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Graph."],"published-print":{"date-parts":[[2013,4]]},"abstract":"<jats:p>\n            We introduce a new family of binary composition operators that solves four major problems of constructive implicit modeling: suppressing bulges when two shapes merge, avoiding unwanted blending at a distance, ensuring that the resulting shape keeps the topology of the union, and enabling sharp details to be added without being blown up. The key idea is that field functions should not only be combined based on their values, but also on their\n            <jats:italic>gradients<\/jats:italic>\n            . We implement this idea through a family of\n            <jats:italic>C<\/jats:italic>\n            <jats:sup>\u221e<\/jats:sup>\n            composition operators evaluated on the GPU for efficiency, and illustrate it by applications to constructive modeling and animation.\n          <\/jats:p>","DOI":"10.1145\/2451236.2451238","type":"journal-article","created":{"date-parts":[[2013,5,3]],"date-time":"2013-05-03T12:30:25Z","timestamp":1367584225000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":51,"title":["A gradient-based implicit blend"],"prefix":"10.1145","volume":"32","author":[{"given":"Olivier","family":"Gourmel","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Toulouse, CNRS, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Loic","family":"Barthe","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Toulouse, CNRS, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marie-Paule","family":"Cani","sequence":"additional","affiliation":[{"name":"Grenoble Universit\u00e9s, CNRS, INRIA Grenoble, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brian","family":"Wyvill","sequence":"additional","affiliation":[{"name":"University of Victoria and University of Bath, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adrien","family":"Bernhardt","sequence":"additional","affiliation":[{"name":"Grenoble Universit\u00e9s, CNRS, INRIA Grenoble, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mathias","family":"Paulin","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Toulouse, CNRS, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Herbert","family":"Grasberger","sequence":"additional","affiliation":[{"name":"University of Victoria, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2013,4,30]]},"reference":[{"key":"e_1_2_2_1_1","unstructured":"Alexe A. Barthe L. Cani M. and Gaildrat V. 2005. Shape modelling by sketching using convolution surfaces. In Pacific Graphics Short Papers.  Alexe A. Barthe L. Cani M. and Gaildrat V. 2005. Shape modelling by sketching using convolution surfaces. In Pacific Graphics Short Papers."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.t01-1-00643"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218654301000114"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021865430400064X"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01606.x"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/2386301.2386312"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/357306.357310"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.114"},{"key":"e_1_2_2_9_1","volume-title":"1997b. Introduction to Implicit Surfaces. 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Eurographics Association, 1--8."},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166157"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01898351"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00670"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.t01-1-00709"},{"key":"e_1_2_2_15_1","doi-asserted-by":"crossref","unstructured":"Pasko A.\n     and \n      Adzhiev V\n  . \n  2004\n  . Function-Based shape modeling: Mathematical framework and specialized language. In Automated Deduction in Geometry Lecture Notes in Artificial Intelligence vol. \n  2930 Springer 132--160.  Pasko A. and Adzhiev V. 2004. Function-Based shape modeling: Mathematical framework and specialized language. 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