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# Approximate Multidegree Reduction of λ-Bézier Curves

Mathematical Problems in Engineering. 2016;2016 DOI 10.1155/2016/8140427

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Journal Title: Mathematical Problems in Engineering

ISSN: 1024-123X (Print); 1563-5147 (Online)

Publisher: Hindawi Limited

LCC Subject Category: Technology: Engineering (General). Civil engineering (General) | Science: Mathematics

Country of publisher: United Kingdom

Language of fulltext: English

Full-text formats available: PDF, HTML, ePUB, XML

AUTHORS

Gang Hu (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

Huanxin Cao (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

Suxia Zhang (Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China)

EDITORIAL INFORMATION

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Time From Submission to Publication: 26 weeks

Abstract | Full Text

Besides inheriting the properties of classical Bézier curves of degree n, the corresponding λ-Bézier curves have a good performance in adjusting their shapes by changing shape control parameter. In this paper, we derive an approximation algorithm for multidegree reduction of λ-Bézier curves in the L2-norm. By analysing the properties of λ-Bézier curves of degree n, a method which can deal with approximating λ-Bézier curve of degree n+1 by λ-Bézier curve of degree m  (m≤n) is presented. Then, in unrestricted and C0, C1 constraint conditions, the new control points of approximating λ-Bézier curve can be obtained by solving linear equations, which can minimize the least square error between the approximating curves and the original ones. Finally, several numerical examples of degree reduction are given and the errors are computed in three conditions. The results indicate that the proposed method is effective and easy to implement.