参数曲线弧长的一种估算方法  

A Method for Estimating the Arc Length of Parametric Curves

作　　者：白鸿武[1,2] 

机构地区：[1]西北工业大学理学院,西安710072 [2]咸阳师范学院数学与信息科学学院,咸阳712000

出　　处：《机械科学与技术》2010年第1期24-27,共4页Mechanical Science and Technology for Aerospace Engineering

基　　金：国家自然科学基金项目(60672135);陕西省教育厅2009年度科学研究计划项目自然科学专项(09JK809)资助

摘　　要：研究了如何估算任意次多项式形式参数曲线的弧长曲线的问题。与目前已有类似方法相比,我们方法的优点是对曲线的次数没有限制。这里的关键问题是如何求出弧长曲线的拐点以及如何对曲线进行分割。利用Bézier曲线的变差缩减性用牛顿迭代法计算出了弧长曲线的全部拐点,进而可以得到原曲线的Bézier曲线形式的近似弧长曲线。数值实验表明,用该方法得到的弧长曲线是令人满意的。We studied the problem of how to estimate the arc lengths of parametric the polynomial form. Compared with the current similar methods, the advantage of constraint to the degree of the curves. The key problem here is how to calculate all length curve and where to divide the original curve. Using the property of variation curves with arbitrary degree in our method is that there is no the inflection points of the arc diminishing for Bezier curves, we calculated all the inflection points of the arc length curve by Newton iteration method and obtained the approxi- mate arc length curve for the original curve in B6zier form. Numerical experiments show that the results of the arc length curve obtained by our method are satisfactory.

关 键 词：弧长参数化 近似 曲线设计 B6zier参数曲线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]