Direct Transformations Formulae Between Polar Gauss and Stereographic Projections

摘要

Definitions of polar Gauss and stereographic projections are introduced, and the two projections sketches of the Arctic Circle are drawed with the help of Geocart software, according to these two projections formulae. From the angles of real and complex numbers respectively, direct transformations formulae between polar Gauss and stereographic projections are derived through series of derivations. Finally, correctness and reliabilities of the formulae are tested and verified by numerical examples by comparing the calculated coordinates of the projections formulae with the calculated coordinates of the projection transformations formulae. The formulae have universal applicability, and it can provide reference for polar mapping and navigation.