Method for solving origami tessellation hole problem using triangle twist folding
Method for solving origami tessellation hole problem using triangle twist folding
复制标题
利用三角形扭转折叠解决折纸镶嵌孔问题的方法
DOI：
10.1093/jcde/qwab074
复制
发表时间：
2022
影响因子：
4.9
通讯作者：
Mitani Jun
中科院分区：
文献类型：
--
作者：
Yamamoto Yohei;Nakazato Riku;Mitani Jun
折纸镶嵌是从一张纸上折叠的几何图形，平面重叠。大多数现有的折纸镶嵌是通过首先在纸上标记折痕线网格，然后沿网格沿着排列重复图案来构造的。然而，这种设计方法是有限的，因为它不能设计出具有不能在网格上表示的图案的折纸镶嵌，例如规则的五边形。本文提出了一种新的折纸镶嵌的构造方法，解决了这个问题，丰富了这些品种。在所提出的方法中，首先确定折纸镶嵌的边界，然后将称为三角形扭曲折叠图案的图案放置在边界内。类似的方法被称为孔问题，尽管在本文中，该问题被重新定义并以适合于折纸镶嵌的形式进行讨论。因此，提出了一种与网格无关的构造方法，并通过使用实现该方法的软件获得了新的折纸镶嵌。
Origami tessellations are geometric pieces folded from a single sheet of paper with flatly overlapped facets. Most existing origami tessellations are constructed by first marking a grid of crease lines on the paper and then arranging repeating patterns along the grid. However, this design method is limited because it cannot design origami tessellations with patterns that cannot be represented on a grid, such as a regular pentagon. This paper proposes a new construction method for origami tessellations that solves this problem and enriches these varieties. In the proposed method, a boundary of an origami tessellation is determined first, and then patterns called triangle twist fold patterns are placed inside the boundary. A similar approach is known as a hole problem, although in this paper, the problem is redefined and discussed in a form suitable for origami tessellations. As a result, a grid-independent construction method was proposed, and new origami tessellations were obtained by using software that implements the method.