Spherical great circle arcs based indicators for evaluating distortions of map projections

doi:10.11947/j.AGCS.2020.20190101

Abstract

Abstract: Map projection is an important research content of cartography. However, distortions are inevitable for any map projection. To evaluate the distortions of map projections, averaged ratio between complementary profiles and spherical great circle arcs based shape and area metrics are proposed. By using Bonne projection as an example and exploiting correlation analyses, it is indicated that great circle arcs based indicators simplify the calculation process of small circle arcs based indicators (i.e., the averaged ratio between complementary profiles),and both great and small circle arcs based indicators are highly correlated with each other. Great circle arcs based indicators are also highly correlated with classical differential calculation based indicators(the Pearson product-moment correlation coefficient between them is greater than 0.988), while the proposed metrics are independent on the differential calculation. By utilizing the method of regression analyses, small regression errors are also achieved(the mean error of linear regression is less than 1.10‰). Finally, in order to reduce the number of sampling points and avoid the inconsistency of sampling points for different map projections, this paper also proposes and verifies a random sampling based calculating process. In all word,great circle arcs based indicators could effectively evaluate the distortions of map projections.

Key words: map projection, geometry distortion, averaged ratio between complementary profiles, great circle based metric, regression analysis, quality evaluation

CLC Number:

P282

YAN Jin, YANG Xuan, LI Ni, GONG Guanghong. Spherical great circle arcs based indicators for evaluating distortions of map projections[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(6): 711-723.

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