{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T11:59:04Z","timestamp":1773921544486,"version":"3.50.1"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2006,4,1]],"date-time":"2006-04-01T00:00:00Z","timestamp":1143849600000},"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":[[2006,4]]},"abstract":"<jats:p>An extended subdivision surface (ESub) is a generalization of Catmull Clark and NURBS surfaces. Depending on the knot intervals and valences of the vertices and faces, Catmull Clark as well as NURBS patches can be generated using the extended subdivision rules. Moreover, an arbitrary choice of the knot intervals and the topology is possible. Special features like sharp edges and corners are consistently supported by setting selected knot intervals to zero or by applying special rules. Compared to the prior nonuniform rational subdivision surfaces (NURSS), the ESubs offer limit-point rules which are indispensable in many applications, for example, for computer-aided design or in adaptive visualization. The refinement and limit-point rules for our nonuniform, nonstationary scheme are obtained via a new method using local B\u00e9zier control points. With our new surface, it is possible to start with existing Catmull Clark as well as NURBS models and to continue the modeling process using the extended subdivision options.<\/jats:p>","DOI":"10.1145\/1138450.1138455","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"268-292","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":40,"title":["Extended subdivision surfaces"],"prefix":"10.1145","volume":"25","author":[{"given":"Kerstin","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"Technical University Braunschweig"}]},{"given":"Lars","family":"Reusche","sequence":"additional","affiliation":[{"name":"Technical University Braunschweig"}]},{"given":"Dieter","family":"Fellner","sequence":"additional","affiliation":[{"name":"Technical University Braunschweig"}]}],"member":"320","published-online":{"date-parts":[[2006,4]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Curves and Surfaces for CAGD","author":"Farin G.","unstructured":"Farin , G. 2002. 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Adaptive ray tracing of subdivision surfaces. In Proceedings of Eurographics. Vol. 22. 535--562."},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","unstructured":"Piegl L. and Tiller W. 1995. The NURBS Book. Springer-Verlag.   Piegl L. and Tiller W. 1995. The NURBS Book. Springer-Verlag.","DOI":"10.1007\/978-3-642-97385-7"},{"key":"e_1_2_1_7_1","volume-title":"Blossoming: A connect---the---dot approach to splines. Tech. rep.","author":"Ramshaw L.","year":"1987","unstructured":"Ramshaw , L. 1987 . Blossoming: A connect---the---dot approach to splines. Tech. rep. , Digital Systems Research Center . Ramshaw, L. 1987. Blossoming: A connect---the---dot approach to splines. 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In Proceedings of IASTED International Conference on Computer Graphics and Imaging. 169--174."},{"key":"e_1_2_1_15_1","unstructured":"Zorin D. and Schr\u00f6der P. 1999. Subdivision for modeling and animation. ACM SIGGRAPH Course Notes.  Zorin D. and Schr\u00f6der P. 1999. Subdivision for modeling and animation. ACM SIGGRAPH Course Notes."}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1138450.1138455","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1138450.1138455","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:06:27Z","timestamp":1750259187000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1138450.1138455"}},"subtitle":["Building a bridge between NURBS and Catmull-Clark surfaces"],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":13,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["10.1145\/1138450.1138455"],"URL":"https:\/\/doi.org\/10.1145\/1138450.1138455","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]},"assertion":[{"value":"2006-04-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}