Error bounds for a class of subdivision schemes based on the two-scale refinement equation

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摘要

Subdivision schemes are iterative procedures for constructing curves and constitute fundamental tools in computer aided design. Starting with an initial control polygon, a subdivision scheme refines the values computed in the previous step according to some basic rules. The scheme is said to be convergent if there exists a limit curve. The computed values define a control polygon in each step. This paper is devoted to estimating error bounds between the limit curve and the control polygon defined after k subdivision stages. In particular, a stop criterion of convergence is obtained. The refinement rules considered in the paper are widely used in practice and are associated with the well known two-scale refinement equation including as particular examples the schemes based on Daubechies’ filters. Our results generalize the previous analysis presented by Mustafa et al. in [G. Mustafa, F. Chen, J. Deng, Estimating error bounds for binary subdivision curves/surfaces, J. Comput. Appl. Math. 193 (2006) 596–613] and [G. Mustafa and M.S. Hashmi Subdivision depth computation for n-ary subdivision curves/surfaces, Vis. Comput. 26 (6–8) (2010) 841–851].

论文关键词:Binary subdivision schemes,Error analysis,Control polygon

论文评审过程:Received 17 February 2009, Revised 23 June 2011, Available online 8 July 2011.

论文官网地址:https://doi.org/10.1016/j.cam.2011.06.031