C-Bézier曲线显式降阶算法  

Algorithm for explicit multi-degree reduction of C-Bézier curves

作　　者：周联[1] 

机构地区：[1]上海海事大学文理学院,上海201306

出　　处：《上海海事大学学报》2012年第4期86-90,共5页Journal of Shanghai Maritime University

基　　金：国家自然科学基金(11226327);上海海事大学校基金(20120099)

摘　　要：基于C-Bézier曲线的约束降阶逼近问题至今仍未得到很好解决,运用分而治之的方法,根据端点约束条件先确定降阶曲线的约束控制顶点;再利用最小二乘法,给出未约束控制顶点.特别地,利用C-Bézier基函数的显式表达式,给出降阶曲线的显式表示.与已有算法比较,本算法具有精度最佳、一次降多阶、显式表示、端点高阶插值等优点.数值实验验证该算法的优质高效.As the problem of degree reduction with constraints of C-Bezier curve has not been solved well till now, by the method of ＂divide and conquer＂, the constrained control points of degree-reduced curve are firstly determined according to the condition of endpoint constraints. Then the unconstrained control points are determined by least square method. In particular, the explicit expression of degree-reduced curve is presented by the explicit expression of C-B^zier basis function. Compared with the existing algo- rithms, this algorithm has some advantages such as optimal precision, doing multi-degree reduction at one time, using explicit expression, maintaining high continuity at two endpoints and so on. Numerical examples show the effectiveness of the algorithm.

关 键 词：C-BÉZIER曲线 显式表示 约束 降阶 

分 类 号：TP391.411[自动化与计算机技术—计算机应用技术]