New Mass-Spring System Integrating Elasticity Parameters in 2D

Besides the finite element method, the massspring discrete modeling is widely used in computer graphics. This discrete model allows to perform very easily interactive deformations and to handle quite complex interactions with only a few equations. Thus, it is perfectly adapted to generate visually correct 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 to deal satisfyingly with this. 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 its interest is limited to some specific non realistic animations. Here, we propose a new general 2D formulation that reconstructs the geometrical model as an assembly of elementary ”bricks”. Each brick (or element) is then transformed into a mass-spring system, in which edges are springs connecting masses placed on the element vertices. The key point of our approach is the determination of the stiffness constant of each spring to reproduce the correct mechanical properties (Young’s modulus, Poisson’s ratio and shear modulus) of the reconstructed object. We validate our methodology with the help of some numerical experimentation of mechanics, like stretching, shearing and loading and then we evaluate the accuracy limits of our approach.