Integrating Tensile Parameters in Hexahedral Mass-Spring System for Simulation

Abstract

Besides finite element method, mass-spring systems are widely used in Computer Graphics. It is indubitably the simplest and most intuitive deformable model. This discrete model allows to perform interactive deformations with ease and 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 physically realistic behaviors. Indeed, none of the existing models has succeeded in dealing with this satisfyingly. We demonstrate that this restriction cannot be over-passed with the classical mass-spring model, and 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.