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Graph."],"published-print":{"date-parts":[[2023,12,5]]},"abstract":"<jats:p>\n            We propose an unified\n            <jats:italic toggle=\"yes\">\u03bb<\/jats:italic>\n            -subdivision scheme with a continuous family of tuned subdivisions for quadrilateral meshes. Main subdivision stencil parameters of the unified scheme are represented as spline functions of the subdominant eigenvalue\n            <jats:italic toggle=\"yes\">\u03bb<\/jats:italic>\n            of respective subdivision matrices and the\n            <jats:italic toggle=\"yes\">\u03bb<\/jats:italic>\n            value can be selected within a wide range to produce desired properties of refined meshes and limit surfaces with optimal curvature performance in extraordinary regions. Spline representations of stencil parameters are constructed based on discrete optimized stencil coefficients obtained by a general tuning framework that optimizes eigenvectors of subdivision matrices towards curvature continuity conditions. To further improve the quality of limit surfaces, a weighting function is devised to penalize sign changes of Gauss curvatures on respective second order characteristic maps. By selecting an appropriate\n            <jats:italic toggle=\"yes\">\u03bb<\/jats:italic>\n            , the resulting unified subdivision scheme produces anticipated properties towards different target applications, including nice properties of several other existing tuned subdivision schemes. Comparison results also validate the advantage of the proposed scheme with higher quality surfaces for subdivision at lower\n            <jats:italic toggle=\"yes\">\u03bb<\/jats:italic>\n            values, a challenging task for other related tuned subdivision schemes.\n          <\/jats:p>","DOI":"10.1145\/3618400","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T10:20:48Z","timestamp":1701771648000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["An Unified\n            <i>\u03bb<\/i>\n            -subdivision Scheme for Quadrilateral Meshes with Optimal Curvature Performance in Extraordinary Regions"],"prefix":"10.1145","volume":"42","author":[{"given":"Weiyin","family":"Ma","sequence":"first","affiliation":[{"name":"City University of Hong Kong, China"}]},{"given":"Xu","family":"Wang","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, China"}]},{"given":"Yue","family":"Ma","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, China"}]}],"member":"320","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2006.00945.x"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/2151237X.2009.10129278"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/42458.42459"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2004.04.003"},{"key":"e_1_2_2_5_1","volume-title":"Accessed","author":"Cashman Thomas J.","year":"2022","unstructured":"Thomas J. 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