2016 Fiscal Year Final Research Report
Towards 3D computational oeigami  theory and software development
Project/Area Number 
25330007

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Multiyear 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)

CoInvestigator(Renkeikenkyūsha) 
MINAMIDE Yasuhiko 東京工業大学, 情報理工学院, 教授 (50252531)

Project Period (FY) 
20130401 – 20170331

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 Eorigami 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 HuzitaJustin's set of elementary operations and verified its effectiveness. (3) We proposed an axiomatic system of ndimensional origami, which generalizes the 2D and 3D origami.

Free Research Field 
情報学基礎・情報学基礎理論
