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The local geometry for each chart is sparsely represented by a set of redundant atom functions, which have the flexibility to represent various geometries with varying smoothness. A global optimization is then proposed to guarantee compatible sparse representations in the overlapping regions of different charts. Our method can construct manifolds of varying smoothness including sharp features (creases, darts, or cusps). As an application, we can easily construct a skinning manifold surface from a given curve network. Examples show that our approach has much flexibility to generate manifold surfaces with good quality.<\/jats:p>","DOI":"10.1145\/2835488","type":"journal-article","created":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T13:07:16Z","timestamp":1456146436000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Construction of Manifolds via Compatible Sparse Representations"],"prefix":"10.1145","volume":"35","author":[{"given":"Ruimin","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ligang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhouwang","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wen","family":"Shan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiansong","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Falai","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2016,2,19]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.02012.x"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1449715.1449740"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1622176.1622189"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2366145.2366197"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/060657704"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03596-8_6"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2008.08.003"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280826"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/18.382009"},{"key":"e_1_2_1_11_1","volume-title":"Sparse and Redundant Representations","author":"Elad Michael","unstructured":"Michael Elad . 2010. 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