计算机绘制粒度分布曲线的插值方法

A Computer Interpolation Method for Drawing Curves of Grain Size Distribution Data

张力样条是在三次样条函数中加入张力系数而构成。根据相同的粒度数据用两种方法在计算机上所作的粒度分布曲线图形的对比，显示出张力样条方法比三次样条方法有明显的优越性，它消除了插值曲线的不必要的摆动，在保持曲线平滑的前提下，能更准确地表达沉积物的粒度特征。用张力样条结合将离散点连成光滑曲线的阿克玛方法进行插值，使复杂的粒度分布曲线的插值同时保持准确性和平滑性，在沉积物粒度的数据的计算机处理方面有明显的意义。

A computer interpolation method based on spline in tension and for drawing curves of grain size distribution data is suggested in this paper. The spline in tension is derived from a cubic spline by adding a tension coefficient in the later part of the curve. The grain size curves drawn with a computer according to the same grain size data with the two methods indicate that the spline in tension is more precise than the cubic spline in drawing grain size distribution curves, because the former can eliminate wiggles, while wiggles is always produced by the latter. However, the interpolation between two data points calculated with no matter the cubic spline function or the tention spline function depends on all points of a data set, which result in the interpolation values produced by the both functions cannot simultanously fit a waving curve and a straight line. So that if the grain size distribution curve is too complicated, wiggles may usually occur near the end of the curve. Akima method can produce interpolation between data points without considering the effects of all points of the data set and some points near the interpolation section of the curve are enough for the calculation. For keeping smooth and precision of the grain size distribution curves simultaneously, the interpolation can be improved by combinding the function of the spline in tension with a method of Akima in the calculation. This can be easly processed with a computer.