Methods of automated definition of elements for mathematical basis of maps
ISBN 978-85-88783-11-9
Authors
1Zagrebin, G.
1MOSCOW STATE UNIVERSITY OF GEODESY AND CARTOGRAPHY Email: gleb@cartlab.ru
Abstract
Over the last century, there are many published maps which have practical and historical value. It is convenient to convert and use these maps into the digital form in geographic information systems in modern conditions. It is necessary to know their mathematical basis for this purpose. The main problem is that there is no any information about map projection in which a map. In the best case there is a map grid and the name of the projection without parameters. So there is a question of the definition projection and its parameters and the reference image in the coordinate system geographic information system. There are some ways to solve this problem. At first, it is the using of the special atlases or the libraries of the map projections in which each mapping the territory corresponds to the projection or more appropriate projections. Therefore, the first step to define the projection is its searching in the Atlas projections and mapping the grid/contour-site with the image in the Atlas of the published card. At second, it is necessary to calculate the searching region/projection according to the anchor points if we cannot find it in the Atlas projections. To do this at first we need to set breakpoints in the nodes of the map grid (or geographical objects in the absence of the grid) so that the mathematical apparatus can accurately calculate the projection and its parameters. For example in conic projections with different parameters map grid from the main Parallels are almost not distinguishable at the same time the southern and Northern part of the differences can be large values. So the point must be set not only in the Central part of the map and maps. We should note that the position of the reference points should help to determine parameters such as the curvature of the grid lines on the same parallel/meridian must be at least three points. The number of the points must match the type of the transformation and the ability to hold control. At the same time a large number of points slows down the work of the operator/cartographer creation maps that will negatively affect operational performance. The Method for automated determination of the projection for the maps: selection from a list of the areas time of publication country of publication maps and other settings (these settings may already be in the metadata map); creating checkpoints; automatical searching of the projection of the libraries projections metadata and control points; adding checkpoints (if necessary); refinement of the list of projections for the count, and the distinctive characteristics of a map grid (the curvature of the lines, display poles, and so on) auto (control points) or in interactive mode; automatic determination of the projection from the list and calculation its parameters by trying all possible values and calculate the mean square error also at this stage is the consideration of deformation of the paper; polynomial transformation from the original image into the coordinate system of the GIS or in the theoretical coordinate system of the original image. The stages of the methodology implemented in created by the author specialized software that provides automation of determining the mathematical foundations of the published maps. The Atlas of the map projections was created as a result of this great work which brings in correspondence the mapping area with a particular map projection and its parameters. There was determineted time for using of each projection and the country in which it is used.
Keywords
map projection; transformation; software