{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T23:54:49Z","timestamp":1773446089971,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation for Outstanding Young Scholars of China","award":["42122025"],"award-info":[{"award-number":["42122025"]}]},{"name":"National Science Foundation for Outstanding Young Scholars of China","award":["41971416"],"award-info":[{"award-number":["41971416"]}]},{"name":"National Science Foundation for Outstanding Young Scholars of China","award":["41876222"],"award-info":[{"award-number":["41876222"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42122025"],"award-info":[{"award-number":["42122025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41971416"],"award-info":[{"award-number":["41971416"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["41876222"],"award-info":[{"award-number":["41876222"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>Compared with complex and lengthy Gauss-Kr\u00fcger projection series expansions and real number expressions, we improve the complex function representation of Gauss-Kr\u00fcger projections and rewrite them into the \u201cmultiple Angle form\u201d, \u201cexponential form\u201d, and \u201cdouble Angle form\u201d. The coefficients were expanded in the power series based on the first eccentricity e and the third flattening n, respectively, and the truncation difference was analyzed when expanded to different orders to obtain the simplified practical formulas for each form on the premise of meeting the accuracy requirements of geodesy. Through numerical analysis, the computational efficiency of the forward and inverse solutions of the Gauss-Kr\u00fcger projection is analyzed, which shows the superiority of the \u201cdouble Angle form\u201d. Through the above measures, the expressions for forward and inverse solutions of the Gauss-Kr\u00fcger projection are obtained, meeting the accuracy requirements with a higher computational efficiency and a more concise form.<\/jats:p>","DOI":"10.3390\/ijgi11110566","type":"journal-article","created":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T04:21:45Z","timestamp":1668399705000},"page":"566","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Optimization of Complex Function Expansions for Gauss-Kr\u00fcger Projections"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6603-7373","authenticated-orcid":false,"given":"Xiaoyong","family":"Li","sequence":"first","affiliation":[{"name":"College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Houpu","family":"Li","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guohui","family":"Liu","sequence":"additional","affiliation":[{"name":"Chart Information Center, Tianjin 300450, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaofeng","family":"Bian","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Grafarend, E., You, R., and Syffus, R. 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