METHODS OF CONSTRUCTING DISCRETELY REPRESENTED EQUIDISTANTS FOR OPTIMIZING THE PLACEMENT OF FORTIFICATION STRUCTURES

Abstract

This study is devoted to the development of an algorithm for geometric modeling of equidistant curves (offset curves) in cases where the base curve is given in discrete form as a set of coordinate points. This approach is of significant importance for architectural and engineering design, geoinformation analysis, spatial modeling, and improving the efficiency of defense technologies that require the determination of safe areas, buffer zones, and functionally optimal placement of defense-related objects, in particular fortification structures. It is especially important that in defense-related problems the input data are often represented in discrete form, for example as coordinates from observation systems, digital maps, or geodetic measurements.

Two methods of geometric modeling of discretely represented equidistants at a specified distance from the edges of a base discretely represented curve (DRC) are proposed. The first method is based on determining the vertices of the equidistant curve by intersecting adjacent edges of the equidistant, constructed using perpendiculars laid off at a given distance from the corresponding edges of the base DRC. The second method defines the equidistant parameter as the distance from a vertex of the equidistant curve to the midpoint of an edge of the base DRC, which allows obtaining another result in the form of coordinates of the equidistant vertices. Both methods enable the construction of both inner and outer equidistants.

Test examples clearly demonstrate the construction of two equidistants at a given distance using both methods, as well as an analysis of special points of the equidistant when the equidistant parameter exceeds the radius of curvature of the base curve, including cusp points on the evolute and a self-intersection point of the equidistant.

The obtained results demonstrate the effectiveness of the proposed methods for modeling geometric objects, particularly in the context of determining rational placement of defense-related objects and spatial analysis. The prospects for further research are identified, aimed at improving methods of geometric modeling of discretely represented equidistants and optimizing computational algorithms to increase accuracy and efficiency.

Keywords: geometric modeling, equidistant curve, discretely represented curve, defense-related objects, fortification structures.