Approximately Conformal, Equivalent and Equidistant Map Projections

Abstract

If geodetic coordinates from an ellipsoid are included in the equations of a projection for mapping a sphere instead of geographical coordinates, the result will be a projection of the ellipsoid into a plane. This will slightly change the distortion distribution of the initial map projection. The question is to what extent the replacement of geographical with geodetic coordinates will affect this change. In this paper, we deal with conformal, equal-area and equidistant projections of the sphere, which we modify by using geodetic coordinates instead of geographical ones. The result will be an approximately conformal, approximately equal-area and approximately equidistant projection. It is shown that in this case the maximum distortion of the angles in approximately conformal projections will be approximately 23.09', the maximum distortion of the area in approximately equal-area projections less than 0.7% and the maximum distortion of lengths in approximately equidistant projections less than 0.7%, therefore on the maps imperceptible.

Keywords

• |map projections|double mapping|approximately conformal projection|approximately equal-area projection|approximately equidistant projection