NONZONAL EXPRESSIONS OF GAUSS–KRÜGER PROJECTION IN POLAR REGIONS
- Dept. of Navigation, Naval University of Engineering, Wuhan, 430033 China
Keywords: Gauss-krüger projection, transverse Mercator projection, polar surveying, reference frame, conformal colatitude, computer algebra system
Abstract. With conformal colatitude introduced, based on the mathematical relationship between exponential and logarithmic functions by complex numbers, strict equation of complex conformal colatitude is derived, and then theoretically strict nonzonal expressions of Gauss projection in polar regions are carried out. By means of the computer algebra system, correctness of these expressions is verified, and sketches of Gauss-krüger projection without bandwidth restriction in polar regions are charted. In the Arctic or Antarctic region, graticule of nonzonal Gauss projection complies with people’s reading habit and reflects real ground-object distribution. Achievements in this paper could perfect mathematical basis of Gauss projection and provide reference frame for polar surveying and photogrammetry.