参数曲线近似弧长参数化的插值方法

AN INTERPOLATING METHOD FOR NEARLY ARCLENGTH PARAMETERIZATION OF PARAMETRIC CURVES

本文提出了参数曲线近似弧长参数化的一种插值方法。参数曲线的弧长函数是单调增的，近似弧长参数化可以转化为弧长函数的保单调分段有理线性插值。用这种插值得到的近似弧长参数化曲线插值原曲线上的一组点。最后，两个实例表明了近似弧长参数化曲线能很好地逼近原曲线，且没有所不希望的波动。

This paper presents an interpolation methods for nearly arc length parameterization of parametric curves. The arc length functions of parametric curves are monotonic descreasing, nearly arc length parameterizations can be converted into monotonitypreserving interpolations of arc length functions by piecewise rational linear polynomials. With the interpolation, resulting nearly arc length parameterized curve interpolatesa set of points of original curve. Two numerical examples illustrate the parameterizedcurves are also likely to have shapes that are close to those of the original curves withnowanted oscillations.