Bézier曲线的近似弧长参数化方法  

An Approximate Arc-Length Parameterization Method for Bézier Curves

作　　者：白鸿武[1] 叶正麟[1] 张书玲[2] 

机构地区：[1]西北工业大学理学院,西安710072 [2]咸阳师范学院数学系,咸阳712000

出　　处：《计算机辅助设计与图形学学报》2006年第8期1165-1168,共4页Journal of Computer-Aided Design & Computer Graphics

基　　金：陕西省教育厅专项科研计划项目(05JK309)

摘　　要：通过求出曲线近似二分之一弧长的点及其相应的参数值,可将曲线分割为2段Bézier曲线,这2段曲线的弧长近似相等,而且都具有单位长度的参数区间;将这2段曲线看作一个整体并对它们的参数进行全局化,可得到一条新曲线,其近似弧长的中点对应于新的全局参数区间的中点;对新生成的Bézier曲线不断重复上述工作,最终得到一条分段Bézier曲线.将该曲线表示为B样条曲线的形式便得到一条近似弧长参数化曲线.A method for approximating arc-length parameterization for Bézier curves by using the subdivision techniques is presented. By finding the point of approximately half the arc-length of the curve and subdividing the curve at the corresponding parameter value, we got two Bézier curves, which have approximately equal arc-length and parameter interval of unit length. Viewing the two curves as a whole and globalizing their parameters, we got a curve such that the point of the approximately half the arc-length corresponds to the midpoint of the new global parameter interval. Repeatedly doing this to the newly generated Bézier curves and we can finally get a piecewise Bézier curve. Then we can get a curve with approximate arc-length parameterization by expressing the curve in B-soline form.

关 键 词：参数化 算法 BÉZIER曲线 有理BÉZIER曲线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]