论文标题
折纸设计的添加算法
An additive algorithm for origami design
论文作者
论文摘要
受添加剂制造的魅力的启发，我们从一个新的角度提出了折纸设计的问题：我们如何从种子的三个维度上种植折叠的表面，从而保证它是平面均等的呢？我们通过两个步骤解决了这个问题：首先识别将两个单独折叠兼容完成的几何条件，将两个单独的折叠置于单个可开发的四倍顶点，然后显示该基础如何使我们在给定折叠种子的边界处生长几何兼容的前沿。这产生了一种完整的游行或添加剂算法，用于可从扁平床单上折叠的可开发四折纸图案的完整空间的逆设计。我们通过生长有序，无序，直和弯曲的折叠折纸以及带有折叠近似值的给定曲率的拟合表面来说明方法的灵活性。总体而言，我们从全局搜索到本地规则的简单转变具有改变基于折纸的元结构设计的潜力。
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.
