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Shape Modification for λ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector
Joint Authors
Hu, Gang
Ji, Xiaomin
Qin, Xinqiang
Zhang, Suxia
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-10-05
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Besides inheriting the properties of classical Bézier curves of degree n, the corresponding λ-Bézier curves have a good performance on adjusting their shapes by changing shape control parameter.
Specially, in the case where the shape control parameter equals zero, the λ-Bézier curves degenerate to the classical Bézier curves.
In this paper, the shape modification of λ-Bézier curves by constrained optimization of position and tangent vector is investigated.
The definition and properties of λ-Bézier curves are given in detail, and the shape modification is implemented by optimizing perturbations of control points.
At the same time, the explicit formulas of modifying control points and shape parameter are obtained by Lagrange multiplier method.
Using this algorithm, λ-Bézier curves are modified to satisfy the specified constraints of position and tangent vector, meanwhile the shape-preserving property is still retained.
In order to illustrate its ability on adjusting the shape of λ-Bézier curves, some curve design applications are discussed, which show that the proposed method is effective and easy to implement.
American Psychological Association (APA)
Hu, Gang& Ji, Xiaomin& Qin, Xinqiang& Zhang, Suxia. 2015. Shape Modification for λ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1074611
Modern Language Association (MLA)
Hu, Gang…[et al.]. Shape Modification for λ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector. Mathematical Problems in Engineering No. 2015 (2015), pp.1-12.
https://search.emarefa.net/detail/BIM-1074611
American Medical Association (AMA)
Hu, Gang& Ji, Xiaomin& Qin, Xinqiang& Zhang, Suxia. Shape Modification for λ-Bézier Curves Based on Constrained Optimization of Position and Tangent Vector. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-12.
https://search.emarefa.net/detail/BIM-1074611
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074611