Constrained polynomial approximation of rational Bézier curves using reparameterization

• Autores: Qianqian Hu, Huixia Xu
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 249, Nº 1, 2013, págs. 133-143
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.02.022
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• Resumen

  • 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 = �Ó(t), such that q(�Ó(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 L2 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 �Ó(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 reparameterizationbased method is feasible and effective, and has a smaller approximation error under the Hausdorff distance than the previous methods.