Zachary Abel, Jason H. Cantarella, E. Demaine, D. Eppstein, Thomas C. Hull, Jason S. Ku, R. Lang, Tomohiro Tachi
{"title":"Rigid origami vertices: conditions and forcing sets","authors":"Zachary Abel, Jason H. Cantarella, E. Demaine, D. Eppstein, Thomas C. Hull, Jason S. Ku, R. Lang, Tomohiro Tachi","doi":"10.20382/jocg.v7i1a9","DOIUrl":null,"url":null,"abstract":"We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.","PeriodicalId":54969,"journal":{"name":"International Journal of Computational Geometry & Applications","volume":"56 1","pages":"171-184"},"PeriodicalIF":0.0000,"publicationDate":"2015-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"53","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computational Geometry & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.20382/jocg.v7i1a9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 53
Abstract
We develop an intrinsic necessary and sufficient condition for single-vertex origami crease patterns to be able to fold rigidly. We classify such patterns in the case where the creases are pre-assigned to be mountains and valleys as well as in the unassigned case. We also illustrate the utility of this result by applying it to the new concept of minimal forcing sets for rigid origami models, which are the smallest collection of creases that, when folded, will force all the other creases to fold in a prescribed way.
期刊介绍：
The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms.
Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.
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