Research Progress in Mathematical Analysis of Map Projection by Computer Algebra

doi:10.11947/j.AGCS.2017.20170396

Abstract

Abstract: Map projection is an important component of modern cartography, and involves many fussy mathematical analysis processes, such as the power series expansions of elliptical functions, differential of complex and implicit functions, elliptical integral and the operation of complex numbers. The derivation of these problems by hand not only consumes much time and energy but also makes mistake easily, and sometimes can not be realized at all because of the impossible complexity. The research achievements in mathematical analysis of map projection by computer algebra are systematically reviewed in five aspects, i.e., the symbolic expressions of forward and inverse solution of ellipsoidal latitudes, the direct transformations between map projections with different distortion properties, expressions of Gauss projection by complex function, mathematical analysis of oblique Mercator projection, polar chart projection with its transformation. Main problems that need to be further solved in this research field are analyzed. It will be helpful to promote the development of map projection.

Key words: map projection, projection transformation, Gauss projection, polar projection, computer algebra

CLC Number:

P282

BIAN Shaofeng, LI Houpu, LI Zhongmei. Research Progress in Mathematical Analysis of Map Projection by Computer Algebra[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(10): 1557-1569.

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