Forward and Inverse Expressions of Polar Gauss Projection without Zoning Limitations

doi:10.11947/j.AGCS.2017.20170009

Abstract

Abstract: As traditional formulae of Gauss projection could not be used in polar regions, strict equation of complex conformal colatitude was derived with relationship between conformal colatitude and isometric latitude introduced, and then strict forward expressions of Gauss projection suit for polar regions were carried out. Based on relationship between exponential and trigonometric functions, inverse expressions of polar Gauss projection were derived by means of symbol iteration method. With reference to the forward expressions, corresponding equations of length ratio and meridian convergence for polar Gauss projection were achieved. Finally, Taking CGCS2000 ellipsoid for example, by comparing with results calculated by formulae of Gauss projection in power series forms, correctness of the proposed expressions was verified. Expressions in this paper are all free from bandwidth, and can be used in the entire poles, which could provide important references for polar mapping and navigation.

Key words: Gauss projection, polar region, forward and inverse solution, length ratio, meridian convergence angle

CLC Number:

P282.1

LI Zhongmei, BIAN Shaofeng, JIN Lixin, CHEN Cheng, LIU Qiang. Forward and Inverse Expressions of Polar Gauss Projection without Zoning Limitations[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(6): 780-788.

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