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We present an algorithm for designing smooth N-symmetry fields on surfaces respecting\n            <jats:italic>generalized symmetries<\/jats:italic>\n            of the shape, while maintaining alignment with local features. Our formulation for constructing symmetry fields is based on global symmetries, which are given as input to the algorithm, with no isometry assumptions. We explore in detail the properties of generalized symmetries (reflections in particular), and we also develop an algorithm for the robust computation of such symmetry maps, based on a small number of correspondences, for surfaces of genus zero.\n          <\/jats:p>","DOI":"10.1145\/2185520.2185607","type":"journal-article","created":{"date-parts":[[2012,8,6]],"date-time":"2012-08-06T18:11:37Z","timestamp":1344276697000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":45,"title":["Fields on symmetric surfaces"],"prefix":"10.1145","volume":"31","author":[{"given":"Daniele","family":"Panozzo","sequence":"first","affiliation":[{"name":"University of Genova and ETH Zurich and New York University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yaron","family":"Lipman","sequence":"additional","affiliation":[{"name":"Weizmann Institute of Science"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Enrico","family":"Puppo","sequence":"additional","affiliation":[{"name":"University of Genova"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Zorin","sequence":"additional","affiliation":[{"name":"New York University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2012,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073207"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01868.x"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0508601103"},{"key":"e_1_2_2_5_1","volume-title":"Image Processing, 2008. 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