Dimension Expansion for Untangling Mass-Spring System

The mass-spring model is popular for representing the dynamics of distance-based systems. In particular, elastic materials can be easily simulated using the mass-spring model, thanks to the simplicity of its spring-length constraint. The model is commonly defined in a typical simulation domain, that is, 2D or 3D Euclidean space. If the elastic body is heavily deformed, however, its mass-spring configuration easily becomes hard or impossible to resolve in the typical domain. In order to tackle the challenge, we propose a dimension expansion method, which utilizes auxiliary coordinates for defining the model. By solving the problem in such an expanded domain, the solver can untangle complex spring configurations that are otherwise locked in local minima. Our study demonstrates the potential of the dimension expansion method for mass-spring-based elastic-body simulations and for different applications such as multi-dimensional data embedding problems.