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Graph."],"published-print":{"date-parts":[[2011,10]]},"abstract":"<jats:p>\n            The control polygon of a rational B\u00e9zier curve is well-defined and has geometric significance; there is a sequence of weights under which the limiting position of the curve is the control polygon. For a rational B\u00e9zier surface patch, there are many possible polyhedral control structures, and none is canonical. We propose a not necessarily polyhedral control structure for rational surface patches, regular control surfaces, which are certain\n            <jats:italic>C<\/jats:italic>\n            <jats:sup>0<\/jats:sup>\n            spline surfaces. While not unique, regular control surfaces are exactly the possible limiting positions of a rational B\u00e9zier patch when the weights vary.\n          <\/jats:p>","DOI":"10.1145\/2019627.2019629","type":"journal-article","created":{"date-parts":[[2011,10,25]],"date-time":"2011-10-25T12:23:05Z","timestamp":1319545385000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Toric degenerations of B\u00e9zier patches"],"prefix":"10.1145","volume":"30","author":[{"given":"Luis David","family":"Garc'ia-Puente","sequence":"first","affiliation":[{"name":"Sam Houston State University, Huntsville, TX"}]},{"given":"Frank","family":"Sottile","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University, College Station, TX"}]},{"given":"Chungang","family":"Zhu","sequence":"additional","affiliation":[{"name":"Dalian University of Technology, Dalian, China"}]}],"member":"320","published-online":{"date-parts":[[2011,10,22]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9045(84)90132-1"},{"key":"e_1_2_2_2_1","doi-asserted-by":"crossref","unstructured":"Cox D. Little J. and Schenck H. 2011. Toric Varieties. Graduate Studies in Mathematics. American Mathematics Society Providence RI.  Cox D. Little J. and Schenck H. 2011. Toric Varieties. Graduate Studies in Mathematics. American Mathematics Society Providence RI.","DOI":"10.1090\/gsm\/124"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11620-9_9"},{"key":"e_1_2_2_4_1","volume-title":"Curves and Surfaces for Computer-Aided Geometric Design. Computer Science and Scientific Computing","author":"Farin G."},{"key":"e_1_2_2_5_1","volume-title":"Introduction to Toric Varieties. Annals of Mathematics Studies","author":"Fulton W."},{"key":"e_1_2_2_6_1","doi-asserted-by":"crossref","unstructured":"Gel\u2032fand I. M. Kapranov M. M. and Zelevinsky A. V. 1994. Discriminants Resultants and Multidimensional Determinants. Birkh\u00e4user Boston Inc. Boston MA.  Gel\u2032fand I. M. Kapranov M. M. and Zelevinsky A. V. 1994. Discriminants Resultants and Multidimensional Determinants. Birkh\u00e4user Boston Inc. Boston MA.","DOI":"10.1007\/978-0-8176-4771-1"},{"key":"e_1_2_2_7_1","volume-title":"Graduate Texts in Mathematics","author":"Harris J."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01459264"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-92-06707-X"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015289823859"},{"key":"e_1_2_2_11_1","volume-title":"Algebraic Geometry and Geometric Modeling","author":"Krasauskas R."},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.2307\/1971448"},{"key":"e_1_2_2_13_1","volume-title":"Topics in Algebraic Geometry and Geometric Modeling. 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