中文摘要：

研究了准均匀三次B样条曲线的多分辨率光顺法,在B样条曲线两种不同定义及方法的基础上,详细描述了准均匀三次B样条曲线的多分辨率表示,并最终实现了三次B样条曲线的小波分解与重构算法.实例研究表明,多分辨光顺算法在提取高频细节后,能够快速实现对曲线的滤波和光顺,并且在光顺的同时,具有减少控制顶点、压缩数据的能力,兼具简单性和快速性的优点.

英文摘要：

The cubic B-spline multiresolution compliance method was studied in this paper. On the basis of the two different definitions and methods of B-spline curve, the multiresolution representation of quasi-uniform cubic B- spline curve was described in detail, and the quasi-uniform cubic B-spline wavelet decomposition and reconstruction al- gorithm were realized. Case study showed that, after the muhiresolution compliance algorithm extracted high-frequency features, then smoothing and filtering the curve could be rapidly performed. At the same time of compliance this meth- od had the ability of reducing the control vertex and compressing the data, and it also had the advantages of both sim- plicity and rapidity.