{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T17:24:47Z","timestamp":1778693087940,"version":"3.51.4"},"reference-count":27,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2006,7,1]],"date-time":"2006-07-01T00:00:00Z","timestamp":1151712000000},"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":[[2006,7]]},"abstract":"<jats:p>\n            Simulating human hair is recognized as one of the most difficult tasks in computer animation. In this paper, we show that the Kirchhoff equations for dynamic, inextensible elastic rods can be used for accurately predicting hair motion. These equations fully account for the nonlinear behavior of hair strands with respect to bending and twisting. We introduce a novel deformable model for solving them: each strand is represented by a\n            <jats:italic>Super-Helix<\/jats:italic>\n            , i.e., a piecewise helical rod which is animated using the principles of Lagrangian mechanics. This results in a realistic and stable simulation, allowing large time steps. Our second contribution is an in-depth validation of the Super-Helix model, carried out through a series of experiments based on the comparison of real and simulated hair motions. We show that our model efficiently handles a wide range of hair types with a high level of realism.\n          <\/jats:p>","DOI":"10.1145\/1141911.1142012","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"1180-1187","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":190,"title":["Super-helices for predicting the dynamics of natural hair"],"prefix":"10.1145","volume":"25","author":[{"given":"Florence","family":"Bertails","sequence":"first","affiliation":[{"name":"EVASION\/INRIA, Grenoble, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Basile","family":"Audoly","sequence":"additional","affiliation":[{"name":"LMM\/CNRS, Audoly Consulting, Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marie-Paule","family":"Cani","sequence":"additional","affiliation":[{"name":"EVASION\/INRIA, Grenoble, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernard","family":"Querleux","sequence":"additional","affiliation":[{"name":"L'Or\u00e9al Recherche, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fr\u00e9d\u00e9ric","family":"Leroy","sequence":"additional","affiliation":[{"name":"L'Or\u00e9al Recherche, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Luc","family":"L\u00e9v\u00eaque","sequence":"additional","affiliation":[{"name":"L'Or\u00e9al Recherche, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2006,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"crossref","unstructured":"Anjyo K. Usami Y. and Kurihara T. 1992. A simple method for extracting the natural beauty of hair. 111--120.  Anjyo K. Usami Y. and Kurihara T. 1992. A simple method for extracting the natural beauty of hair. 111--120.","DOI":"10.1145\/142920.134021"},{"key":"e_1_2_2_2_1","unstructured":"Audoly B. and Pomeau Y. 2006. Elasticity and Geometry: from hair curls to the nonlinear response of shells. Oxford University Press Oxford UK. To appear.  Audoly B. and Pomeau Y. 2006. Elasticity and Geometry: from hair curls to the nonlinear response of shells. Oxford University Press Oxford UK. To appear."},{"key":"e_1_2_2_3_1","doi-asserted-by":"crossref","unstructured":"Bando Y. Chen B.-Y. and Nishita T. 2003. Animating hair with loosely connected particles. Computer Graphics Forum (Eurographics'03) 22 3 411--418.  Bando Y. Chen B.-Y. and Nishita T. 2003. Animating hair with loosely connected particles. Computer Graphics Forum (Eurographics'03) 22 3 411--418.","DOI":"10.1111\/1467-8659.00688"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/133994.134084"},{"key":"e_1_2_2_5_1","volume-title":"ACM SIGGRAPH Symposium on Computer Animation, 207--213","author":"Bertails F."},{"key":"e_1_2_2_6_1","volume-title":"Proc. Graphics Interface, 71--78","author":"Bertails F."},{"key":"e_1_2_2_7_1","volume-title":"Eurographics '05 (short papers).","author":"Bertails F."},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/545261.545273"},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073368.1073389"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.1230211"},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Hadap S. and Magnenat-Thalmann N. 2001. Modeling dynamic hair as a continuum. Computer Graphics Forum (Eurographics'01) 20 3 329--338.  Hadap S. and Magnenat-Thalmann N. 2001. Modeling dynamic hair as a continuum. Computer Graphics Forum (Eurographics'01) 20 3 329--338.","DOI":"10.1111\/1467-8659.00525"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5977"},{"key":"e_1_2_2_13_1","volume-title":"EG CAS '01","author":"Koh C."},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1006\/gmod.2001.0547"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1001\/archderm.1988.01670090015003"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882345"},{"key":"e_1_2_2_17_1","volume-title":"EG CAS'01","author":"Nocent O."},{"key":"e_1_2_2_18_1","volume-title":"Strands: Interactive simulation of thin solids using cosserat models. 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In International Symposium on Surgery Simulation and Soft Tissue Modeling Springer-Verlag no. 2673 in Lecture Notes in Computer Science 15--26.","DOI":"10.1007\/3-540-45015-7_2"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073294"},{"key":"e_1_2_2_23_1","doi-asserted-by":"crossref","unstructured":"Robbins C. 2002. Chemical and Physical Behavior of Human Hair. 4th ed. Springer.  Robbins C. 2002. Chemical and Physical Behavior of Human Hair. 4th ed. Springer.","DOI":"10.1007\/b97447"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/vis.4340020410"},{"key":"e_1_2_2_25_1","volume-title":"Proceedings of Pacific Graphics'03","author":"Ward K."},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/97879.565650"},{"key":"e_1_2_2_27_1","unstructured":"Wolfram S. 1999. The Mathematica book (4th edition). Cambridge University Press New York NY USA.   Wolfram S. 1999. The Mathematica book (4th edition). 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