Shape Modification for -Bézier Curves Based on Constrained Optimization of Position and Tangent Vector

Gang Hu, Xiaomin Ji, Xinqiang Qin and Suxia Zhang

Mathematical Problems in Engineering, 2015, vol. 2015, 1-12

Abstract:

Besides inheriting the properties of classical Bézier curves of degree , the corresponding -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 -Bézier curves degenerate to the classical Bézier curves. In this paper, the shape modification of -Bézier curves by constrained optimization of position and tangent vector is investigated. The definition and properties of -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, -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 -Bézier curves, some curve design applications are discussed, which show that the proposed method is effective and easy to implement.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2015/735629.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2015/735629.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:735629

DOI: 10.1155/2015/735629

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().