使用Origami Tessellations编程曲率
Programming Curvature using Origami Tessellations
摘要：
Origami描述了从平板上的图案创建折叠结构的规则，但没有规定如何设计图案以适应目标形状。在这里，从最简单的周期性折纸图案，产生一个自由度的可折叠的结构，我们表明，尺度无关的基本几何结构和约束优化算法，可用于确定空间调制模式，产生近似给定的恒定或变化的曲率表面。纸上模型证实了我们计算的可行性。我们还评估了实现这些几何结构的困难，通过量化的能量障碍，分离的亚稳态平坦和折叠状态。此外，我们的特点之间的权衡的准确性，该模式符合目标表面，并与创建更精细的折叠相关的努力。我们的方法使折纸图案的裁剪，以悬垂复杂的表面独立的绝对规模，并量化这样做的能量和材料成本。
英文摘要：
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one degree-of-freedom collapsible structures, we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, and quantify the energetic and material cost of doing so.
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