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Flexion and Skewness in Map Projections of the Earth
Journal article   Open access   Peer reviewed

Flexion and Skewness in Map Projections of the Earth

David M Goldberg and J. Richard GottIII
Cartographica, v 42(4), pp 297-318
23 Aug 2006
DOI: https://doi.org/10.3138/carto.42.4.297
url
https://doi.org/10.48550/arxiv.astro-ph/0608501View
Submitted Open arXiv.org - Non-exclusive license to distribute

Abstract

Physics - Astrophysics of Galaxies Physics - Cosmology and Nongalactic Astrophysics Physics - Earth and Planetary Astrophysics Physics - High Energy Astrophysical Phenomena Physics - Instrumentation and Methods for Astrophysics Physics - Solar and Stellar Astrophysics
Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different world map projections. We find that the Winkel-Tripel projection (already adopted for world maps by the National Geographic), has low distortion on most measures and excellent quality overall.

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