{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:16:06Z","timestamp":1762175766620,"version":"3.41.0"},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2005,1,1]],"date-time":"2005-01-01T00:00:00Z","timestamp":1104537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2005,1]]},"abstract":"In this article, we present a subdivision scheme for mixed triangle\/quad meshes that is <i>C<\/i><sup>2<\/sup> everywhere except for isolated, extraordinary points. The rules that we describe are the same as Stam and Loop's scheme [2003] except that we perform an unzipping pass prior to subdivision. This simple modification improves the smoothness along the ordinary triangle\/quad boundary from <i>C<\/i><sup>1<\/sup> to <i>C<\/i><sup>2<\/sup>, and creates a scheme capable of subdividing arbitrary meshes. Finally, we end with a proof based on Levin and Levin's [2003] joint spectral radius calculation to show our scheme is indeed <i>C<\/i><sup>2<\/sup> along the triangle\/quad boundary.<\/jats:p>","DOI":"10.1145\/1037957.1037959","type":"journal-article","created":{"date-parts":[[2005,1,26]],"date-time":"2005-01-26T16:35:53Z","timestamp":1106757353000},"page":"28-36","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":23,"title":["On\n C<\/i>\n 2<\/sup>\n triangle\/quad subdivision"],"prefix":"10.1145","volume":"24","author":[{"given":"Scott","family":"Schaefer","sequence":"first","affiliation":[{"name":"Rice University, Houston, TX"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joe","family":"Warren","sequence":"additional","affiliation":[{"name":"Rice University, Houston, TX"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,1]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1016\/0010-4485(78)90110-0","article-title":"Recursively generated b-spline surfaces on arbitrary topological meshes","volume":"10","author":"Catmull E.","year":"1978","journal-title":"Comput. 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