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This proof leads to a set of angular constraints that must be satisfied for an immersion to exist in\n            <jats:italic>R<\/jats:italic>\n            <jats:sup>3<\/jats:sup>\n            . This formulation lets us easily specify conditions to avoid inverted tetrahedra and multiply-covered vertices, thus leading to locally injective maps. We then present a constrained optimization method that modifies input angles when they do not satisfy constraints. Additionally, we develop a fast spectral reconstruction method to robustly recover positions from dihedral angles. We demonstrate the applicability of our representation with examples of volume parameterization, shape interpolation, mesh optimization, connectivity shapes, and mesh compression.\n          <\/jats:p>","DOI":"10.1145\/2766900","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T12:26:38Z","timestamp":1438086398000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["Dihedral angle-based maps of tetrahedral meshes"],"prefix":"10.1145","volume":"34","author":[{"given":"Gilles-Philippe","family":"Paill\u00e9","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Montr\u00e9al"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Ray","sequence":"additional","affiliation":[{"name":"INRIA Nancy - Grand Est"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre","family":"Poulin","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Montr\u00e9al"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alla","family":"Sheffer","sequence":"additional","affiliation":[{"name":"University of British Columbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno","family":"L\u00e9vy","sequence":"additional","affiliation":[{"name":"INRIA Nancy - Grand Est"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,7,27]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461931"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344859"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.20965"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/11\/11\/013"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0040-9383(95)00047-X"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1391989.1391995"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461983"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/2010324.1964999"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461986"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/167088.167207"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/10\/8\/083006"},{"key":"e_1_2_2_12_1","unstructured":"Graphite 2015 Jan. http:\/\/alice.loria.fr.  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