1. Changing the coordinate system of vector map.

If the coordinate system of a map is unknown, it can be bound to a map with certain coordinate system by points in this task.

If the parameters of the input and output coordinate systems are uniquely defined (spheroid, datum, projection), then for transformation it is possible to use rigorous formulas of the spherical geodesy. In this case to transform the map is necessary in the task «Transformation of map by template» («Thread region to sheets» dialog).

But often the parameters of the input or output coordinate systems are unknown. Only the coordinates of points in the output or both coordinate systems are known. In this case, the transformation can be done in this task.

If the transformation is performed for a small area, then the transformation is enough accurately described by a polynomial.

The degree of a polynomial is chosen manually by sequential increase in the number of coefficients as long as the standard deviation becomes less than the admission of the accuracy of transformation. Be aware that to obtain reliable parameters, the points should be placed evenly and their number should significantly exceed the number of polynomial coefficients.

If the use of a polynomial does not yield the desired accuracy, then to take into consideration local nonlinearity of coupling coordinate systems it is possible having applied types of transformation «linear - a non-linear rubber sheet». In these types of transformation the  coordinates transformation parameters are calculated separately for each triangle of a Delaunay triangulation constructed from the measured points. Therefore the more points, equally located, are measured, the more accurately the total surface of nonlinear distortions is described by a set of transformation parameters of individual triangles.

When using the conversion-type «rubber sheet» residual differences in the points will always be equal to zero, which complicates the search for erroneous measurements. To find inexactly the measured points is possible by residual divergences at polynomial method of transformation, or having compared the matrixes of distortions constructed by a polynomial and a «rubber sheet». Comparing the matrixes, special attention should be paid to the points at which the values of nonlinear distortions are significantly different, perhaps these differences are caused by measurement errors.

2. Elimination of non-local deformations of vector map.

At each technological stage of creation and updating of vector maps random and systematic errors are introduced into position of the contours relative to their actual location. As a result, vector map often does not meet its demands for accuracy. Often these distortions are detected by combining the previously digitized map with photomaps during the upgrade.

These errors can be eliminated by performing a transformation of map by using transformation «rubber sheet». The input and output coordinate systems are virtually identical, therefore to measure points more conveniently in one window.

Measurement of points is best to do in two stages. First, to measure the points at which the displacement exceeds the tolerance, then to measure in addition points in locations where there is a bit of measured points. As a result, the measured points should be approximately evenly spaced on a sheet of map. Should be measured solid contours, which are not shifted relative to the true position when creating the map.

3. Elimination of the mutual displacement of the various map layers.

On some maps the different layers in different ways are shifted relative to their true position. This happens, if the map was be digitized by a paper map, at print of which there was a shift of objects of different colors. In this case, the transformation should be done separately for each set are equally displaced objects. For this purpose transformation should be executed several times, having marked the transformed objects by layers before starting the task. Displacements usually have linear character, therefore for elimination of distortions there is enough application of affine transformation.