Towards 3D computational oeigami - theory and software development
| Project/Area Number |
25330007
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Theory of informatics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
IDA Tetsuo 筑波大学, システム情報系(名誉教授), 名誉教授 (70100047)
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| Co-Investigator(Renkei-kenkyūsha) |
MINAMIDE Yasuhiko 東京工業大学, 情報理工学院, 教授 (50252531)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| 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 / 折紙幾何定理の自動証明 / Geometric Algebra / 計算理論 / 幾何定理自動証明 / 立体モデル化 / 折紙の理論 / 幾何代数 / 定理証明支援系 / 折紙ソフトウェア / プログラム検証 |
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| 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.
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Report
(5 results)
Research Products
(22 results)
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[Journal Article] A New Formalization of Origami in Geometric Algebra2016
Author(s)
Tetsuo Ida, Jacques Fleuriot, Fadoua Ghourabi
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Journal Title
Proceedings of ADG 2016: Eleventh International Workshop on Automated Deduction in Geometry, Strasbourg, France, June 27-29, 2016
Volume: hal-01334334
Related Report
Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
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[Book] Post-Proceedings of 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, {SYNASC} 2016, Timisoara, Romania, September2016
Author(s)
James H. Davenport, Viorel Negru, Tetsuo Ida,Tudor Jebelean, Dana Petcu,Stephen M. Watt,Daniela Zaharie
Total Pages
476
Publisher
IEEE, Computer Society
Related Report
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