"Physically Based Modeling using the Mass Spring System with an Analysis of Numerical Solutions"
Chad Miller 2005
Abstract
This study focuses on soft body dynamics using the mass spring system to model cloth. A soft body, such as jello, cloth or water, is one that can be easily deformed. The mass spring system uses springs to connect particles that have mass. These springs behave according to Hooke's Law which defines a spring force that is used to predict each particle's acceleration, velocity and position at time t. The thesis further analyzes the standard numeral solutions for physically based systems - Euler, Euler Midpoint, and Runge Kutta, for accuracy of a cloth model animation implemented for this project.
In the cloth animations presented below, all parameters are identical except for the numerical solver applied in the simulation. The time step for each solver is 0.1. The only external force acting on the cloth is gravity. The cloth is fixed at its upper corners. The Euler simulation destabilizes after 12 frames, the Midpoint simulation destabilizes after 25 frames and the Runge Kutta remains stable and behaves in a reasonably accurate manner.