{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,26]],"date-time":"2023-01-26T03:50:21Z","timestamp":1674705021748},"reference-count":18,"publisher":"Association for Computing Machinery (ACM)","issue":"2","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[1993,4]]},"abstract":"\n In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions\n F<\/jats:italic>\n and\n G<\/jats:italic>\n , compute a representation of the function\n H<\/jats:italic>\n =\n F o G<\/jats:italic>\n . We examine this problem in detail for the case when\n F<\/jats:italic>\n and\n G<\/jats:italic>\n are given in either Be\u00b4zier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.\n <\/jats:p>","DOI":"10.1145\/151280.151290","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:29:00Z","timestamp":1027769340000},"page":"113-135","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":69,"title":["Functional composition algorithms via blossoming"],"prefix":"10.1145","volume":"12","author":[{"given":"Tony D.","family":"DeRose","sequence":"first","affiliation":[{"name":"Univ. of Washington, Seattle"}]},{"given":"Ronald N.","family":"Goldman","sequence":"additional","affiliation":[{"name":"Rice Univ., Houston, TX"}]},{"given":"Hans","family":"Hagen","sequence":"additional","affiliation":[{"name":"Univ. Kaiserslautern, Kaiserslautern, Germany"}]},{"given":"Stephen","family":"Mann","sequence":"additional","affiliation":[{"name":"Univ. of Washington, Seattle"}]}],"member":"320","published-online":{"date-parts":[[1993,4]]},"reference":[{"key":"e_1_2_1_1_2","volume-title":"Knot Insertion and Deletion Algorithm for B-spline Curves and Surfaces","author":"C~ MAN","unstructured":"BARRY, P., AND C~ )LI) MAN , R. Algorithms for progressive curves: Extending B-splines and blossoming techniques to the monomial, power, and Newton dual forms of a curve . In Knot Insertion and Deletion Algorithm for B-spline Curves and Surfaces . SIAM , to appear. BARRY, P., AND C~)LI)MAN, R. Algorithms for progressive curves: Extending B-splines and blossoming techniques to the monomial, power, and Newton dual forms of a curve. In Knot Insertion and Deletion Algorithm for B-spline Curves and Surfaces. SIAM, to appear."},{"key":"e_1_2_1_2_2","volume-title":"Knot Insertion and Deletion Algorithm for B-spline Curves and Surfaces","author":"Am MAN","unstructured":"BARRY, P., Am ) GOLI) MAN , R. Knot insertion algorithms . In Knot Insertion and Deletion Algorithm for B-spline Curves and Surfaces . SIAM , to appear. BARRY, P., Am) GOLI)MAN, R. Knot insertion algorithms. In Knot Insertion and Deletion Algorithm for B-spline Curves and Surfaces. SIAM, to appear."},{"key":"e_1_2_1_3_2","first-page":"1","volume":"12","author":"Bm R","year":"1980","unstructured":"Bm :FCKN~: R , I. Construction of B6zier points of quadrilaterals from those of triangles. Comput. Aided Des. 12 , 1 ( 1980 ), 21 24. Bm:FCKN~:R, I. Construction of B6zier points of quadrilaterals from those of triangles. Comput. Aided Des. 12, 1 (1980), 21 24.","journal-title":"Comput. Aided Des."},{"key":"e_1_2_1_4_2","first-page":"5","volume":"19","author":"It MEN","year":"1982","unstructured":"DA It MEN , W. 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A coordinate-free approach to geometric programming . In Math for Siggraph. ACM Siggraph Course Notes 23, 1989 . Also available as Tech. Rep. 89-09-16, Dept. of Computer Science and Engineering, Univ. of Washington, Seattle , Sept. 1989 . DERosE, T. D. A coordinate-free approach to geometric programming. In Math for Siggraph. ACM Siggraph Course Notes 23, 1989. Also available as Tech. Rep. 89-09-16, Dept. of Computer Science and Engineering, Univ. of Washington, Seattle, Sept. 1989."},{"key":"e_1_2_1_8_2","first-page":"35","volume-title":"NURBS for Curve and Surface Design. SLAM","author":"Ros E","year":"1991","unstructured":"DE Ros E , T.D. Rational B6zier curves and surfaces on projective domains . In NURBS for Curve and Surface Design. SLAM , 1991 , 35 - 45 . DERosE, T.D. Rational B6zier curves and surfaces on projective domains. In NURBS for Curve and Surface Design. SLAM, 1991, 35-45."},{"key":"e_1_2_1_9_2","volume-title":"Curves and Surfaces for Computer Aided Geometric Design","year":"1990","unstructured":"FARIN, G. Curves and Surfaces for Computer Aided Geometric Design , 2 nd ed. Academic Press , New York , 1990 . FARIN, G. Curves and Surfaces for Computer Aided Geometric Design, 2nd ed. Academic Press, New York, 1990.","edition":"2"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4485(87)90149-7"},{"key":"e_1_2_1_11_2","volume-title":"The Art of Computer Programming","year":"1969","unstructured":"1~4u'ru, D.E. The Art of Computer Programming . Vol. 1 , Sorting and Searching. Addison- Wesley, Reading, Mass ., 1969 . 1~4u'ru, D.E. The Art of Computer Programming. Vol. 1, Sorting and Searching. Addison- Wesley, Reading, Mass., 1969."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/77055.77059"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1145\/97879.97917","volume-title":"SIGGRAPH '90 Proceedings","author":"Loop C. T.","year":"1990","unstructured":"Loop , C. T. , AND DERo SE , T. D. Generalized B-spline surfaces of arbitrary topology . In SIGGRAPH '90 Proceedings ( 1990 ). ACM, New York , 347 - 356 . 10.1145\/97879.97917 Loop, C. T., AND DERoSE, T. D. Generalized B-spline surfaces of arbitrary topology. In SIGGRAPH '90 Proceedings (1990). ACM, New York, 347-356. 10.1145\/97879.97917"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(87)90013-6"},{"key":"e_1_2_1_16_2","first-page":"4","volume":"10","author":"R~ P.","year":"1978","unstructured":"S^mX)NNIE R~ ;, P. Spline and B~zier polygons associated with a polynomial spline curve. Comput. Aided Des. 10 , 4 ( 1978 ), 257-261. 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