THE CONSTRUCTION OF EQUIDISTANT TO A FLAT BROKEN LINE IN THE FORMATION OF THE STRUCTURE OF RING WATER NETWORKS

Abstract

The paper notes that the uniform arrangement of lines and nodes of the water pipelines determines the rational laying of the water pipelines in the city structure. This is explained as taking into account the lack of previous uncertainty in the position of the nodes of the traditional order of laying the main water pipelines. The location of water pipeline nodes on the city border is not allowed since it is necessary to feed the territory from both sides, which corresponds to the economics of building and operating the network. Based on the analysis of recent studies and publications, it was determined that it is advisable to use support lines to evenly place pipelines in the city’s street network in the process of constructing new and reconstructing existing water pipeline and distribution systems. It is indicated that such lines should be taken equidistant on the city plan. They are equidistant from each other and from the perimeter of the city. The research objective is presented as the development of a method for determining reference lines for uniform tracing of pipelines of the city's main water pipeline network. The study examines the oriented closed polyline, which is formed by points on the plane and defines the boundary of urban development. The orientation of the equidistant relative to the inner closed region of the plane is determined. It is indicated that the position of each point of the equidistant is completely determined by three consecutive points of the limit contour; they do not lie on one straight line. The area and diameter of the triangle with the vertices on the equidistant are used, as well as the offset value of the equidistant. The paper considers a convex oriented contour and writes down the equation of lines passing through the points of the polygonal line. To maintain equality of distances and find the coordinates of a point, a system of equations with two unknowns is written and the main determinant of the system is calculated. The solution to the system is obtained by Cramer's formulas. It is noted that, depending on the value of the main determinant of the system of equations, the midpoint may be excluded from consideration, which changes the shape of the polyline. To get a lot of equidistant on the urban plan, you need to set the offset values in steps that depend on the average distance between the streets.