The approximation order of four-point interpolatory curve subdivision

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摘要

In this paper we derive an approximation property of four-point interpolatory curve subdivision, based on local cubic polynomial fitting. We show that when the scheme is used to generate a limit curve that interpolates given irregularly spaced points, sampled from a curve in any space dimension with a bounded fourth derivative, and the chosen parameterization is chordal, the accuracy is fourth order as the mesh size goes to zero. In contrast, uniform and centripetal parameterizations yield only second order.

论文关键词:65D05,65D10,Interpolatory subdivision,Chordal parameterization,Approximation order

论文评审过程:Available online 22 March 2011.

论文官网地址:https://doi.org/10.1016/j.cam.2011.03.018