Smoothed Particles A New Paradigm for Animating Highly Deformable Bodies.pdf

Smoothed Particles: A new paradigm for animating highly deformable bodies Mathieu Desbrun Marie-Paule Gascuel iMAGIS? - GRAVIR / IMAG BP 53, F-38041 Grenoble cedex 09, France Abstract This paper presents a new formalism for simulating highly deformable bodies with a particle system. Smoothed particles represent sample points that enable the approximation of the values and derivatives of local phys- ical quantities inside a medium. They ensure valid and stable simulation of state equations that describe the physical behavior of the material. We extend the initial formalism, first introduced for simulating cos- mological fluids, to the animation of inelastic bodies with a wide range of stiffness and viscosity. We show that the smoothed particles paradigm leads to a coherent definition of the object’s surface as an iso-surface of the mass density function. Implementation issues are discussed, including an efficient integration scheme using individually adapted time steps to integrate particle motion. Animation requires a linear complexity in the number of particles, offering reasonable time and memory use. 1 Introduction Modeling and simulating deformable bodies has attracted a lot of attention in Computer Graphics. Elastic materials that recover their rest shape after any deformation are generally simulated with finite-difference [TPBF87] or finite- element [GMTT89, PW89] methods. Nevertheless, these approaches, which ap- proximate the body by a mesh of nodes of fixed topology, are not adapted to the animation of substances able to undergo large inelastic deformations. In this case, the use of particle systems is more appropriate. These systems are unstruc- tured in the sense that interactions between point masses do not depend on a specified graph of connections, but on distance. Consequently, particle systems seem the easiest approach for modeling large changes in shape and in topology. ?iMAGIS is a joint project of CNRS, INRIA, Institut National Polytechnique de Gr