Time-Step Dependent Spring’s Stiffness for Numerical Stability of Mass-Spring Models

Classic Mass-Spring Models (MSMs) tend to provide instable deformations for high spring’s stiffness values. These high values cause overshooting at the integration step of the seconds Newton’s law of motion. In this paper, we propose an improvement of current state-of-the-art MSMs where we adapt the time step integration with respect to the spring’s stiffness. To further stabilize the proposed approach, we explicitly enforce the fixed boundaries of the deformed object to remain static at every iteration of the algorithm. We provide synthetic experimental results to show the relevance of our approach. We also quantitatively compare the results obtained with the proposed approach to deformations obtained with a nonlinear finite element method.