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Compared to the latter, purely curvature\u2010based model \u2013 the so\u2010called\n                    <jats:italic>chained<\/jats:italic>\n                    formulation \u2013, the\n                    <jats:italic>mixed<\/jats:italic>\n                    formulation that we propose here drastically reduces the algorithmic complexity of the solving scheme \u2013 from quadratic to quasi\u2010linear \u2013 and simplifies the handling of positional constraints, including contacts. As such, it recovers the main advantages of classical position\u2010based models, while at the same time preserving the high\u2010order convergence of curvature\u2010based models, hence offering an interesting trade\u2010off. Furthermore, the smooth, piecewise circular arc representation of super\u2010circles allows to avoid the spurious jumps in contact forces that are difficult to get rid of with position\u2010based models. Our model is validated quantitatively against demanding mechanical tests involving contact, friction, snapping, and vibrations. Moreover, its versatility, robustness and efficiency are demonstrated through several interactive dynamic scenarios featuring multiple planar elastic rods subject to various types of boundary conditions and constraints. The corresponding source code, Circonflex, is freely delivered to the research community under the GNU GPL v3 licence.\n                  <\/jats:p>","DOI":"10.1111\/cgf.70414","type":"journal-article","created":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T08:12:14Z","timestamp":1777623134000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mixed Super\u2010Circles"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-6962-5873","authenticated-orcid":false,"given":"Emile","family":"Hohnadel","sequence":"first","affiliation":[{"name":"Universit\u00e9 Grenoble\u2010Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble  France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8706-6576","authenticated-orcid":false,"given":"Thibaut","family":"M\u00e9tivet","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Grenoble\u2010Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble  France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8930-3048","authenticated-orcid":false,"given":"Florence","family":"Bertails\u2010Descoubes","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Grenoble\u2010Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble  France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,5,1]]},"reference":[{"key":"e_1_2_1_9_2_2","doi-asserted-by":"crossref","unstructured":"AcaryV. 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