Comparisons and Direct Transformation Formulae between Azimuthal Conformal and Gnomonic Projections

Definitions of azimuthal conformal and gnomonic projections were introduced, and contrastive analyses of graticules shapes between these two projections were conducted. Based on theories of perspective azimuthal projection and space geometrical relationships, transformation between azimuthal conformal and gnomonic projections was carried out through series of derivation. Direct transformation formulae between coordinates of the two projections were established with respect to standard parallel. Finally, correctness and reliability of these formulae were tested and verified by numerical examples. The formulae could be widely used and enrich theories of projection transformation to a certain degree, which would offer reference value for charting in polar regions.