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We propose a particular decoupling of scaling and rotation which allows us to find near to conformal deformations as minimizers of a quadratic, convex Dirichlet energy. Applied to tetrahedral meshes we find deformations with low quasiconformal distortion as the principal eigenvector of a (quaternionic) Laplace matrix. The resulting algorithms can be implemented with highly optimized standard linear algebra libraries and yield deformations comparable in quality to far more expensive approaches.<\/jats:p>","DOI":"10.1145\/2766916","type":"journal-article","created":{"date-parts":[[2015,7,28]],"date-time":"2015-07-28T12:26:38Z","timestamp":1438086398000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Close-to-conformal deformations of volumes"],"prefix":"10.1145","volume":"34","author":[{"given":"Albert","family":"Chern","sequence":"first","affiliation":[{"name":"Caltech"}]},{"given":"Ulrich","family":"Pinkall","sequence":"additional","affiliation":[{"name":"TU Berlin"}]},{"given":"Peter","family":"Schr\u00f6der","sequence":"additional","affiliation":[{"name":"Caltech"}]}],"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\/1531326.1531340"},{"key":"e_1_2_2_3_1","first-page":"141","article-title":"On Certain Results Relating to Quaternions","volume":"26","author":"Cayley A.","year":"1845","unstructured":"Cayley , A. 1845 . 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