Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable four-fold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight and curved folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based meta-structure design.
翻译:在添加制造的诱惑下,我们从一个新的角度提出了折纸设计问题:我们如何从种子的三个维度上将折叠的表面从种子的3个维度上发展成一个折叠的表层,从而保证它能与平面相容?我们分两个步骤解决这个问题:首先确定两个分离折叠相容完成的几何条件,形成一个单一可开发的四倍顶点,然后展示这个基础如何让我们在给定折叠种子的边界上发展一个几何相容的前方。这产生一个完整的行进算法,或添加算法,用于从平板折叠中折叠叠成的可开发的二次折叠形模式的完整空间的反向设计。我们通过增加定序、混乱、直形和曲线折叠成的折叠式折面和与折叠合的弯曲的表面来展示我们的方法的灵活性。总的来说,我们从全球搜索到本地规则的简单视角的转变了基于纸质的元结构设计的潜力。