参数曲线近似弧长参数化方法

１．引 言 曲线参数化是对一条曲线建立参数方程的过程，而弧长参数化是指以曲线本身的弧长为参数建立参数方程．但是，我们知道曲线的弧长是由曲线的参数方程来计算的．设曲线的参数方程为它的弧长可表示为 显然，弧长函数Ｓ（ｔ）一般没有解析表达式，即使有，它的反函数ｔ＝ｔ（ｓ）也未必能求出．因此，精确地实现一般参数曲线的弧长参数化是不可能的．然而，在实际应用中弧长参数化是十分重要的．例如，在 ＣＡＤ系统中，沿一条参数曲线等距离（弧长）分布铆钉；数控加工中要求快速实现刀具运动轨迹的弧长空间位置“时空”转换，这里要…

A Method for Nearly Arc-Length Parameterization of Parametric Curve

This paper presents a methofor nearlarc-length parameterization based on the rational quadratic function. The arc-length function of parametric curve is mon- tonic increasing, the monotonity preserving approximating function based on ratio- nal quadratic function for the axc-length function is derived. The resulting nearly arc-length parameterization curve interpolates a set of points of original curve, at each of the points, nearly arc-length parameterization curve is accurate. Finally, two examples illustrate that the metod is very efficient.