Integrating Tensile Parameters in Mass-Spring System for Deformable Object Simulation

Besides finite element method, mass-spring system is widely used in Computer Graphics. It is indubitably the simplest and most intuitive deformable model that takes into account elastic considerations. This discrete model allows to perform with ease interactive deformations as well as to handle complex interactions. Thus, it is perfectly adapted to generate visually plausible animations. However, a drawback of this simple formulation is the relative difficulty to control efficiently realistic physically-based behaviors. Indeed, none of the existing models has succeeded in dealing with this satisfyingly. Moreover, we demonstrate that the mostly cited technique in the literature, proposed by Van Gelder, is far to be exact in most real cases, and consequently, this model can not be used in simulation. So, we propose a new general 3D formulation that reconstructs the geometrical model as an assembly of elementary hexahedral "bricks". Each brick (or element) is then transformed into a mass-spring system. Edges are replaced by springs that connect masses representing the vertices. The key point of our approach is the determination of the stiffness springs to reproduce the correct mechanical properties (Young's modulus and Poisson's ratio) of the reconstructed object. We validate our methodology by performing some numerical experiments. Finally, we evaluate the accuracy of our approach, by comparing our results with the deformation obtained by finite element method. Index Terms—Discrete Modeling, Physical Simulation, Mass-Spring System, Rheological Parameters. F