{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,20]],"date-time":"2023-11-20T22:21:41Z","timestamp":1700518901494},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[1989,7]]},"abstract":"\n In this paper we introduce a class of surface patch representations, called S-patches, that unify and generalize triangular and tensor product B\u00e9zier surfaces by allowing patches to be defined over any convex polygonal domain; hence, S-patches may have any number of boundary curves. Other properties of S-patches are geometrically meaningful control points, separate control over positions and derivatives along boundary curves, and a geometric construction algorithm based on de Casteljau's algorithm. Of special interest are the regular S-patches, that is, S-patches defined on regular domain polygons. Also presented is an algorithm for smoothly joining together these surfaces with\n \n C\n k<\/jats:sup>\n <\/jats:italic>\n continuity.\n <\/jats:p>","DOI":"10.1145\/77055.77059","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:29:00Z","timestamp":1027769340000},"page":"204-234","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":124,"title":["A multisided generalization of B\u00e9zier surfaces"],"prefix":"10.1145","volume":"8","author":[{"given":"Charles T.","family":"Loop","sequence":"first","affiliation":[{"name":"Univ. of Washington, Seattle"}]},{"given":"Tony D.","family":"DeRose","sequence":"additional","affiliation":[{"name":"Univ. of Washington, Seattle"}]}],"member":"320","published-online":{"date-parts":[[1989,7]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(84)90003-7"},{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-8396(84)90003-7","volume":"1","year":"1984","unstructured":"design. Comput. Aided Geom. Des. 1 , 1 ( July 1984 ), 87-94. design. Comput. Aided Geom. Des. 1, 1 (July 1984), 87-94.","journal-title":"Comput. Aided Geom. Des."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/964967.801160"},{"key":"e_1_2_1_4_2","first-page":"131","volume-title":"Geometric Modeling.\" Algorithms and New Trends","author":"DE BOOR C.","year":"1987","unstructured":"DE BOOR , C. B-form basics . In Geometric Modeling.\" Algorithms and New Trends , G. Farin, Ed. SIAM, Philadelphia , Pa ., 1987 , pp. 131 - 148 . DE BOOR, C. B-form basics. In Geometric Modeling.\" Algorithms and New Trends, G. Farin, Ed. SIAM, Philadelphia, Pa., 1987, pp. 131-148."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/44479.44482"},{"key":"e_1_2_1_7_2","volume-title":"ACM","author":"DEROSE T.D.","year":"1988","unstructured":"DEROSE , T.D. Geometric programming : A coordinate-free approach. 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A construction for visual C~ continuity of polynomial surface patches. Comput. Graph. image Process. 20 , 3 (Nov. i982), 272 - 282 . FARIN, G. A construction for visual C~ continuity of polynomial surface patches. Comput. Graph. image Process. 20, 3 (Nov. i982), 272-282.","journal-title":"Comput. Graph. image Process."},{"key":"e_1_2_1_11_2","first-page":"43","volume-title":"Eds. North-Holland","author":"FARIN G.","year":"1983","unstructured":"FARIN , G. Smooth interpolation to scattered 3D data. In Surfaces in CAGD, R. E. Barnhill and W. Boehm , Eds. North-Holland , Amsterdam , 1983 , pp. 43 - 63 . FARIN, G. Smooth interpolation to scattered 3D data. In Surfaces in CAGD, R. E. Barnhill and W. Boehm, Eds. North-Holland, Amsterdam, 1983, pp. 43-63."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(86)90016-6"},{"key":"e_1_2_1_13_2","unstructured":"FAmN G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. A__a^_:_ Press ~r .. xr~_ _ ~oo Z'~IS~Ut~LtlIIS .L~\/~lVV I uz\/t .{~7oo. FAmN G. Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. A__a^_:_ Press ~r .. xr~_ _ ~oo Z'~IS~Ut~LtlIIS .L~\/~lVV I uz\/t .{~7oo."},{"key":"e_1_2_1_14_2","first-page":"25","volume-title":"Eds. North-Holland","author":"GREGORY J.A.","year":"1983","unstructured":"GREGORY , J.A. Cl rectangular and non-rectangular surface patches. In Surfaces and CAGD, R. E. Barnhill and W. Boehm , Eds. North-Holland , Amsterdam , 1983 , pp. 25 - 33 . GREGORY, J.A. Cl rectangular and non-rectangular surface patches. In Surfaces and CAGD, R. E. Barnhill and W. Boehm, Eds. North-Holland, Amsterdam, 1983, pp. 25-33."},{"key":"e_1_2_1_15_2","volume-title":"Mathematics of Surfaces","author":"GREC ORY","year":"1986","unstructured":"GREC , ORY , J. A. N-sided surface patches . In Mathematics of Surfaces , J. Gregory, Ed. Clarendon Press, Oxford~ E_ng!and, 1986 , ppo 217-232o GREC, ORY, J.A. 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