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Graph."],"published-print":{"date-parts":[[2014,11,19]]},"abstract":"<jats:p>\n            Smooth space deformation has become a vital tool for the animation and design of 2D and 3D shapes. Linear methods, under the umbrella term of \"linear blend skinning\", are the\n            <jats:italic>de facto<\/jats:italic>\n            standard for 3D animations. Unfortunately such approaches do not trivially extend to deforming\n            <jats:italic>vector graphics<\/jats:italic>\n            , such as the cubic B\u00e9zier splines prevalent in 2D or subdivision surfaces in 3D. We propose a variational approach to reposition the control points of cubic B\u00e9zier splines and Catmull-Clark subdivision surfaces---or any linear subdivision curves or surfaces---to produce curves or surfaces which match a linear blend skinning deformation as closely as possible. Exploiting the linearity of linear blend skinning, we show how this optimization collapses neatly into the repeated multiplication of a matrix per handle. We support\n            <jats:italic>C<\/jats:italic>\n            <jats:sup>0<\/jats:sup>\n            ,\n            <jats:italic>C<\/jats:italic>\n            <jats:sup>1<\/jats:sup>\n            ,\n            <jats:italic>G<\/jats:italic>\n            <jats:sup>1<\/jats:sup>\n            , and fixed-angle continuity constraints between adjacent B\u00e9zier curves in a spline. Complexity scales linearly with respect to the number of input curves and run-time performance is fast enough for real-time editing and animation of high-resolution shapes.\n          <\/jats:p>","DOI":"10.1145\/2661229.2661270","type":"journal-article","created":{"date-parts":[[2014,11,18]],"date-time":"2014-11-18T14:21:03Z","timestamp":1416320463000},"page":"1-9","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":18,"title":["Skinning cubic B\u00e9zier splines and Catmull-Clark subdivision surfaces"],"prefix":"10.1145","volume":"33","author":[{"given":"Songrun","family":"Liu","sequence":"first","affiliation":[{"name":"George Mason University"}]},{"given":"Alec","family":"Jacobson","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Yotam","family":"Gingold","sequence":"additional","affiliation":[{"name":"George Mason University"}]}],"member":"320","published-online":{"date-parts":[[2014,11,19]]},"reference":[{"key":"e_1_2_2_1_1","unstructured":"Adobe Systems Inc. 2014. 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