Identification of Spring Parameters for Deformable Object Simulation

Mass spring models are frequently used to simulate deformable objects because of their conceptual simplicity and computational speed. Unfortunately, the model parameters are not related to elastic material constitutive laws in an obvious way. Several methods to set optimal parameters have been proposed but, so far, only with limited success. We analyze the parameter identification problem and show the difficulties, which have prevented previous work from reaching wide usage. Our main contribution is a new method to derive analytical expressions for the spring parameters from an isotropic linear elastic reference model. The method is described and expressions for several mesh topologies are derived. These include triangle, rectangle, and tetrahedron meshes. The formulas are validated by comparing the static deformation of the MSM with reference deformations simulated with the finite element method.