极区非奇异高斯投影复变函数表示

摘要

Based on expressions of Gauss projection by complex numbers , the conformal latitude by complex numbers was introduced to solve the singularity problem of isometric latitude in polar regions . Secondly ,conformal colatitude by complex numbers was introduced on the basis of conformal latitude by complex numbers ,with the polar point taken as the origin of coordinates in Gauss projection ,the non-singular formula of Gauss projection in polar regions by complex numbers was set up .Finally ,compared with traditional power series and expressions by complex numbers of Gauss projection ,the non-singular formula proved to be highly accurate .The new expression of Gauss projection in polar regions could overcome imperfection of zonation of traditional Gauss projection ,which makes Gauss projection a uniform integrated form in pol ar regions .%在高斯投影复变函数的基础上，引入复变等角纬度的概念，避免等量纬度在极点的奇异性。其次，在复变等角纬度的基础上引入复变等角余纬度，并将极点作为高斯投影的坐标原点，建立了极区非奇异高斯投影复变函数表示形式。最后，与传统高斯投影幂级数及以往复变函数表示式相比较，验证了该公式的准确性。新的极区高斯投影表达式克服了传统高斯投影分带的缺陷，使得高斯投影在极区有一个统一的完整的“一体化表示形式”。