2019 Fiscal Year Final Research Report
Generation of Curves and Surfaces based on the Properties of Differential Geometry
| Project/Area Number |
17K00172
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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 |
High performance computing
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| Research Institution | Nihon University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
斎藤 隆文 東京農工大学, 工学(系)研究科(研究院), 教授 (60293007)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | 形状モデリング / 曲率 / 対数美的曲線 / 美的曲線・曲面 |
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| Outline of Final Research Achievements |
Free-form curves, such as Bezier curves or B-spline curves, are widely used in CAD and computer graphics. Free-form curves are curves with many excellent properties, however they have the problem that the curvature is not easy to control. In this research, the curvature function is represented by an explicit Bezier curve or an explicit B-spline curve, and a method for controlling the curvature variation is constructed under the condition that the positions, the tangential directions (and curvatures) of both endpoints are specified. By implementing the method, we confirmed that curves can be generated in real time. This study made it possible to control the curvature variation satisfying the specified conditions.
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| Free Research Field |
形状処理工学
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| Academic Significance and Societal Importance of the Research Achievements |
自動車のボディなどに代表する高度に美的な曲面を生成するには，曲面を生成する曲線自体も高度に美的である必要がある．高度に美的な曲線は，曲率変化が単調であるか，または少ない数の曲率単調な領域を持つことが必要である．本研究は，曲率変化を陽に指定し，指定された条件を満足するによう曲線を生成することで，曲率変化の指定が可能な曲線生成手法の構築を行いプログラムとして実装した．本研究により，従来手法よりも，より広い範囲で曲率変化を制御することが可能となり，また，曲線生成の際に曲率制御の重要性がより認識されることが期待される．
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