Approximate Multidegree Reduction of λ-Bézier Curves
Joint Authors
Hu, Gang
Zhang, Suxia
Cao, Huanxin
Source
Mathematical Problems in Engineering
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-05-26
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 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.
American Psychological Association (APA)
Hu, Gang& Cao, Huanxin& Zhang, Suxia. 2016. Approximate Multidegree Reduction of λ-Bézier Curves. Mathematical Problems in Engineering،Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112658
Modern Language Association (MLA)
Hu, Gang…[et al.]. Approximate Multidegree Reduction of λ-Bézier Curves. Mathematical Problems in Engineering No. 2016 (2016), pp.1-12.
https://search.emarefa.net/detail/BIM-1112658
American Medical Association (AMA)
Hu, Gang& Cao, Huanxin& Zhang, Suxia. Approximate Multidegree Reduction of λ-Bézier Curves. Mathematical Problems in Engineering. 2016. Vol. 2016, no. 2016, pp.1-12.
https://search.emarefa.net/detail/BIM-1112658
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1112658