【摘要】：地圖投影是現(xiàn)代地圖學(xué)的重要組成部分,涉及大量的橢圓函數(shù)冪級(jí)數(shù)展開(kāi)、隱函數(shù)復(fù)合函數(shù)微分、橢圓積分、復(fù)變函數(shù)運(yùn)算等一系列煩瑣的數(shù)學(xué)分析過(guò)程,人工推導(dǎo)不但費(fèi)時(shí)費(fèi)力,而且容易出錯(cuò),有時(shí)由于難以忍受的復(fù)雜性等各種原因,甚至根本無(wú)法實(shí)現(xiàn)。本文主要從橢球各緯度間正反解符號(hào)表達(dá)式、不同變形性質(zhì)地圖投影間的直接變換、高斯投影的復(fù)變函數(shù)表示、斜軸墨卡托投影數(shù)學(xué)分析、極區(qū)海圖投影及變換等5個(gè)方面,論述了地圖投影計(jì)算機(jī)代數(shù)分析取得的研究進(jìn)展,討論了該領(lǐng)域有待進(jìn)一步解決的主要問(wèn)題,對(duì)推動(dòng)地圖投影學(xué)的發(fā)展具有積極意義。
[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.
【作者單位】： 海軍工程大學(xué)導(dǎo)航工程系;
【基金】：國(guó)家自然科學(xué)基金(41631072;41571441;41604010)~~
【分類(lèi)號(hào)】：P282.1
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本文編號(hào)：2295966