Discrete (pixel) presentation of a transport network of city for topological authentication and fractal analysis her geometrical constituents
Abstract
Work is sanctified to development of methods of discrete (pixel) presentation of a transport network of city for topological authentication and fractal estimation her structural constituents.
Development of a transport network of cities goes, as a rule, by complication of topological structure of routes of movement and mutual relations between geometrical descriptions them separate elements. Such tendencies testify to the necessity of development of effective mathematical methods of design of new and optimization of already existent networks, that algorithms of analysis and quantitative estimation of quality of functioning of a transport system of city will be the basis of.
Properties of a municipal transport network depend substantial character on complication of her geometry and topological structure. The analysis of literary sources showed that a transport network of city, from topological positions, it can examine as an aggregate of large number of the up-diffused points or areas (зупинкових knots or limited territories) that co-operate inter se through transport channels, id est routes. Thus, a topology of a difficult transport network is a casual fractal, as her small part is similar whole. The dimension of this great number of points, areas and lines has a fractional dimension. Expecting the dimension of network, it is possible in number to express her system properties and to find general conformities to law of improvement of existing and construction of new transport streams.
At determination of fractal dimension of image a cellular method a geometrical network structure, at every step iterations, is covered by cages determined size. Consequently, it is suggested, at once, to present an image in a discrete kind on a grate with the cages of low-limit (there can be a size of pixel), to identify the fragments of the set structure, and in further to expect necessary geometrical parameters and conduct their analysis. Thus, it is necessary to classify separate objects and fragments, and also find out geometrical criteria, after that the degree of fractal of both fragments and structure will be determined on the whole.
For authentication of images topological classification of discrete models of geometrics and combined great numbers is offered on a plane. Basic descriptions of connectedness of separate cages of discrete binary models of great numbers of arbitrary dimension are certain. Offered structure of practical authentication of combinations of geometrics, that meet on the images of municipal rout charts.
Further researches from this subjects are conducted in the direction of selection and calculation of geometrical descriptions of objects for the offered discrete cellular models.
Keywords: a transport network of city, discrete presentation, topological authentication, fractal analysis, combined great numbers, cellular model.
