| Project/Area Number |
16H03941
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
Kajiwara Kenji 九州大学, マス・フォア・インダストリ研究所, 教授 (40268115)
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| Co-Investigator(Kenkyū-buntansha) |
増田 哲 青山学院大学, 理工学部, 教授 (00335457)
太田 泰広 神戸大学, 理学研究科, 教授 (10213745)
廣瀬 三平 芝浦工業大学, デザイン工学部, 准教授 (20743230)
井ノ口 順一 筑波大学, 数理物質系, 教授 (40309886)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥15,730,000 (Direct Cost: ¥12,100,000、Indirect Cost: ¥3,630,000)
Fiscal Year 2019: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2018: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
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| Keywords | 離散微分幾何 / 可積分系 / クライン幾何 / 曲面・曲線 / 離散正則函数 / ソリトン方程式 / パンルヴェ方程式 / 対数型美的曲線 / 離散可積分系 / 離散ソリトン方程式 / ガルニエ系 / 離散曲面 / 離散曲線 / 幾何学的形状生成 / ソリトン / τ函数 |
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| Outline of Final Research Achievements |
Discrete integrable differential geometry and its application have been studied, focusing on the integrable structure behind the discrete geometric objects. We have obtained the results on the discrete surfaces/curves and their deformation theory, discrete holomorphic functions, construction of discrete models of curves/surfaces, and stable and precise numerical method for the surfaces and interfaces. In particular, regarding the discrete surfaces/curves and their deformation theory, we formulated a good framework for the log-aesthetic curves developed in the area of the industrial design by using the Klein geometry and succeeded in generalization. Based on those results, we have proposed a project for JST CREST aiming at the development to the various areas of design, which has been successfully accepted.
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| Academic Significance and Societal Importance of the Research Achievements |
さまざまな離散的な曲面，曲線やその変形，またCGなどで用いられる複素正則函数の離散化を扱う理論的な基礎を確立し，その応用の一つとして設計諸分野で美しくアート性の高い形状の設計を容易にする美的形状の基本要素に関する数学的な理論を構築し，また土壌中の水浸透減少に関する高精度かつ高速な数値モデルを定式化した．
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