Approximation of points by polynomial surfaces in the Wolfram Mathematica package

Ivashchenko Andrey Viktorovich, Vavanov Dmitry Alekseevich

Variants of approximation of an array of points in three-dimensional space by surfaces described by polynomial equations are considered. A practical task was set: to generate a surface from the known coordinates of points in three-dimensional space, and then use it with BIM modeling tools as a topographic surface. It is possible to approximate points in three-dimensional space with different surfaces, and since the relief of the untreated earth's surface is generally random, no restrictions are imposed on the nature of the surface, except that it must be described by the equation: z=f (x, y).The results are analyzed in terms of the reliability of the obtained relief and the complexity of the equation.

Keywords:Surface approximation, approximation algorithms, array processing, topographic surface, Mathematica program, Revit package.