Smarticles: A Method for Identifying and Correcting Instability and Error Caused by Explicit Integration Techniques in Physically Based Simulations

Author

Susan Aileen Marano, California Polytechnic State University, San Luis ObispoFollow

DOI: https://doi.org/10.15368/theses.2014.125
Available at: https://digitalcommons.calpoly.edu/theses/1304

Date of Award

6-2014

Degree Name

MS in Computer Science

Department/Program

Computer Science

Advisor

Zoe Wood

Abstract

Using an explicit integration method in physically based animations has many advantages including conceptual and computational simplicity, however, it re- quires small time steps to ensure low numerical instability. Simulations with large numbers of individually interacting components such as cloth, hair, and fluid models, are limited by the sections of particles most susceptible to error. This results in the need for smaller time steps than required for the majority of the system. These sections can be diverse and dynamic, quickly changing in size and location based on forces in the system. Identifying and handling these trou- blesome sections could allow for a larger time step to be selected, while preventing a breakdown in the simulation.

This thesis presents Smarticles (smart particles), a method of individually de- tecting particles exhibiting signs of instability and stabilizing them with minimal adverse effects to visual accuracy. As a result, higher levels of error introduced from large time steps can be tolerated with minimal overhead. Two separate approaches to Smarticles were implemented. They attempt to find oscillating particles by analyzing a particle’s (1) past behavior and (2) behavior with re- spect to its neighbors along a strand. Both versions of Smarticles attempt to correct unstable particles using velocity dampening. Smarticles was applied to a two dimensional hair simulation modeled as a continuum using smooth particle hydrodynamic. Hair strands are formed by linking particles together using one of two methods: position based dynamics or mass-spring forces.

Both versions of Smarticles, as well as a control of normal particles, were directly compared and evaluated based on stability and visual fluidity. Hair particles were exposed to various forms of external forces under increasing time step lengths. Testing showed that both versions of Smarticles working together allowed an average increase of 18.62% in the time step length for hair linked with position based dynamics. In addition, Smarticles was able to significantly reduce visible instability at even larger time steps. While these results suggest Smarticles is successful, the method used to correct particle instability may jeopardize other important aspects of the simulation. A more accurate correction method would likely need to be developed to make Smarticles an advantageous method.