{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T06:09:49Z","timestamp":1784268589990,"version":"3.55.0"},"reference-count":37,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2013,7,21]],"date-time":"2013-07-21T00:00:00Z","timestamp":1374364800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2013,7,21]]},"abstract":"<jats:p>The quality of a global parametrization is determined by a number of factors, including amount of distortion, number of singularities (cones), and alignment with features and boundaries. Placement of cones plays a decisive role in determining the overall distortion of the parametrization; at the same time, feature and boundary alignment also affect the cone placement. A number of methods were proposed for automatic choice of cone positions, either based on singularities of cross-fields and emphasizing alignment, or based on distortion optimization.<\/jats:p>\n          <jats:p>\n            In this paper we describe a method for placing cones for seamless global parametrizations with alignment constraints. We use a close relation between variation-minimizing cross-fields and related 1-forms and conformal maps, and demonstrate how it leads to a constrained optimization problem formulation. We show for boundary-aligned parametrizations metric distortion may be reduced by\n            <jats:italic>cone chains<\/jats:italic>\n            , sometimes to an arbitrarily small value, and the trade-off between the distortion and the number of cones can be controlled by a regularization term. Constrained parametrizations computed using our method have significantly lower distortion compared to the state-of-the art field-based method, yet maintain feature and boundary alignment. In the most extreme cases, parametrization collapse due to alignment constraints is eliminated.\n          <\/jats:p>","DOI":"10.1145\/2461912.2461970","type":"journal-article","created":{"date-parts":[[2013,7,16]],"date-time":"2013-07-16T18:06:45Z","timestamp":1373998005000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":73,"title":["Controlled-distortion constrained global parametrization"],"prefix":"10.1145","volume":"32","author":[{"given":"Ashish","family":"Myles","sequence":"first","affiliation":[{"name":"New York University"}],"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":[[2013,7,21]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2008.01142.x"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531383"},{"key":"e_1_2_2_3_1","unstructured":"Bommes D. Lvy B. Pietroni N. Puppo E. Silva C. Tarini M. and Zorin D. 2012. Quad Meshing. Eurographics Association Cagliari Sardinia Italy M.-P. Cani and F. Ganovelli Eds. 159--182.  Bommes D. Lvy B. Pietroni N. Puppo E. Silva C. Tarini M. and Zorin D. 2012. Quad Meshing. Eurographics Association Cagliari Sardinia Italy M.-P. Cani and F. Ganovelli Eds. 159--182."},{"key":"e_1_2_2_4_1","unstructured":"Bunin G. 2008. Towards unstructured mesh generation using the inverse poisson problem. arXiv preprint arXiv:0802.2399.  Bunin G. 2008. 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