Optimal conformal map projections in harmonic polynomials in terms of Gauss-Schreiber coordinates

Abstract

The Gauss–Schreiber projection generates a kind of rectangular isometric coordinates that allow to represent, in a continuous form, a terrestrial sector in NS extension including the poles. When they are applied in harmonic polynomials, they enable the optimal mapping of regions that are impracticable for other variables commonly used, e.g. Mercator or stereographic. In this paper, we present the detailed development of the polynomial in Gauss–Schreiber coordinates and an algorithm for map projection optimisation according to the Chebyshev–Gravé's thesis. The result is practical and allows the use of stereographic polar coordinates to be replaced.

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