Hohnadel, EmileMétivet, ThibautBertails-Descoubes, FlorenceMasia, BelenThies, Justus2026-04-172026-04-1720261467-8659https://diglib.eg.org/handle/10.1111/cgf70414https://doi.org/10.1111/cgf70414We introduce mixed super-circles, a position-curvature formulation of the original dynamic 2D super-helix model. Compared to the purely curvature-based chained formulation, the mixed formulation drastically reduces the algorithmic complexity of the solving scheme from quadratic to quasi-linear and simplifies the handling of positional constraints including contacts. It recovers the advantages of classical position-based models while preserving the high-order convergence of curvature-based models. The smooth piecewise circular arc representation avoids spurious jumps in contact forces that are difficult to eliminate with position-based models. The model is validated quantitatively against demanding mechanical tests involving contact, friction, snapping and vibrations. Its versatility, robustness and efficiency are demonstrated through interactive scenarios with multiple planar elastic rods under various boundary conditions and constraints. The corresponding source code, Circonflex, is released under the GNU GPL v3 licence.CC-BY-4.0Computing methodologies → Physical simulationModeling and simulation10.1111/cgf.7041412 pages