标题： 使用折纸图案编程曲率 显示英文标题

标题： Programming Curvature using Origami Tessellations

摘要： 折纸描述了从平面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开始，该图案可产生一个自由度的可折叠结构，我们表明可以使用与尺度无关的基本几何构造和约束优化算法来确定空间调制的图案，这些图案可近似给定的具有恒定或变化曲率的表面。 纸张模型证实了我们计算的可行性。 我们还通过量化分隔亚稳态平坦状态和折叠状态的能量势垒来评估实现这些几何结构的难度。 此外，我们研究了图案对目标表面的符合精度与创建更细折叠所需努力之间的权衡。 我们的方法使能够根据绝对尺度独立地定制折纸图案，以覆盖复杂的表面，并量化这样做的能量和材料成本。 显示英文摘要

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.