弹性测地网格及其平面-空间展开
On Elastic Geodesic Grids and Their Planar to Spatial Deployment
摘要：
我们提出了一种新型的平面到空间可展开结构，我们称之为弹性测地线网格。我们的方法的目的是在近似的自由曲面与空间网格的弯曲薄板，可以部署从一个平面配置使用一个简单的运动机制。这样的弹性结构易于制造和易于部署，并且具有结合了物理学和美学的近似形状。我们提出了一个解决方案的基础上网络的测地线曲线的目标表面上，我们介绍了一组条件和假设，可以密切满足在实践中。我们的配方允许一个纯粹的几何方法，避免了数值形状优化的必要性，建立在微分几何的理论见解之上。我们提出了一个解决方案的弹性测地线网格的设计，计算和物理模拟，并提出了几个制造的小规模的例子，不同的复杂性。此外，我们提供了一个经验证明，我们的方法通过比较的结果，激光扫描的制造模型。我们的方法的目的是作为一种形式发现工具，弹性网格壳在建筑和其他创造性的学科，并应给设计师一个易于处理的方式，探索这种结构。
英文摘要：
We propose a novel type of planar-to-spatial deployable structures that we call elastic geodesic grids. Our approach aims at the approximation of freeform surfaces with spatial grids of bent lamellas which can be deployed from a planar configuration using a simple kinematic mechanism. Such elastic structures are easy-to-fabricate and easy-to-deploy and approximate shapes which combine physics and aesthetics. We propose a solution based on networks of geodesic curves on target surfaces and we introduce a set of conditions and assumptions which can be closely met in practice. Our formulation allows for a purely geometric approach which avoids the necessity of numerical shape optimization by building on top of theoretical insights from differential geometry. We propose a solution for the design, computation, and physical simulation of elastic geodesic grids, and present several fabricated small-scale examples with varying complexity. Moreover, we provide an empirical proof of our method by comparing the results to laser-scans of the fabricated models. Our method is intended as a form-finding tool for elastic gridshells in architecture and other creative disciplines and should give the designer an easy-to-handle way for the exploration of such structures.
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