{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T05:57:28Z","timestamp":1780466248979,"version":"3.54.1"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T00:00:00Z","timestamp":1612828800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2017YFB0504103"],"award-info":[{"award-number":["2017YFB0504103"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["19lgpy43 (37000-31610444)"],"award-info":[{"award-number":["19lgpy43 (37000-31610444)"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Ancient pagodas are usually parts of hot tourist spots in many oriental countries due to their unique historical backgrounds. They are usually polygonal structures comprised by multiple floors, which are separated by eaves. In this paper, we propose a new method to investigate both the rotational and reflectional symmetry of such polygonal pagodas through developing novel geometric models to fit to the 3D point clouds obtained from photogrammetric reconstruction. The geometric model consists of multiple polygonal pyramid\/prism models but has a common central axis. The method was verified by four datasets collected by an unmanned aerial vehicle (UAV) and a hand-held digital camera. The results indicate that the models fit accurately to the pagodas\u2019 point clouds. The symmetry was realized by rotating and reflecting the pagodas\u2019 point clouds after a complete leveling of the point cloud was achieved using the estimated central axes. The results show that there are RMSEs of 5.04 cm and 5.20 cm deviated from the perfect (theoretical) rotational and reflectional symmetries, respectively. This concludes that the examined pagodas are highly symmetric, both rotationally and reflectionally. The concept presented in the paper not only work for polygonal pagodas, but it can also be readily transformed and implemented for other applications for other pagoda-like objects such as transmission towers.<\/jats:p>","DOI":"10.3390\/s21041228","type":"journal-article","created":{"date-parts":[[2021,2,10]],"date-time":"2021-02-10T04:33:46Z","timestamp":1612931626000},"page":"1228","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Symmetry Analysis of Oriental Polygonal Pagodas Using 3D Point Clouds for Cultural Heritage"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3318-7540","authenticated-orcid":false,"given":"Ting On","family":"Chan","sequence":"first","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"},{"name":"Guangdong Provincial Key Laboratory of Urbanization and Geo-Simulation, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linyuan","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"},{"name":"Guangdong Provincial Key Laboratory of Urbanization and Geo-Simulation, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yimin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"},{"name":"Guangdong Provincial Key Laboratory of Urbanization and Geo-Simulation, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Lang","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"},{"name":"China Regional Coordinated Development and Rural Construction Institute, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tingting","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"},{"name":"China Regional Coordinated Development and Rural Construction Institute, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6847-614X","authenticated-orcid":false,"given":"Yeran","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Geography, College of Science, Swansea University, Swansea SA28PP, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6091-3114","authenticated-orcid":false,"given":"Qianxia","family":"Li","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"},{"name":"Guangdong Provincial Key Laboratory of Urbanization and Geo-Simulation, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9395-1424","authenticated-orcid":false,"given":"Ruxu","family":"Du","sequence":"additional","affiliation":[{"name":"School of Geography and Planning, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"669","DOI":"10.4028\/www.scientific.net\/AMM.488-489.669","article-title":"The Symmetry in the Traditional Chinese Architecture","volume":"488","author":"Tang","year":"2014","journal-title":"Appl. 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