Inverse Transformation for Several Pseudo-cylindrical Map Projections Using Jacobian Matrix

Abstract

The normal practice in ‘mathematical cartography’ is transforming the graticule of meridians and parallels of a sphere onto a plane. The conversion from geographical to plane coordinates is called forward transformation. The inverse transformation, which yields geographical coordinates captured from paper maps, is a more recent development, due to the need for transformation between different map projections especially in Geographic Information Systems (GIS). Deriving the invers equations is sometimes not easy for the projections that have complicated forward functions including parametric variables. This paper describes an iteration algorithm using jacobian matrix for the inverse transformation of the pseudo-cylindrical map projections with non-linear forward projection equations. The method has been tested for ten pseudocylindrical world map projection.