线性优化算法，有效地逼近自由形状的自支撑的。推力网络的丰富的几何形状使我们在离散微分几何中的不同主题之间建立了密切的联系，例如艾里应力势的有限元离散化，完美的图形拉普拉斯算子，以及通过多面体表面的曲率计算容许载荷。特别是，这种几何观点使我们能够通过具有平面的自支撑四边形网格来重新网格化自支撑形状，并导致该理论的另一种应用：节点力矩较低的钢/玻璃结构。
Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because of the very geometric nature of their failure, analyzing and modeling such strutures is more a geometry processing problem than one of classical continuum mechanics. This paper uses the thrust network method of analysis and presents an iterative nonlinear optimization algorithm for efficiently approximating freeform shapes by self-supporting ones. The rich geometry of thrust networks leads us to close connections between diverse topics in discrete differential geometry, such as a finite-element discretization of the Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces. This geometric viewpoint allows us, in particular, to remesh self-supporting shapes by self-supporting quad meshes with planar faces, and leads to another application of the theory: steel/glass constructions with low moments in nodes.