椭球几何学是地球科学尤其是大地测量学的基础。高斯投影是地形图、GIS和各类工程建设的基础投影方式，应用极其广泛，但正南北走向、分带极大地限制了其应用场合。这两类问题，由于受过去人工推导的限制，解决的绝非完美。计算机代数为这两类问题的进一步完善和发展，提供了强大的支持。本项目拟以具有强大符号运算能力的计算机代数为工具，革新椭球几何学和高斯投影数学分析理论；广泛利用空间解析几何和微分几何理论，建立大地主题解算新算法；通过椭球的平移、膨胀、变形，使椭球更适用于地区控制网；通过研究法截线、大椭圆线，建立非南北走向的任意高斯投影复变函数表示，使之更适用于任意走向长线型工程；结合工程建设，如我国高速铁路建设，研究任意方向高斯投影的变形控制方案。项目预期研究成果将革新和丰富传统的几何大地测量和高斯投影理论，导出一些理论上更严密，形式上更简单，精度上更精确的符号化表达式，具有广泛的应用前景。

Ellipsoid geometry is the foundation of geosciences, especially of geodesy. As the basic projection of topographic maps, GIS and various kinds of engineering projects, Gauss projection is widely used. However, the south-north direction and zoning greatly limit its application. These two types of problems are not solved perfectly due to the limitations of the artificial deduction in the past. Computer algebra provides strong support for further improvement and development of these two types of issues. This project intends to use the computer algebra with strong symbolic computing power to innovate the theory of ellipsoid geometry and Gauss projection mathematical analysis, to establish a new algorithm for calculating the earth's theme by means of spatial analytic geometry and differential geometry theory, to make the ellipsoid more suitable for regional control network by ellipsoidal transformation method, to build the expressions of arbitrary Gauss projection by complex function, which can be used for any long-line engineering with normal section line and large ellipse line studied. What’s more, by combining with engineering construction, such as China's high-speed railway construction, the deformation control program for Gaussian projection with different directions will be studied. Expected research results of the project will innovate and enrich the traditional theory of both geometric geodesy and Gauss projection, derive a number of simpler in form, theoretically more rigorous and accurate symbolic expressions, which has broad application prospect.