2013 Fiscal Year Final Research Report
Optimal Slines with Constraints on Derivatives of Arbitrary Degree
| Project/Area Number |
23560541
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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 |
Control engineering
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
KANO Hiroyuki 東京電機大学, 理工学部, 教授 (00246654)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIOKA Hiroyuki 福岡工業大学, 情報工学部, 准教授 (10349798)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 平滑化スプライン / Bスプライン / 制御スプライン / 曲線曲面 / 等式不等式制約 / ２次計画法 / 軌道計画 / 形状モデリング |
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| Research Abstract |
Spline functions have been used as powerful tools for designing curves and surfaces in many fields of engineering and science such as computer aided design, numerical analysis, image processing, robotics, data analysis, etc. However, the fact that slines are piecewise functions leads to complicated treatments and in this study we develop a concise and systematic method for constructing optimal smoothing splines. In particular, we pay special attension to constrained splines, where various types of constraints can be imposed on designing curves and surfaces. The types of constraints include pointwise constraints, interval constraints, constraints on derivatives and integrals, either as equalities and/or inequalities. We developed theories and algorithms for interpolating and smoothing optimal splines with these constraints in a unified framework. We employed both B-spline approach and control theoretic approach.
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