Constrained polynomial approximation of rational Bezier curves using reparameterization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:249

Article

Hu, Qianqian¹  Xu, Huixia² 

[1] Zhejiang Gongshang Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

[2] Zhejiang Wanli Univ, Inst Math, Ningbo 315100, Zhejiang, Peoples R China

关键词: Rational Bezier curves;    Polynomial approximation;    Mobius parameter transformation;    Reparameterization;    The least squares method;   

DOI  :  10.1016/j.cam.2013.02.022

来源: Elsevier

【 摘 要 】

This paper proposes a novel method for polynomial approximation of rational Bezier curves with constraints. Different from the previous techniques, for a given rational Bezier curve r(t), a polynomial curve q(s) with a parameter transformation s = phi(t), such that q(phi(t)) is the closest point to the point r(t), is considered to approximate it. To minimize the distance between these two curves in the L-2 norm produces a similar effect as that of the Hausdorff distance. We use a rational function s(t) of a Mobius parameter transformation to approximate the function phi(t). The method can preserve parametric continuity or geometric continuity of any u, v(u, v >= 0) orders at two endpoints, respectively. And applying the least squares method, we deduce a matrix-based representation of the control points of the approximation curve. Finally, numerical examples show that the reparameterization-based method is feasible and effective, and has a smaller approximation error under the Hausdorff distance than the previous methods. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free