广义可展弹性测地线网格
Generalized Deployable Elastic Geodesic Grids
摘要：
给定一个设计者在三维空间中创建的自由曲面，我们的方法计算一个由完全平面和直的弹性元素组成的网格。只有通过将平面元素的端部固定到适当的位置，2d网格才会弯曲并近似于给定的3d表面。我们的方法是纯粹基于微分几何的曲线和曲面的概念，并避免任何物理模拟。特别是，我们引入了一个定义良好的弹性网格能量功能，允许识别网络的曲线，最大限度地减少弯曲能量，并在同一时间依偎到所提供的输入表面以及。此外，我们推广这种网格的概念的情况下，表面边界不需要是凸的，这允许创建复杂的和视觉上令人愉快的形状。该算法最终确保了2d网格是完美的平面，使得生成的网格壳便宜，易于制造，运输，组装，最后也部署。此外，由于整个结构是预应变的，它也具有承载能力。我们评估我们的方法使用物理模拟，我们还提供了一个完整的制造流水线桌面大小的模型，并提出了多个例子的表面与椭圆和双曲曲率区域。我们的方法是设计师，建筑师和工程师快速原型设计的工具，因为它非常快，可以在几秒钟内获得结果。
英文摘要：
Given a designer created free-form surface in 3d space, our method computes a grid composed of elastic elements which are completely planar and straight. Only by fixing the ends of the planar elements to appropriate locations, the 2d grid bends and approximates the given 3d surface. Our method is based purely on the notions from differential geometry of curves and surfaces and avoids any physical simulations. In particular, we introduce a well-defined elastic grid energy functional that allows identifying networks of curves that minimize the bending energy and at the same time nestle to the provided input surface well. Further, we generalize the concept of such grids to cases where the surface boundary does not need to be convex, which allows for the creation of sophisticated and visually pleasing shapes. The algorithm finally ensures that the 2d grid is perfectly planar, making the resulting gridshells inexpensive, easy to fabricate, transport, assemble, and finally also to deploy. Additionally, since the whole structure is pre-strained, it also comes with load-bearing capabilities. We evaluate our method using physical simulation and we also provide a full fabrication pipeline for desktop-size models and present multiple examples of surfaces with elliptic and hyperbolic curvature regions. Our method is meant as a tool for quick prototyping for designers, architects, and engineers since it is very fast and results can be obtained in a matter of seconds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
