Pavlenko O. Geometric modeling of vertical planning of a horizontal land plot by means of point BN-calculus

The object of the study is vertical planning of the land plot. The aim of the research is to solve the important scientific and technical problem of vertical planning of a horizontal land plot by means of the Balyuba-Naidysh point calculation. During the research methods of differential, analytical geometry, group theory, numerical methods, affine transformations were used. In the course of the study, for the first time, in terms of BN-calculus, an algorithm for finding the point of tangency of a curve defined by a point equation with a straight line is found in the plane of this curve from its convex side; An algorithm is developed to compile the initial finite discrete set of points to form a discretely represented surface in the form of discretely represented contours; a name has been introduced and a "Method for the growth of cells" has been developed; The method of calculation of volumes for elements of a topographical surface is developed; A generalized method for calculating a design mark and finding, in a discrete representation, a line of zero works, has been developed. In the process of research, a methodology was developed for determining the design mark and the line of zero works to optimize the vertical planning of the land plot, as well as the transition from the original disordered point cloud to the ordered two-dimensional discrete topographic surface, which fully reproduces the surface of this set of points, starting points, in comparison with the initial cloud, makes it possible to reduce the errors and costs of calculations in the process of vertical of land planning.