中文摘要：

本文讨论参数曲线的近似弧长参数化插值方法。基于保单调插值方法,用分段五次（或五次以上）Bernstein多项式构造了弧长函数的反函数局部逼近解t=T（s）,且T（s）是C^2连续的。将t=T（s）代入原参数曲线,得到C^2连续的近似弧长参数化曲线。这种近似弧长参数化曲线不但插值原参数曲线上的一组点,且在这组点有着精确的弧长参数化。进一步研究表明近似弧长参数化曲线可由原参数曲线经参数变换得到,所以它们有着完全相同的几何形状。最后,导出了近似弧长参数化曲线切失模长与1有二阶误差。

英文摘要：

This paper discusses nearly arc-length parameterized curve. Based on the piecewise rational polynomial monotonicity preserving interpolation, the local approximation for the inverse function of the are-length function is obtained by piecewise quintic （or more than degree 5） Bernstein polynomials, and the approximation is second order continuously differential. A C2 nearly arc-length parameterized curve is obtained by substituting the approximation into the original parametric curve. The nearly arc-length parameterized curve interpolates the ordered points in the original curve and even has its accurate arc length parameterized at this set of ordered points. Moreover, our further study shows that the nearly arc length parameterized curve carries the exactly same geometric shape of the original curve because it comes from a kind of parametric transformation of the original curve. Finally, second order error estimation of tangent vector module from 1 is derived for the nearly arc length parameterized curve.