Re-parameterization of Bézier Curves by Square Approximation with Endpoint Constraints  

作　　者：白鸿武 叶正麟 王烈 

机构地区：[1]Faculty of Science,Northwestern Polytechnical University [2]Department of Mathematics,Xianyang Normal University

出　　处：《Journal of Southwest Jiaotong University(English Edition)》2009年第3期259-264,共6页西南交通大学学报（英文版）

基　　金：The National Natural Science Foundationof China (No.60672135);the Natural Science Foundation of Department of Education of Shaanxi Province, China(No.09JK809)

摘　　要：In order to get an approximation with better effect of pararneterization of Bezier curves, we proposed a method for arc-length parameterization and the corresponding algorithms by square approximation for the discrete even de-parameterization of the curves. This method is simple and easy to implement, and the property of the approximation has no change compared with the original curve. A quantitative criterion for estimating the effect of parameterization is also built to quantitatively characterize the parameterization effect of the algorithms. As a result, the nearly arc-length parameterized curve has a smaller relative deviation using either the algorithm with point constraint at endpoints or the algorithm with point constraint plus the first derivative constraint at endpoints. Experiments show that after re-parameterization with our algorithms, the relative deviation will have at least a 20% reduction.In order to get an approximation with better effect of pararneterization of Bezier curves, we proposed a method for arc-length parameterization and the corresponding algorithms by square approximation for the discrete even de-parameterization of the curves. This method is simple and easy to implement, and the property of the approximation has no change compared with the original curve. A quantitative criterion for estimating the effect of parameterization is also built to quantitatively characterize the parameterization effect of the algorithms. As a result, the nearly arc-length parameterized curve has a smaller relative deviation using either the algorithm with point constraint at endpoints or the algorithm with point constraint plus the first derivative constraint at endpoints. Experiments show that after re-parameterization with our algorithms, the relative deviation will have at least a 20% reduction.

关 键 词：PARAMETERIZATION Square approximation APPROXIMATION Bezier curves End constraints 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]