{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:23:47Z","timestamp":1760235827068,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,26]],"date-time":"2021-09-26T00:00:00Z","timestamp":1632614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61773032"],"award-info":[{"award-number":["61773032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012456","name":"National Social Science Fund of China","doi-asserted-by":"publisher","award":["19BXW120"],"award-info":[{"award-number":["19BXW120"]}],"id":[{"id":"10.13039\/501100012456","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>We studied the numerical approximation problem of distortion in map projections. Most widely used differential methods calculate area distortion and maximum angular distortion using partial derivatives of forward equations of map projections. However, in certain map projections, partial derivatives are difficult to calculate because of the complicated forms of forward equations, e.g., equations with iterations, integrations, or multi-way branches. As an alternative, the spherical great circle arcs\u2013based metric employs the inverse equations of map projections to transform sample points from the projection plane to the spherical surface, and then calculates a differential-independent distortion metric for the map projections. We introduce a novel forward interpolated version of the previous spherical great circle arcs\u2013based metric, solely dependent on the forward equations of map projections. In our proposed numerical solution, a rational function\u2013based regression is also devised and applied to our metric to obtain an approximate metric of angular distortion. The statistical and graphical results indicate that the errors of the proposed metric are fairly low, and a good numerical estimation with high correlation to the differential-based metric can be achieved.<\/jats:p>","DOI":"10.3390\/ijgi10100649","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T04:55:33Z","timestamp":1632718533000},"page":"649","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Regression and Evaluation on a Forward Interpolated Version of the Great Circle Arcs\u2013Based Distortion Metric of Map Projections"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0308-6407","authenticated-orcid":false,"given":"Jin","family":"Yan","sequence":"first","affiliation":[{"name":"School of Management and Engineering, Capital University of Economics and Business, Beijing 100070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tiansheng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Management and Engineering, Capital University of Economics and Business, Beijing 100070, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ni","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"},{"name":"State Key Laboratory of Virtual Reality Technology and Systems, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghong","family":"Gong","sequence":"additional","affiliation":[{"name":"School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,26]]},"reference":[{"key":"ref_1","unstructured":"ICA Executive Committee (2021, September 26). 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