{"title":"Quadrature Rules to Calculate Distortions of Map Projections","authors":"Krisztián Kerkovits","doi":"10.1080/00087041.2020.1714278","DOIUrl":null,"url":null,"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.","PeriodicalId":55971,"journal":{"name":"Cartographic Journal","volume":"57 1","pages":"249 - 260"},"PeriodicalIF":1.0000,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00087041.2020.1714278","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cartographic Journal","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1080/00087041.2020.1714278","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOGRAPHY","Score":null,"Total":0}
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.
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.
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