Distances on a map are referred to as grid distances and coordinates on the map are referred to as grid coordinates. To convert from grid coordinates to ground coordinates for a limited areal extent, a mean elevation factor and a mean scale factor for a region can be multiplied to create a combined factor. Using the single combined factor for the region, a custom map projection can be created that allows easy transformation from ground coordinate systems to grid coordinate systems or from grid coordinates to ground coordinates. Using OpenCities Map, custom coordinate systems can be created as described in this Help chapter: Editing Coordinate Systems.

Create a folder to hold custom coordinate systems, copy and rename delivered seed DTY file to the new folder. Add the MS_GEOCOORDINATE_USERLIBRARIES variable to point to that folder as instructed in help. Copy the standard coordinate system to the folder. The coordinate system must use either the Lambert Conformal Conic or Transverse Mercator map projection.

Edit the coordinate system that has been copied and set the Projection to either the Lambert Conformal Conic with Affine Processor or to Transverse Mercator with Affine Processor, whichever applies.

Note that six additional parameters for an affine transformation have been added. Change the name of the coordinate system to an appropriate name.

Map transformations initiate two processes: the map projection transformation followed by an affine transformation. Compute the inverse of the combined factor and insert the value for the affine parameters A1 and B2.

The affine parameters are inserted into the following transformation:

X = A1 * x + A2 * y + A0

Y = B1 * x + B2 * y + B0

To help distinguish ground coordinates from grid coordinates, large positive or negative values can be inserted into A0 for X and B0 for Y. The A2 and B1 parameters should be 0.

The affine transformation becomes a 2D conformal transformation with translation and scale parameters, but no rotation.

Those who need to use ground distances can work in design files with the custom coordinate system and attach reference files that have used a standard coordinate system.

Example:

An alignment file is provided with the following offsets and scale factors.

Add 150,000 to each X

Add 1,600,000 to each Y

Scale factor:  0.9999491860

The scale factor may be a mapping scale factor averaged for the project area or a combined mapping and elevation factor averaged for the project area.

The parameters for the projection with Affine Processor would be:

A0 = -150000

B0 = -1600000

A1 = 1/0.9999491860

B2 = 1/0.9999491860

A2 = 0

B1 = 0

The following GCS started with IN83-EF and was edited to: