{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:42Z","timestamp":1753881222591,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,9,18]],"date-time":"2011-09-18T00:00:00Z","timestamp":1316304000000},"content-version":"vor","delay-in-days":260,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["60973155"],"award-info":[{"award-number":["60973155"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>The techniques for parametrizing nonsingular cubic surfaces have shown to\nbe of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be <jats:italic>F<\/jats:italic><jats:sub>3<\/jats:sub>, <jats:italic>F<\/jats:italic><jats:sub>4<\/jats:sub>, or\n<jats:italic>F<\/jats:italic><jats:sub>5<\/jats:sub> surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper.<\/jats:p>","DOI":"10.1155\/2011\/349315","type":"journal-article","created":{"date-parts":[[2011,9,18]],"date-time":"2011-09-18T19:00:12Z","timestamp":1316372412000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Geometric Information and Rational Parametrization of Nonsingular Cubic Blending Surfaces"],"prefix":"10.1155","volume":"2011","author":[{"given":"Minghao","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tieru","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shugong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2011,9,18]]},"reference":[{"volume-title":"The Twenty-Seven Lines Upon the Cubic Surface","year":"1911","author":"Henderson A.","key":"e_1_2_8_1_2"},{"key":"e_1_2_8_2_2","first-page":"299","volume-title":"The Mathematics of Surfaces II","author":"Sederberg T.","year":"1987"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/269799.269800"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2009.06.001"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167\u20108396(01)00048\u20106"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00607\u2010006\u20100192\u20100"},{"key":"e_1_2_8_7_2","unstructured":"WuT. GaoW. andFengG. Blending of implicit algebraic surfaces Proceedings of the ASCM August 1995 Beijing China 125\u2013131."},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167\u20108396(00)00023\u20106"},{"key":"e_1_2_8_9_2","unstructured":"LeiN. Blending of two quadratic surfaces and Wu Wen-ts\u00fcn\u2032s formulae Ph.D. thesis 2002 Jilin University Jilin China ZBL0948.68182."},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.03.084"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/38.59032"},{"key":"e_1_2_8_12_2","first-page":"383","article-title":"Wu Wen-ts\u00fcn\u2032s formulae for the blending of pipe surfaces","volume":"17","author":"Wu T.","year":"2001","journal-title":"Northeastern Mathematical Journal"},{"key":"e_1_2_8_13_2","unstructured":"LiC. A software system on blending of pipe surfaces M.S. thesis 2000 Jilin University Jilin China ZBL1031.65030."},{"volume-title":"The Non-Singular Cubic Surfaces","year":"1942","author":"Segre B.","key":"e_1_2_8_14_2"},{"key":"e_1_2_8_15_2","first-page":"628","article-title":"A complete discrimination system for polynomials","volume":"39","author":"Yang L.","year":"1996","journal-title":"Science in China"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2011\/349315.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2011\/349315.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2011\/349315","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T15:09:47Z","timestamp":1718032187000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2011\/349315"}},"subtitle":[],"editor":[{"given":"Ke","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2011,1]]},"references-count":15,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,1]]}},"alternative-id":["10.1155\/2011\/349315"],"URL":"https:\/\/doi.org\/10.1155\/2011\/349315","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2011,1]]},"assertion":[{"value":"2011-03-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-06-07","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-09-18","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"349315"}}