地图投影计算机代数分析研究进展
发布时间：2018-10-26 14:04
【摘要】：地图投影是现代地图学的重要组成部分,涉及大量的椭圆函数幂级数展开、隐函数复合函数微分、椭圆积分、复变函数运算等一系列烦琐的数学分析过程,人工推导不但费时费力,而且容易出错,有时由于难以忍受的复杂性等各种原因,甚至根本无法实现。本文主要从椭球各纬度间正反解符号表达式、不同变形性质地图投影间的直接变换、高斯投影的复变函数表示、斜轴墨卡托投影数学分析、极区海图投影及变换等5个方面,论述了地图投影计算机代数分析取得的研究进展,讨论了该领域有待进一步解决的主要问题,对推动地图投影学的发展具有积极意义。
[Abstract]:Map projection is an important part of modern cartography, involving a large number of elliptic function power series expansion, implicit function complex function differential, elliptic integral, complex function operation and a series of cumbersome mathematical analysis process. Manual derivation is not only time-consuming and laborious, but also error-prone, sometimes impossible to achieve due to intolerable complexity and other reasons. In this paper, the symbolic expressions of forward and negative solutions between ellipsoid latitudes, the direct transformation between maps with different deformation properties, the complex variable function representation of Gao Si projection, the mathematical analysis of inclined axis Mercator projection, the projection and transformation of polar charts, etc. This paper discusses the research progress of map projection computer algebra analysis, and discusses the main problems that need to be solved in this field, which is of great significance to the development of map projection science.
【作者单位】： 海军工程大学导航工程系;
【基金】：国家自然科学基金(41631072;41571441;41604010)~~
【分类号】：P282.1
，
本文编号：2295966
[Abstract]:Map projection is an important part of modern cartography, involving a large number of elliptic function power series expansion, implicit function complex function differential, elliptic integral, complex function operation and a series of cumbersome mathematical analysis process. Manual derivation is not only time-consuming and laborious, but also error-prone, sometimes impossible to achieve due to intolerable complexity and other reasons. In this paper, the symbolic expressions of forward and negative solutions between ellipsoid latitudes, the direct transformation between maps with different deformation properties, the complex variable function representation of Gao Si projection, the mathematical analysis of inclined axis Mercator projection, the projection and transformation of polar charts, etc. This paper discusses the research progress of map projection computer algebra analysis, and discusses the main problems that need to be solved in this field, which is of great significance to the development of map projection science.
【作者单位】： 海军工程大学导航工程系;
【基金】：国家自然科学基金(41631072;41571441;41604010)~~
【分类号】：P282.1
，
本文编号：2295966
本文链接：https://www.wllwen.com/kejilunwen/dizhicehuilunwen/2295966.html
