An Adaptive Contact Model for the Robust Simulation of Knots

In this paper, we present an adaptive model for dynamically deforming hyper-elastic rods. In contrast to existing approaches, adaptively introduced control points are not governed by geometric subdivision rules. Instead, their states are determined by employing a non-linear energy-minimization approach. Since valid control points are computed instantaneously, post-stabilization schemes are avoided and the stability of the dynamic simulation is improved.  Due to inherently complex contact configurations, the simulation of knot tying using rods is a challenging task. In order to address this problem, we combine our adaptive model with a robust and accurate collision handling method for elastic rods. By employing our scheme, complex knot configurations can be simulated in a physically plausible way.

An Adaptive Contact Model for the Robust Simulation of Knots

A Fast and Stable Penalty Method for Rigid Body Simulation

Two methods have been used extensively to model resting contact for rigid body simulation. The first approach, the penalty method, applies virtual springs to surfaces in contact to minimize interpenetration. This method, as typically implemented, results in oscillatory behavior and considerable penetration. The second approach, based on formulating resting contact as a linear complementarity problem, determines the resting contact forces analytically to prevent interpenetration. The analytical method exhibits expected-case polynomial complexity in the number of contact points, and may fail to find a solution in polynomial time when friction is modeled. We present a fast penalty method that minimizes oscillatory behavior and leads to little penetration during resting contact; our method compares favorably to the analytical method with regard to these two measures, while exhibiting much faster performance both asymptotically and empirically.

A Fast and Stable Penalty Method for Rigid Body Simulation