Mixed Super‐Circles

Abstract We introduce mixed super‐circles, a position‐curvature formulation of the original dynamic 2D super‐helix model. Compared to the latter, purely curvature‐based model – the so‐called chained formulation –, the mixed formulation that we propose here drastically reduces the algorithmic complexity of the solving scheme – from quadratic to quasi‐linear – and simplifies the handling of positional constraints, including contacts. As such, it recovers the main advantages of classical position‐based models, while at the same time preserving the high‐order convergence of curvature‐based models, hence offering an interesting trade‐off. Furthermore, the smooth, piecewise circular arc representation of super‐circles allows to avoid the spurious jumps in contact forces that are difficult to get rid of with position‐based 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.