Several theoretical misconceptions in the description of the Gauss–Krüger (GK) projection exist in the literature, particularly concerning the conditions for conformality and the use of imprecise mathematical definitions. This work addresses these issues by rigorously restating the necessary and sufficient conditions for conformality. Building upon this theoretical foundation, four commonly used analytical formulations of the ellipsoidal GK projection and one special formulation of the spherical GK projection are systematically reorganized. In addition, two new definitions based on Jacobi elliptic functions and integrals are introduced as both supplements to and extensions of existing methods. These definitions are mutually independent yet interrelated. In particular, the two new definitions are mathematically equivalent to, and just as concise as, Lee’s exact method. It is hoped that this contribution will stimulate further theoretical engagement with the GK projection within the geodetic and cartographic communities.
Guo et al. (Thu,) studied this question.