2013 Fiscal Year Final Research Report
Visualization in geometry and construction of 3-dimensional mathematical models
| Project/Area Number |
23654022
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KOHNO Toshitake 東京大学, 数理(科)学研究科(研究院), 教授 (80144111)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUBOI Takashi 東京大学, 大学院・数理科学研究科, 教授 (40114566)
AHARA Kazushi 明治大学, 理工学部, 准教授 (80247147)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 離散データ / 代数曲面 / 定曲率曲面 / ガウス曲率 / 平均曲率 / 三次曲面 / 極小曲面 / 複素解析関数 |
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| Research Abstract |
Geometric objects of present research are given in various forms such as algebraic equations, complex analytic functions and differential equations. Starting from discrete data of surfaces we investigated a method to compute optimal values of invariants in differential geometry such as Gauss curvature and mean curvature. In the process of constructing geometric models it turns out that it is efficient to include information about normal direction at each point and we established techniques to construct models based on such enhanced data. We succeeded in constructing models of 27 lines on a cubic surface and a surface of constant negative curvature made of aluminum with high accuracy. We obtained a satisfactory procedure to establish an interface for constructing models from discrete data.
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