{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:41:32Z","timestamp":1774924892528,"version":"3.50.1"},"reference-count":36,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2013,11,1]],"date-time":"2013-11-01T00:00:00Z","timestamp":1383264000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100004963","name":"Seventh Framework Programme","doi-asserted-by":"publisher","award":["FP7-287723 REVERIE, FP7-323567 Harvest4D"],"award-info":[{"award-number":["FP7-287723 REVERIE, FP7-323567 Harvest4D"]}],"id":[{"id":"10.13039\/501100004963","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Chaire MODIM of Telecom ParisTech"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2013,11]]},"abstract":"<jats:p>\n            Shape approximation algorithms aim at computing simple geometric descriptions of dense surface meshes. Many such algorithms are based on mesh decimation techniques, generating coarse triangulations while optimizing for a particular metric which models the distance to the original shape. This approximation scheme is very efficient when enough polygons are allowed for the simplified model. However, as coarser approximations are reached, the intrinsic piecewise linear point interpolation which defines the decimated geometry fails at capturing even simple structures. We claim that when reaching such extreme simplification levels, highly instrumental in shape analysis, the approximating representation should explicitly and progressively model the volumetric extent of the original shape. In this paper, we propose\n            <jats:italic>Sphere-Meshes<\/jats:italic>\n            , a new shape representation designed for extreme approximations and substituting a\n            <jats:italic>sphere<\/jats:italic>\n            interpolation for the classic point interpolation of surface meshes. From a technical point-of-view, we propose a new shape approximation algorithm, generating a sphere-mesh at a prescribed level of detail from a classical polygon mesh. We also introduce a new metric to guide this approximation, the\n            <jats:italic>Spherical Quadric Error Metric<\/jats:italic>\n            in R\n            <jats:sup>4<\/jats:sup>\n            , whose minimizer finds the sphere that best approximates a set of tangent planes in the input and which is sensitive to surface orientation, thus distinguishing naturally between the\n            <jats:italic>inside<\/jats:italic>\n            and the\n            <jats:italic>outside<\/jats:italic>\n            of an object. We evaluate the performance of our algorithm on a collection of models covering a wide range of topological and geometric structures and compare it against alternate methods. Lastly, we propose an application to deformation control where a sphere-mesh hierarchy is used as a convenient rig for altering the input shape interactively.\n          <\/jats:p>","DOI":"10.1145\/2508363.2508384","type":"journal-article","created":{"date-parts":[[2013,11,6]],"date-time":"2013-11-06T14:09:19Z","timestamp":1383746959000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":69,"title":["Sphere-Meshes"],"prefix":"10.1145","volume":"32","author":[{"given":"Jean-Marc","family":"Thiery","sequence":"first","affiliation":[{"name":"Telecom ParisTech -- CNRS LTCI -- Institut Mines-Telecom"}]},{"given":"\u00c9milie","family":"Guy","sequence":"additional","affiliation":[{"name":"Telecom ParisTech -- CNRS LTCI -- Institut Mines-Telecom"}]},{"given":"Tamy","family":"Boubekeur","sequence":"additional","affiliation":[{"name":"Telecom ParisTech -- CNRS LTCI -- Institut Mines-Telecom"}]}],"member":"320","published-online":{"date-parts":[[2013,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Shape Modeling International","author":"Alliez P.","year":"2003","unstructured":"Alliez , P. , de Verdi\u00e8re , E. C. , Devillers , O. , and Isenburg , M . 2003 . In Shape Modeling International , 2003 , IEEE, 49--58. Alliez, P., de Verdi\u00e8re, E. C., Devillers, O., and Isenburg, M. 2003. In Shape Modeling International, 2003, IEEE, 49--58."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009475"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/376957.376986"},{"key":"e_1_2_1_4_1","volume-title":"Image Processing, 1996. Proceedings., International Conference on","volume":"3","author":"Attali D.","unstructured":"Attali , D. , and Montanvert , A . 1996. Modeling noise for a better simplification of skeletons . In Image Processing, 1996. Proceedings., International Conference on , vol. 3 , IEEE, 13--16. Attali, D., and Montanvert, A. 1996. Modeling noise for a better simplification of skeletons. In Image Processing, 1996. 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