MODIFIED CYLINDRICAL PROJECTIONS IN CURRENT STANDARDS OF DISPLAY DEVICES

Abstract

The purpose of this work is to justify the need to develop display-oriented mathematical bases with orthogonal map grid and to find the parameters of normal conformal, equal-area and equidistance cylindrical projections for geographical maps of the world, adapted to the size of the screen frame. Method. Visualization of geographical images on GIS display devices requires the design of optimal parameters of elements of the mathematical basis of maps, which involves choosing or surveying a map projection, selecting a scale range of images, setting a map grid, etc., provided that the screen space is used as efficiently as possible. In order to effectively filling the rectangular frame of the display device, it's expedient to use the map projections with orthogonal grid of meridians and parallels, which include normal cylindrical projections. For ensuring the correlation between the sizes of the map image and display device the modified variants of cylindrical projections with a variable latitude of the tangent parallel or of the secant parallels are used. The advantages of this type of projection, in addition, include the possibility of operative calculation of the map grid parameters, high reproduction accuracy of forms and areas, the triviality of calculation of distortion parameters and inverse dependencies, the correlation between screen and geodetic or rectangular coordinate systems. Modified cylindrical projections are parameterized by latitude function, which allows the variation of distortion parameters depending on the position and size of the mapped area. Results. It has been experimentally proved that for the purpose of the most effective using of the display space, it is expedient to use orthogonal map grids with rectilinear meridians and parallels. The possibility and expediency using the modified cylindrical projections as mathematical bases of geographical maps of the world, which are intended for reproduction on display devices, is substantiated. The method of computing the optimal parameters of normal conformal, equal-area and equidistance cylindrical projections is proposed. The possibility of obtaining initial parameters and calculating projections at arbitrary relations of frame parameters of the display device by setting their values in the final equation of the corresponding map projections is established. Scientific novelty and practical significance. The scientific researches on the improvement of the mathematical bases of geographical maps in order to adapt them to the current standards of display devices in Ukraine were not performed. The obtained results can be used by software developers for creating cartographic web-services, as well as by cartographers – for developing the conditional mathematical bases of geographical maps of various territorial coverage. The use of modified variants of conformal, equal-area and equidistance cylindrical projections will significantly improve the quality of the design of map content of web-pages, will ensure the complete using of the screen space, high detailing of the map image and maximum display accuracy.