Towards 3D computational oeigami - theory and software development

2016 Fiscal Year Final Research Report

• Project/Area Number: 25330007
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Theory of informatics
• Research Institution: University of Tsukuba
• Principal Investigator: IDA Tetsuo 筑波大学, システム情報系(名誉教授), 名誉教授 (70100047)
• Co-Investigator(Renkei-kenkyūsha): MINAMIDE Yasuhiko 東京工業大学, 情報理工学院, 教授 (50252531)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 計算モデル論 / 計算折紙 / 立体折紙 / 記号計算 / 自動定理証明 / ソフトウェア検証 / 計算幾何

Outline of Final Research Achievements

We studied 3D origami from a computational point of view. Namely, we modeled the 3D origami folding employing computer algebra systems and proof assistants to construct the theoretical framework for 3D origami technology. At the same time, we have developed software system that supports the development of the research on 3D origami based on E-origami system Eos developed prior to this research project. Specific outcomes are as follows.
(1) We analyzed and implemented knot folding. Knot folding requires the analysis of the overlapping of origami faces from the viewpoint of 3D origami. (2) We found that the geometric algebra is effective for modeling 3D origami. We developed a version of the geometric algebra for 3D origami modeling, and expressed in the geometric algebra the set of fold operations known as Huzita-Justin's set of elementary operations and verified its effectiveness. (3) We proposed an axiomatic system of n-dimensional origami, which generalizes the 2D and 3D origami.

Free Research Field

情報学基礎・情報学基礎理論