{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T11:42:15Z","timestamp":1787312535051,"version":"3.56.0"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2003,4,7]],"date-time":"2003-04-07T00:00:00Z","timestamp":1049673600000},"content-version":"vor","delay-in-days":37,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[2003,3]]},"abstract":"Abstract<\/jats:title>\n \n In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad\u2010only meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known Catmull\u2010Clark and Loop subdivision algorithms. We show that our surfaces are<\/jats:italic>\n \n C<\/jats:italic>\n 1<\/jats:sup>\n <\/jats:styled-content>\n everywhere and provide a proof that it is impossible to construct such a<\/jats:italic>\n \n C<\/jats:italic>\n 2<\/jats:sup>\n <\/jats:styled-content>\n scheme at the quad\/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad\/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples.<\/jats:italic>\n <\/jats:p>\n \n ACM CSS:<\/jats:bold>\n I.3.5 Computer Graphics\u2014\n Curve, surface, solid, and object representations<\/jats:italic>\n <\/jats:p>","DOI":"10.1111\/1467-8659.t01-2-00647","type":"journal-article","created":{"date-parts":[[2004,12,21]],"date-time":"2004-12-21T19:46:27Z","timestamp":1103658387000},"page":"79-85","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":81,"title":["Quad\/Triangle Subdivision"],"prefix":"10.1111","volume":"22","author":[{"given":"Jos","family":"Stam","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Charles","family":"Loop","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2003,4,7]]},"reference":[{"key":"e_1_2_6_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(78)90110-0"},{"key":"e_1_2_6_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(78)90111-2"},{"key":"e_1_2_6_4_2","unstructured":"C. T.Loop.Smooth subdivision surfaces based on triangles M. S. Thesis Department of Mathematics University of Utah August 1987."},{"key":"e_1_2_6_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(94)00007-F"},{"key":"e_1_2_6_6_2","unstructured":"D. N.Zorin.Subdivision and multiresolution surface representations PhD thesis Caltech Pasadena California 1997."},{"key":"e_1_2_6_7_2","first-page":"395","article-title":"Exact evaluation of Catmull\u2010Clark subdivision surfaces at arbitrary parameter values","author":"Stam J.","year":"1998","journal-title":"Computer Graphics Proceedings, Annual Conference Series"},{"key":"e_1_2_6_8_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00540"},{"key":"e_1_2_6_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00038-3"},{"key":"e_1_2_6_10_2","doi-asserted-by":"crossref","unstructured":"D.ZorinandP.Schr\u00f6der.A unified framework for primal\/dual quadrilateral subdivision schememes. Computer Aided Geometric Design. Special issue on Subdivision Surfaces 18:429\u2013454 2001.","DOI":"10.1016\/S0167-8396(01)00040-1"},{"key":"e_1_2_6_11_2","author":"Warren J.","year":"2001","journal-title":"Subdivision Methods For Geometric Design: A Constructive Approach"},{"key":"e_1_2_6_12_2","first-page":"113","article-title":"piecewise smooth subdivision with normal control","author":"Biermann H.","year":"2000","journal-title":"SIGGRAPH 2000 Conference Proceedings, Annual Conference Series"},{"key":"e_1_2_6_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166121"},{"key":"e_1_2_6_14_2","article-title":"Necessary conditions for subdivision surfaces","author":"Prautzsch H.","year":"1997","journal-title":"Tech. report, Sonderforschungsbereich 404"},{"key":"e_1_2_6_15_2","unstructured":"A.LevinandD.Levin.Smoothness analysis of bivariate quasi\u2010uniform subdivision schemes. Unpublished manuscript 2001."}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-8659.t01-2-00647","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/1467-8659.t01-2-00647","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,15]],"date-time":"2023-10-15T20:00:26Z","timestamp":1697400026000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/1467-8659.t01-2-00647"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["10.1111\/1467-8659.t01-2-00647"],"URL":"https:\/\/doi.org\/10.1111\/1467-8659.t01-2-00647","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3]]},"assertion":[{"value":"2003-04-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}