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Graph."],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>\n            We propose a novel method to generate sparse integer-constrained cone singularities with low distortion constraints for conformal parameterizations. Inspired by [Fang et al. 2021; Soliman et al. 2018], the cone computation is formulated as a constrained optimization problem, where the objective is the number of cones measured by the\n            <jats:italic>\u2113<\/jats:italic>\n            <jats:sub>0<\/jats:sub>\n            -norm of Gaussian curvature of vertices, and the constraint is to restrict the cone angles to be multiples of\n            <jats:italic>\u03c0<\/jats:italic>\n            \/2 and control the distortion while ensuring that the Yamabe equation holds. Besides, the holonomy angles for the non-contractible homology loops are additionally required to be multiples of\n            <jats:italic>\u03c0<\/jats:italic>\n            \/2 for achieving rotationally seamless conformal parameterizations. The Douglas-Rachford (DR) splitting algorithm is used to solve this challenging optimization problem, and our success relies on two key components. First, replacing each integer constraint with the intersection of a box set and a sphere enables us to manage the subproblems in DR splitting update steps in the continuous domain. Second, a novel solver is developed to optimize the\n            <jats:italic>\u2113<\/jats:italic>\n            <jats:sub>0<\/jats:sub>\n            -norm without any approximation. We demonstrate the effectiveness and feasibility of our algorithm on a data set containing 3885 models. Compared to state-of-the-art methods, our method achieves a better tradeoff between the number of cones and the parameterization distortion.\n          <\/jats:p>","DOI":"10.1145\/3528223.3530118","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T21:06:27Z","timestamp":1658523987000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Computing sparse integer-constrained cones for conformal parameterizations"],"prefix":"10.1145","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3166-4136","authenticated-orcid":false,"given":"Mo","family":"Li","sequence":"first","affiliation":[{"name":"University of Science and Technology of China, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7934-6060","authenticated-orcid":false,"given":"Qing","family":"Fang","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8901-8156","authenticated-orcid":false,"given":"Wenqing","family":"Ouyang","sequence":"additional","affiliation":[{"name":"Chinese University of Hongkong (Shenzhen), China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4352-1431","authenticated-orcid":false,"given":"Ligang","family":"Liu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8479-0107","authenticated-orcid":false,"given":"Xiao-Ming","family":"Fu","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China, China"}]}],"member":"320","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00115-1"},{"key":"e_1_2_2_2_1","volume-title":"Some nonlinear problems in Riemannian geometry","author":"Aubin Thierry","unstructured":"Thierry Aubin. 2013. 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