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Graph."],"published-print":{"date-parts":[[2020,8,31]]},"abstract":"<jats:p>\n            We propose a novel method to efficiently compute bijective parameterizations with low distortion on disk topology meshes. Our method relies on a second-order solver. To design an efficient solver, we develop two key techniques. First, we propose a coarse shell to substantially reduce the number of collision constraints that are used to guarantee overlap-free boundaries. During the optimization process, the shell ensures the Hessian matrix with a fixed nonzero structure and a low density, thereby significantly accelerating the optimization. The second is a triangle inequality-based barrier function that effectively ensures non-intersecting boundaries. Our barrier function is\n            <jats:italic toggle=\"yes\">C<\/jats:italic>\n            <jats:sup>\u221e<\/jats:sup>\n            inside the locally supported region and its convex second-order approximation is able to be analytically obtained. Compared to state-of-the-art methods for optimizing bijective parameterizations, our method exhibits better scalability and is about six times faster. The performance of our bijective parameterization algorithm is comparable to state-of-the-art methods of locally flip-free parameterizations. A large number of experimental results have shown the capability and feasibility of our method.\n          <\/jats:p>","DOI":"10.1145\/3386569.3392435","type":"journal-article","created":{"date-parts":[[2020,8,12]],"date-time":"2020-08-12T11:44:27Z","timestamp":1597232667000},"update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":40,"title":["Efficient bijective parameterizations"],"prefix":"10.1145","volume":"39","author":[{"given":"Jian-Ping","family":"Su","sequence":"first","affiliation":[{"name":"University of Science and Technology of China, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chunyang","family":"Ye","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ligang","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao-Ming","family":"Fu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2020,8,12]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2816795.2818099"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982412"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/192161.192168"},{"key":"e_1_2_2_4_1","volume-title":"Convex Optimization","author":"Boyd Stephen","unstructured":"Stephen Boyd and Lieven Vandenberghe. 2004. 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