{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:14:27Z","timestamp":1758824067982},"reference-count":20,"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":"<jats:title>Abstract<\/jats:title><jats:p> <jats:italic>Interpolating curves by subdivision surfaces is one of the major constraints that is partially addressed in the literature. So far, no more than two intersecting curves can be interpolated by a subdivision surface such as Doo\u2010Sabin or Catmull\u2010Clark surfaces. One approach that has been used in both of theses surfaces is the polygonal complex approach where a curve can be defined by a control mesh rather than a control polygon. Such a definition allows a curve to carry with it cross derivative information which can be naturally embodied in the mesh of a subdivision surface. This paper extends the use of this approach to interpolate an unlimited number of curves meeting at an extraordinary point on a subdivision surface. At that point, the curves can all meet with either<\/jats:italic>\n          <jats:styled-content>\n              <jats:italic>C<\/jats:italic>\n              <jats:sup>0<\/jats:sup>\n            <\/jats:styled-content>\n          <jats:italic>or<\/jats:italic>\n          <jats:styled-content>\n              <jats:italic>C<\/jats:italic>\n              <jats:sup>1<\/jats:sup>\n            <\/jats:styled-content>\n          <jats:italic>continuity, yet still have common tangent plane. A straight forward application is the generation of subdivision surfaces through 3\u2010regular meshes of curves for which an easy interface can be used.<\/jats:italic> <\/jats:p>","DOI":"10.1111\/1467-8659.t01-1-00648","type":"journal-article","created":{"date-parts":[[2004,12,22]],"date-time":"2004-12-22T00:46:27Z","timestamp":1103676387000},"page":"87-97","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Interpolating an Unlimited Number of Curves Meeting at Extraordinary Points on Subdivision Surfaces*"],"prefix":"10.1111","volume":"22","author":[{"given":"Ahmed H.","family":"Nasri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,4,7]]},"reference":[{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(94)00007-F"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996304346"},{"key":"e_1_2_8_4_2","article-title":"Subdivision for modeling and animation","author":"Zorin D.","year":"2000","journal-title":"ACM SIGGRAPH Course Notes"},{"key":"e_1_2_8_5_2","author":"Warren J.","year":"2002","journal-title":"Subdivision Methods For Geometric Design: A Constructive Approach"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003710100154"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s003710100155"},{"key":"e_1_2_8_8_2","first-page":"113","article-title":"Piecewise smooth subdivision surfaces with normal control","author":"Biermann H.","year":"2000","journal-title":"Computer Graphics Proceedings"},{"key":"e_1_2_8_9_2","first-page":"57","article-title":"Interpolating nets of curves by somooth subdivision surfaces","author":"Levin A.","year":"1999","journal-title":"Computer Graphics Proceedings"},{"key":"e_1_2_8_10_2","first-page":"387","article-title":"Non\u2010uniform recursive subdivision surfaces","author":"Sederberg T.","year":"1998","journal-title":"Computer Graphics Proceedings"},{"key":"e_1_2_8_11_2","first-page":"35","article-title":"Efficient, fair interpolation using Catmull\u2010Clark surfaces","author":"Halstead M.","year":"1993","journal-title":"Computer Graphics Proceedings"},{"key":"e_1_2_8_12_2","unstructured":"J.Schweitzer.Analysis and applications of subdivision surfaces Ph.D. Thesis University Of Washington Seattle 1996."},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4485(01)00093-8"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(00)00015-7"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0097-8493(02)00082-1"},{"key":"e_1_2_8_16_2","first-page":"177","article-title":"Behaviour of recursive division surfaces near extraordinary points","author":"Doo D.","year":"1988","journal-title":"Seminal Graphics"},{"key":"e_1_2_8_17_2","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1109\/GMAP.2000.838258","article-title":"A polygonal approach for interpolating meshes of curves by subdivisin surfaces","author":"Nasri A.","year":"2000","journal-title":"Proceedings of Geometric Modeling and Processing 2000"},{"key":"e_1_2_8_18_2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1145\/280811.280992","article-title":"Recursively generated b\u2010spline surfaces on arbitrary tmeshes","author":"Catmull E.","year":"1998","journal-title":"Seminal Graphics"},{"key":"e_1_2_8_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(74)90028-8"},{"key":"e_1_2_8_20_2","unstructured":"A.Nasri.Desinging subdivision surfaces interpolating triangular meshes of curves. American University of Beirut Computer Science 2002 Technical Report TR\u201020004."},{"key":"e_1_2_8_21_2","unstructured":"A.Levy T.MunznerandM.Philips. Geomview 1.6.6 GL version http:\/\/www.Geomview.org."}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-8659.t01-1-00648","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/1467-8659.t01-1-00648","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T00:00:31Z","timestamp":1697414431000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/1467-8659.t01-1-00648"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["10.1111\/1467-8659.t01-1-00648"],"URL":"https:\/\/doi.org\/10.1111\/1467-8659.t01-1-00648","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"}}]}}