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.

中文翻译：

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计算地图投影失真的正交规则

摘要

在地图投影理论中，通常使用数值正交规则来估计整体地图失真。但是，尚不清楚哪种方法最有效地近似该积分。在本文中，通过计算机代数系统分析性地计算了总体地图失真。将各种积分方法与精确结果进行比较。还对不规则球形多边形执行一些计算。考虑到实验，作者建议利用一阶高斯求积法，因为它总是会给出合理的结果，尽管它并不是对所有情况都最佳。