Curved foldings with common creases and crease patterns

作     者：Honda, Atsufumi Naokawa, Kosuke Saji, Kentaro Umehara, Masaaki Yamada, Kotaro 

作者机构：Department of Applied Mathematics Faculty of Engineering Yokohama National University 79-5 Tokiwadai Hodogaya Yokohama240-8501 Japan Department of Computer Science Faculty of Applied Information Science Hiroshima Institute of Technology 2-1-1 Miyake Saeki Hiroshima731-5193 Japan Department of Mathematics Faculty of Science Kobe University Rokko Kobe657-8501 Department of Mathematical and Computing Sciences Tokyo Institute of Technology Tokyo152-8552 Japan Department of Mathematics Tokyo Institute of Technology Tokyo152-8551 Japan 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2019年

核心收录：

摘      要：Consider a curve Γ in a domain D in the plane R2. Thinking of D as a piece of paper, one can make a curved folding P in the Euclidean space R3. 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 (i.e. four possibilities in total) are presented here for the first time (figure presented).MSC Codes 53A05, 51M15 Copyright © 2019, The Authors. All rights reserved.