{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T17:19:33Z","timestamp":1774286373301,"version":"3.50.1"},"reference-count":29,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2008,8,1]],"date-time":"2008-08-01T00:00:00Z","timestamp":1217548800000},"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":[[2008,8]]},"abstract":"<jats:p>This paper addresses the long-standing problem of the unavoidable gaps that arise when expressing the intersection of two NURBS surfaces using conventional trimmed-NURBS representation. The solution converts each trimmed NURBS into an untrimmed T-Spline, and then merges the untrimmed T-Splines into a single, watertight model. The solution enables watertight fillets of NURBS models, as well as arbitrary feature curves that do not have to follow iso-parameter curves. The resulting T-Spline representation can be exported without error as a collection of NURBS surfaces.<\/jats:p>","DOI":"10.1145\/1360612.1360678","type":"journal-article","created":{"date-parts":[[2008,8,5]],"date-time":"2008-08-05T13:35:10Z","timestamp":1217943310000},"page":"1-8","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":120,"title":["Watertight trimmed NURBS"],"prefix":"10.1145","volume":"27","author":[{"given":"Thomas W.","family":"Sederberg","sequence":"first","affiliation":[{"name":"Brigham Young University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. Thomas","family":"Finnigan","sequence":"additional","affiliation":[{"name":"Brigham Young University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Li","sequence":"additional","affiliation":[{"name":"University of Science and Technology of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongwei","family":"Lin","sequence":"additional","affiliation":[{"name":"Zhejiang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heather","family":"Ipson","sequence":"additional","affiliation":[{"name":"Brigham Young University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,8]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Bjorck A. 1996. Numerical Methods for Least squares Problems. SIAM.  Bjorck A. 1996. Numerical Methods for Least squares Problems . SIAM.","DOI":"10.1137\/1.9781611971484"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280826"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2004.03.002"},{"key":"e_1_2_2_4_1","first-page":"1","article-title":"Closing the gap between CAD model and downstream application (report on the SIAM Workshop on Integration of CAD and CFD, UC Davis, April 12--13, 1999)","volume":"32","author":"Farouki R. T.","year":"1999","unstructured":"Farouki , R. T. 1999 . Closing the gap between CAD model and downstream application (report on the SIAM Workshop on Integration of CAD and CFD, UC Davis, April 12--13, 1999) . SIAM News 32 , 5, 1 -- 3 . Farouki, R. T. 1999. Closing the gap between CAD model and downstream application (report on the SIAM Workshop on Integration of CAD and CFD, UC Davis, April 12--13, 1999). SIAM News 32, 5, 1--3.","journal-title":"SIAM News"},{"key":"e_1_2_2_5_1","first-page":"2","article-title":"Operations on images using quad trees","volume":"1","author":"Hunter G. M.","year":"1979","unstructured":"Hunter , G. M. , and Steiglitz , K. 1979 . Operations on images using quad trees . IEEE Transactions on Pattern Analysis and Machine Intelligence 1 , 2 (April), 145--153. Hunter, G. M., and Steiglitz, K. 1979. Operations on images using quad trees. IEEE Transactions on Pattern Analysis and Machine Intelligence 1, 2 (April), 145--153.","journal-title":"IEEE Transactions on Pattern Analysis and Machine Intelligence"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2005.48"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(88)90006-4"},{"key":"e_1_2_2_8_1","volume-title":"Proc. of CSG'96","author":"Krishnan S.","unstructured":"Krishnan , S. , and Manocha , D . 1996. Efficient representations and techniques for computing b-rep's of csg models with nurbs primitives . In Proc. of CSG'96 , 101--122. Krishnan, S., and Manocha, D. 1996. Efficient representations and techniques for computing b-rep's of csg models with nurbs primitives. In Proc. of CSG'96, 101--122."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/237748.237751"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195901000419"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383280"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00042-5"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1057432.1057454"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/383507.383520"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1138450.1138455"},{"key":"e_1_2_2_17_1","volume-title":"Planning Report: Interoperability Cost Analysis of the US Automotive Supply Chain","author":"M\u00fcller K.","year":"1999","unstructured":"M\u00fcller , K. , Reusche , L. , and Fellner , D . 1999 . Planning Report: Interoperability Cost Analysis of the US Automotive Supply Chain . National Institute of Standards and Technology . M\u00fcller, K., Reusche, L., and Fellner, D. 1999. Planning Report: Interoperability Cost Analysis of the US Automotive Supply Chain. National Institute of Standards and Technology."},{"key":"e_1_2_2_18_1","doi-asserted-by":"crossref","unstructured":"Patrikalakis N. M. and Maekawa T. 2002. Intersection problems. In Handbook of Computer Aided Geometric Design North-Holland G. Farin J. Hoschek and M.-S. Kim Eds. 623--649.  Patrikalakis N. M. and Maekawa T. 2002. Intersection problems. In Handbook of Computer Aided Geometric Design North-Holland G. Farin J. Hoschek and M.-S. Kim Eds. 623--649.","DOI":"10.1016\/B978-044451104-1\/50026-5"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344908"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/356924.356930"},{"key":"e_1_2_2_21_1","unstructured":"Sederberg T. W. Li X. Lin H. and Finnigan G. T. Nonuniform NURBS. In Preparation.  Sederberg T. W. Li X. Lin H. and Finnigan G. T. Nonuniform NURBS. In Preparation ."},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(84)90140-3"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280942"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882295"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015715"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280946"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2007.06.009"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2003.11.004"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280945"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1138450.1138453"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1360612.1360678","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1360612.1360678","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T13:58:02Z","timestamp":1750255082000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1360612.1360678"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2008,8]]}},"alternative-id":["10.1145\/1360612.1360678"],"URL":"https:\/\/doi.org\/10.1145\/1360612.1360678","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8]]},"assertion":[{"value":"2008-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}