Meshless Approximation Methods and Applications in Physics Based Modeling and Animation

Abstract

With growing computing power, physical simulations have become increasingly important in computer graphics. Content creation for movies and interactive computer games relies heavily on physical models, and physicallyinspired interactions have proven to be a great metaphor for shape modeling. This tutorial will acquaint the reader with meshless methods for simulation and modeling. These methods differ from the more common grid or mesh-based methods in that they require less constraints on the spatial discretization. Since the algorithmic structure of simulation algorithms so critically depends on the underlying discretization, we will first treat methods for function approximation from discrete, irregular samples: smoothed particle hydrodynamics and moving least squares. This discussion will include numerical properties as well as complexity considerations. In the second part of this tutorial, we will then treat a number of applications for these approximation schemes. The smoothed particle hydrodynamics framework is used in fluid dynamics and has proven particularly popular in real-time applications. Moving least squares approximations provide higher order consistency, and are therefore suited for the simulation of elastic solids. We will cover both basic elasticity and applications in modeling.