Processing of materials of laser scanning of roads on the basis of recursive cubic splines

摘要

The problem of approximation of discrete dependence (t_i,y_i) by means of continuous function f(t) arises in tasks of the analysis and data processing of measurements y_i at successive time points of t_i. The solution of the presented task becomes significantly complicated in cases when measurements form a continuous stream, and the results of processing are required to be used before full reception of measurements. The computational schemes based on recurrent spline of degree 3 depths 1 and 2 which provide accuracy for polynomials of the third degree were used in the work. The main results consist in elaboration of mathematical formulas and the proof of stability of the constructed computing schemes. Relevance of the work consists in possibility of application of the constructed splines, for example, for processing materials of laser scanning of roads. Advantages of the constructed splines are the piecewise cubic character of the recovering of the simulated smooth spatial curve and possibility of nonuniform sampling on the route when the quantity of spline knots are less than the number of samples of a function. Examples of calculation of parameters of computing schemes, and also results of numerical experiments are presented.