Theories for Mass-Spring Simulation in Computer Graphics: Stability, Costs and Improvements

Spring-mass systems are widely used in computer animation to model soft objects. Although the systems can be numerically solved either by explicit methods or implicit methods, it has been difficult to obtain stable results from explicit methods. This paper describes detailed discussion on stabilizing explicit methods in spring-mass simulation. The simulation procedures are modeled as a linear digital system, and system stability is mathematically defined. This allows us to develop theories of simulation stability. The application of these theories to explicit methods allows them to become as stable as implicit methods. Furthermore, a faster explicit method is proposed. Experiments confirm the theories and demonstrate the efficiency of the proposed methods. key words: computer graphics, computer animation, physically-based animation