A Computer-Based Method for Drawing a Smooth and Monotone Curve of the Grain Size Distribution Data

To draw a computer plotted cumulative curve by an interPolation function, it is essential to Possess the characters of monotonicity and smoothness. Based on a method to construct a sort of monotone and smooth interpolation function, the computer drawing of the cumulative curve of the tgrain size data has been realized with the monotonicity and the first or more than first order of smoothness of the cumulative curve. By the derivative function of the interpolation function, the homologous frequency curve has been plotted in the computer as well with its smoothness corresponding to that of the cumulative curve. Because the grain siza distribution (in phi scale ) of sediments follows the normal distribution and Rosin's distribution, while as an approximating function, the cubic spline interpolation function can satisfy (with some restriction) the monotonicity of the probability distribution functions of these two sorts of distribution in an interval, in which there is more than 90% of the area under the probability density curve, so in the method introduced in this paper, the cubic spline function is taken to be the interpolation function in the main part of the data interval [a,b]. In those subintervals in which there exist points of s' (x)0,two classes of the elementary functions are assigned to be the interpolation functions with the character of monotonicity and at least first order of smoothness at all knots. By this interpolation function.besides plotting the monotone and smooth cumulative curve and corresponding frequency curve,grain size parameters of moment and graphic measures can be calculated through the interpolation and percentiles computation. From the information revealed by the frequency curve, such as number of the peaks, location of each Peak, the Peak values, correlation among the peaks, and so on, the further studies could be taken out on the characteristics of the dynamics, environment,source and transportation of the sediment. The method has provided a basis for developing a software of the grain size analysis data processing to treat the data effectively and with high quality.And it is of benefit to remedy the defect of other means in exptessing grain size distribution characters and to make it more exactly and more comprehensively.