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Graph."],"published-print":{"date-parts":[[2018,4,30]]},"abstract":"<jats:p>\n            We introduce a variational approach for modeling\n            <jats:italic>n<\/jats:italic>\n            -symmetry vector and direction fields on surfaces that supports interpolation and alignment constraints, placing singularities and local editing, while providing real-time responses. The approach is based on novel biharmonic and\n            <jats:italic>m<\/jats:italic>\n            -harmonic energies for\n            <jats:italic>n<\/jats:italic>\n            -fields on surface meshes and the integration of hard constraints to the resulting optimization problems. Real-time computation rates are achieved by a model reduction approach employing a Fourier-like\n            <jats:italic>n<\/jats:italic>\n            -vector field decomposition, which associates frequencies and modes to\n            <jats:italic>n<\/jats:italic>\n            -vector fields on surfaces. To demonstrate the benefits of the proposed\n            <jats:italic>n<\/jats:italic>\n            -field modeling approach, we use it for controlling stroke directions in line-art drawings of surfaces and for the modeling of anisotropic BRDFs, which define the reflection behavior of surfaces.\n          <\/jats:p>","DOI":"10.1145\/3177750","type":"journal-article","created":{"date-parts":[[2018,3,14]],"date-time":"2018-03-14T12:34:20Z","timestamp":1521030860000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Modeling\n            <i>n<\/i>\n            -Symmetry Vector Fields using Higher-Order Energies"],"prefix":"10.1145","volume":"37","author":[{"given":"Christopher","family":"Brandt","sequence":"first","affiliation":[{"name":"Delft University of Technology, XE Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonardo","family":"Scandolo","sequence":"additional","affiliation":[{"name":"Delft University of Technology, XE Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elmar","family":"Eisemann","sequence":"additional","affiliation":[{"name":"Delft University of Technology, XE Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"Hildebrandt","sequence":"additional","affiliation":[{"name":"Delft University of Technology, XE Delft, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,3,13]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1080\/10867651.2000.10487522"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2723158"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015772"},{"key":"e_1_2_2_5_1","doi-asserted-by":"crossref","unstructured":"Mario Botsch Leif Kobbelt Mark Pauly Pierre Alliez and Bruno Levy. 2010. 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