{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:36:24Z","timestamp":1774877784875,"version":"3.50.1"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2006,4,1]],"date-time":"2006-04-01T00:00:00Z","timestamp":1143849600000},"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":[[2006,4]]},"abstract":"<jats:p>We propose an automatic method for finding symmetries of 3D shapes, that is, isometric transforms which leave a shape globally unchanged. These symmetries are deterministically found through the use of an intermediate quantity: the generalized moments. By examining the extrema and spherical harmonic coefficients of these moments, we recover the parameters of the symmetries of the shape. The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its subparts. Applications of this work range from coherent remeshing of geometry with respect to the symmetries of a shape to geometric compression, intelligent mesh editing, and automatic instantiation.<\/jats:p>","DOI":"10.1145\/1138450.1138462","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"439-464","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":106,"title":["Accurate detection of symmetries in 3D shapes"],"prefix":"10.1145","volume":"25","author":[{"given":"Aur\u00e9lien","family":"Martinet","sequence":"first","affiliation":[{"name":"ARTIS, INRIA Rh\u00f4ne-Alpes, Saint Ismier, France"}]},{"given":"Cyril","family":"Soler","sequence":"additional","affiliation":[{"name":"ARTIS, INRIA Rh\u00f4ne-Alpes, Saint Ismier, France"}]},{"given":"Nicolas","family":"Holzschuch","sequence":"additional","affiliation":[{"name":"ARTIS, INRIA Rh\u00f4ne-Alpes, Saint Ismier, France"}]},{"given":"Fran\u00e7ois X.","family":"Sillion","sequence":"additional","affiliation":[{"name":"ARTIS, INRIA Rh\u00f4ne-Alpes, Saint Ismier, France"}]}],"member":"320","published-online":{"date-parts":[[2006,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1985.1676605"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2003.07.002"},{"key":"e_1_2_1_4_1","volume-title":"The Theory of Spherical and Ellipsoidal Harmonics","author":"Hobson E. W.","unstructured":"Hobson , E. W. 1931. The Theory of Spherical and Ellipsoidal Harmonics . Cambridge University Press , Cambridge, UK . Hobson, E. W. 1931. The Theory of Spherical and Ellipsoidal Harmonics. Cambridge University Press, Cambridge, UK."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1021\/jp953350u"},{"key":"e_1_2_1_6_1","volume-title":"Proceedings of the International Workshop on Computational Geometry---Methods, Algorithms and Applications (CG '91)","volume":"553","author":"Jiang X.-Y.","unstructured":"Jiang , X.-Y. and Bunke , H . 1991. Determination of the symmetries of polyhedra and an application to object recognition . In Proceedings of the International Workshop on Computational Geometry---Methods, Algorithms and Applications (CG '91) . Lecture Notes in Computer Science , vol. 553 . Springer, London, UK, 113--121. Jiang, X.-Y. and Bunke, H. 1991. Determination of the symmetries of polyhedra and an application to object recognition. In Proceedings of the International Workshop on Computational Geometry---Methods, Algorithms and Applications (CG '91). Lecture Notes in Computer Science, vol. 553. Springer, London, UK, 113--121."},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of the 2003 Eurographics\/ACM Siggraph Symposium on Geometry Processing (SGP '03)","author":"Kazhdan M. M.","unstructured":"Kazhdan , M. M. , Funkhouser , T. A. , and Rusinkiewicz , S . 2003. Rotation invariant spherical harmonic representation of 3D shape descriptors . In Proceedings of the 2003 Eurographics\/ACM Siggraph Symposium on Geometry Processing (SGP '03) . Eurographics Association, Aire-la-Ville, Switzerland, 167--175. Kazhdan, M. M., Funkhouser, T. A., and Rusinkiewicz, S. 2003. Rotation invariant spherical harmonic representation of 3D shape descriptors. In Proceedings of the 2003 Eurographics\/ACM Siggraph Symposium on Geometry Processing (SGP '03). 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