Formalization of origami and origami-programming based on algebraic graph rewriting
| Project/Area Number |
22650001
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Fundamental theory of informatics
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| Research Institution | University of Tsukuba |
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Principal Investigator |
IDA Tetsuo 筑波大学, 名誉教授 (70100047)
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| Co-Investigator(Kenkyū-buntansha) |
MARIN Mircea 筑波大学, 大学院・システム情報工学研究科, 講師 (60396603)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,280,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥480,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | 計算折紙論 / 記号計算 / 書換え系 / 自動幾何定理証明 / 制約問題 / 代数的グラフ書換系 / グロブナ基底計算 / 計算折紙 / グラフ書き換え / 検証支援系 / 制約計算 / 計算理論 / グラフ書換系 / 折紙計算論 / 定理自動証明 |
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| Research Abstract |
Abstraction of paper fold (origami) and establishment of a formal theory of fold are our ultimate goal. Towards that goal, we formalized origami by algebraic graph rewriting theory and verified certain geometrical propertiesof origami. The results we obtained are as follows:
(1) We develop a graph rewriting language for origami and its interpreter.
(2) In order to concretize the graph rewriting to be used to simulate actual origami and to verify geometrical properties, we developed algorithms for transformingbasic folds to algebraic expressions.
(3) In parallel with the above developments we extended and improved e-origami system Eos that we have developed. The extension enables us to automatically verify more geometrical theorems and to speed up the computation of proving.
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Report
(4 results)
Research Products
(13 results)
