Implicit-Explicit simulation of Mass-Spring-Charge Systems

Point masses connected by springs, or mass-spring systems, are widely used in computer animation to approximate the behavior of deformable objects. One of the restrictions imposed by these models is that points that are not topologically constrained (linked by a spring) are unable to interact with each other explicitly. Such interactions would introduce a new dimension for artistic control and animation within the computer graphics community. Beyond graphics, such a model could be an effective proxy to use for model-based learning of complex physical systems such as molecular biology. We propose to imbue masses in a mass-spring system with electrostatic charge leading a system with internal forces between all pairs of charged points -- regardless of whether they are linked by a spring. We provide a practical and stable algorithm to simulate charged mass-spring systems over long time horizons. We demonstrate how these systems may be controlled via parameters such as guidance electric fields or external charges, thus presenting fresh opportunities for artistic authoring. Our method is especially appropriate for computer graphics applications due to its robustness at larger simulation time steps.