Curved foldings with common creases and crease patterns
Curved foldings with common creases and crease patterns
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具有常见折痕和折痕图案的弯曲折叠
DOI：
10.1016/j.aam.2020.102083
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发表时间：
2020
影响因子：
1.1
通讯作者：
Yamada Kotaro
中科院分区：
文献类型：
--
作者：
Honda Atsufumi;Naokawa Kosuke;Saji Kentaro;Umehara Masaaki;Yamada Kotaro
考虑平面R2中区域D中的曲线Γ.把D看作一张纸，我们可以在欧几里得空间R 3中做一个弯曲的折叠P。P作为空间曲线的奇异集C称为P的折痕，初始给定的平面曲线Γ称为P的折痕模式.本文证明了一般情况下存在四个不同的非全等曲线折叠，其中给定的一对折叠由折痕和折痕模式组成.其中两种可能性是已知的，但似乎其他两种可能性（即总共四种可能性）是第一次在这里提出。
Consider a curve Γ in a domain D in the plane R 2. Thinking of D as a piece of paper, one can make a curved folding P in the Euclidean space R 3. The singular set C of P as a space curve is called the crease of P and the initially given plane curve Γ is called the crease pattern of P. In this paper, we show that in general there are four distinct non-congruent curved foldings with a given pair consisting of a crease and crease pattern. Two of these possibilities were already known, but it seems that the other two possibilities (ie four possibilities in total) are presented here for the first time.