极区高斯投影与日晷投影的比较

Comparisons Between Gauss and Gnomonic Projections in Polar Regions

为解决传统球面高斯投影公式在极点处的奇异问题,通过引入余纬度对原有投影公式进行改进,推导了极区高斯投影非奇异公式;基于该公式推导了极区经纬线投影方程,并结合日晷投影进行长度变形及子午线偏移角分析。结果表明,在余纬度很小时,高斯投影与日晷投影非常接近,即其经纬网与日晷投影近似;在极圈内高斯投影长度变形小于日晷投影,其经线与日晷投影经线的最大偏移角为2.468 8°,而在纬度80°以上,最大偏移角为0.438 6°。极区非奇异高斯投影公式满足了极区内连续投影的需求,可为极区海图绘制提供理论依据。

To overcome the singularity of traditional formulae o~ Gauss proiection on the sphere in po- lar regions, the traditional formulae were improved and lastly nonsingular formulae of Gauss projec- tion in polar regions were carried out with introduction of colatitude. Based on the nonsingular formu- lae, equations of meridian and parallel were got. Compared with gnomonic projection~ analysis of length deformation and meridian deviation angle of Gauss projection were done. It ＇s showed that when the colatitude was small, Gauss projection was similar to gnomonic projection, in other words, graticules of the two projections were approximate. Length deformation of Gauss projection was smal- ler than gnomonic projection^s, and the largest meridian deviation angle of Gauss projection from gno- monic projection is 2. 468 8° in polar circles, while the largest value above the line of latitude=80° is 0. 438 6°. The nonsingular formulae in polar regions could satisfy the need for continuous polar projec- tion and provide theoretical basis for polar charting.