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

International Scientific Conference of Young Scientists: Advanced Materials in Construction and Engineering

材料科学;土木建筑工程;工业技术

Esharov, E.A.^1 ; Shumilov, B.M.^1

Tomsk State University of Architecture and Building, Department of Applied Mathematics, Tomsk

634003, Russia^1

关键词: Computational schemes;    Computing scheme;    Continuous functions;    Mathematical formulas;    Nonuniform sampling;    Number of samples;    Numerical experiments;    Proof of stability;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/71/1/012046/pdf
DOI  :  10.1088/1757-899X/71/1/012046

来源: IOP

【 摘 要 】

The problem of approximation of discrete dependence (ti, yi) by means of continuous function f(t) arises in tasks of the analysis and data processing of measurements yiat successive time points of ti. 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.