{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T05:55:22Z","timestamp":1712469322736},"reference-count":25,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2016,8,15]],"date-time":"2016-08-15T00:00:00Z","timestamp":1471219200000},"content-version":"vor","delay-in-days":14,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[2016,8]]},"abstract":"Abstract<\/jats:title>Let X = {f1<\/jats:sub>, \u2026, fn<\/jats:sub>} be a set of scalar functions of the form fi<\/jats:sub> : \u211d2<\/jats:sup> \u2192 \u211d which satisfy some natural properties. We describe a subdivision algorithm for computing a clustered \u03b5\u2010isotopic approximation of the minimization diagram of X. By exploiting soft predicates and clustering of Voronoi vertices, our algorithm is the first that can handle arbitrary degeneracies in X, and allow scalar functions which are piecewise smooth, and not necessarily semi\u2010algebraic.<\/jats:p>We apply these ideas to the computation of anisotropic Voronoi diagram of polygonal sets; this is a natural generalization of anisotropic Voronoi diagrams of point sites, which extends multiplicatively weighted Voronoi diagrams. We implement a prototype of our anisotropic algorithm and provide experimental results.<\/jats:p>","DOI":"10.1111\/cgf.12979","type":"journal-article","created":{"date-parts":[[2016,8,16]],"date-time":"2016-08-16T04:05:39Z","timestamp":1471320339000},"page":"229-247","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Planar Minimization Diagrams via Subdivision with Applications to Anisotropic Voronoi Diagrams"],"prefix":"10.1111","volume":"35","author":[{"given":"H.","family":"Bennett","sequence":"first","affiliation":[{"name":"Courant Institute, NYU New York USA"}]},{"given":"E.","family":"Papadopoulou","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, USI Lugano Switzerland"}]},{"given":"C.","family":"Yap","sequence":"additional","affiliation":[{"name":"Courant Institute, NYU New York USA"}]}],"member":"311","published-online":{"date-parts":[[2016,8,15]]},"reference":[{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044482537-7\/50006-1"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1142\/8685"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.08.021"},{"key":"e_1_2_7_5_2","unstructured":"BeckerR. 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