Algorithm for constructing an arbitrary route on a discrete plane and its executable description

Abstract

Nowadays, modeling, in particular simulation, is becoming one of the most common methods of analysis and design in the field of transport. A large number of tasks in this area are related to the construction and study of the characteristics of routes on a plane. The use of computers as a tool for this first and foremost requires the creation of adequate and efficient ways to represent these routes in waters and territories in a computing environment. The classic representation of this kind is discrete space, in which each element of the physical surface is one-to-one mapped to the element in the computer memory. As a result, a rectangular array of data is correlated with the real physical space, each element of which contains certain properties of the original object selected for modeling, the composition of which is determined by the specifics of the task. This method of representation is considered to be the most efficient from a computational point of view. At the same time, it has a significant drawback, which is explained by the different nature of the properties of the original object and its computer model, namely, the continuity and discreteness of the basic representations. Any curves and even straight lines that are not orthogonal to the coordinate system are depicted in the form of stepped fragments, which can sometimes lead to the loss of the most basic characteristics. The most obvious example is the difference in these representations of distances, or proximity metrics: Euclidean and Manhattan. In addition, the digitization of curvilinear objects, understood as their transfer from a continuous geometric plane to a discrete space, is a complex and ambiguously solvable task. An efficient and objective algorithm used to solve this problem is described in the paper.