Quadrature Rules to Calculate Distortions of Map Projections

IF 1 4区地球科学 Q3 GEOGRAPHY

Cartographic Journal Pub Date : 2020-07-02 DOI:10.1080/00087041.2020.1714278

Krisztián Kerkovits

引用次数: 4

Abstract

ABSTRACT In map projection theory, it is usual to utilize numerical quadrature rules to estimate the overall map distortion. However, it is not known which method is the most efficient to approximate this integral. In this paper, overall map distortion is calculated analytically by a computer algebra system. Various integration methods are compared to the exact results. Some calculations are also performed on irregular spherical polygons. Considering the experiments, the author suggests utilizing the first-order Gaussian quadrature as it always gave reasonable results, although it is not the best for all cases.

查看原文本刊更多论文

计算地图投影畸变的正交规则

在地图投影理论中，通常使用数值正交规则来估计地图的整体畸变。然而，我们不知道哪种方法是最有效的近似这个积分。本文用计算机代数系统解析地计算了整个地图的变形。比较了各种积分方法的精确结果。对不规则球面多边形也进行了一些计算。考虑到实验，作者建议使用一阶高斯正交，因为它总是给出合理的结果，尽管它不是对所有情况都是最好的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Cartographic Journal GEOGRAPHY-

CiteScore

2.60

自引率

10.00%

发文量

期刊介绍： The Cartographic Journal (first published in 1964) is an established peer reviewed journal of record and comment containing authoritative articles and international papers on all aspects of cartography, the science and technology of presenting, communicating and analysing spatial relationships by means of maps and other geographical representations of the Earth"s surface. This includes coverage of related technologies where appropriate, for example, remote sensing, geographical information systems (GIS), the internet and global positioning systems. The Journal also publishes articles on social, political and historical aspects of cartography.