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To mitigate the gap between the smoothness and the number of faces, this paper devises a novel improved mesh subdivision method to coordinate the smoothness and the number of faces in a harmonious way. First, this paper introduces a variable threshold, rather than a constant threshold used in existing adaptive subdivision methods, to reduce the number of redundant faces while keeping the smoothness in each subdivision iteration. Second, to achieve the above goal, a new crack-solving method is developed to remove the cracks by refining the adjacent faces of the subdivided area. Third, as a result, the problem of coordinating the smoothness and the number of faces can be formulated as a multi-objective optimization problem, in which the possible threshold sequences constitute the solution space. Finally, the Non-dominated sorting genetic algorithm II (NSGA-II) is improved to efficiently search the Pareto frontier. Extensive experiments demonstrate that the proposed method consistently outperforms existing mesh subdivision methods in different settings.<\/jats:p>","DOI":"10.3233\/ica-210661","type":"journal-article","created":{"date-parts":[[2021,7,27]],"date-time":"2021-07-27T13:10:12Z","timestamp":1627391412000},"page":"23-41","source":"Crossref","is-referenced-by-count":77,"title":["An improved loop subdivision to coordinate the smoothness and the number of faces via multi-objective optimization"],"prefix":"10.1177","volume":"29","author":[{"given":"Yaqian","family":"Liang","sequence":"first","affiliation":[{"name":"School of Computer Science, Wuhan University, Wuhan, Hubei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fazhi","family":"He","sequence":"additional","affiliation":[{"name":"School of Computer Science, Wuhan University, Wuhan, Hubei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiantao","family":"Zeng","sequence":"additional","affiliation":[{"name":"Center for Evidence-Based and Translational Medicine, Zhongnan Hospital of Wuhan University, Wuhan, Hubei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinkun","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Computer Science, Wuhan University, Wuhan, Hubei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"2","key":"10.3233\/ICA-210661_ref1","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1109\/TVCG.2017.2658570","article-title":"Augmented reality versus virtual reality for 3D object manipulation","volume":"24","author":"Krichenbauer","year":"2018","journal-title":"IEEE Transactions on Visualization and Computer Graphics"},{"key":"10.3233\/ICA-210661_ref2","doi-asserted-by":"crossref","unstructured":"Egger B, Smith WAP, Tewari A, Wuhrer S, Zollhoefer M, Beeler T, et\u00a0al. 3D morphable face models\u00a0\u2013 past, present, and future. 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