3D Cloth Simulation

Eva SchifferAaron Bryden

Goal

Learn about methods of 3D cloth simulation

Implement a simulation with:

point masses and a simple spring system

the choice of explicit, and implicit integration

Existing methods, springs

Cloth is modeled as a system of point masses

All springs use the same force equation

Three types of springs:

structural springs

sheer springs

bend springs

( )llkxkf ssspring −−=−= 0

( )21 vvkvkf dddamp −−=−=

Equations from Steve RotenBerg’s Class’s notes

Existing methods,explicit integration

set time step, s

use state(t + s) = state(t) + s * forces(state(t), t)

the state includes position and velocity

must calculate each step by s

good: simple to implement, okay for very high damping factors

bad: slow, needs short s and/or high damping or it will “explode”

Existing methods, implicit integration

use state(t + s) = state(t) + s * forces(state(t+s), t+s) or

This means that we have to solve for values of deltax and deltav

Uses modified conjugate gradient solver that exploits the sparsity that results from each node only being connect to nearby nodes.

What we did

Basic spring forces

particle system and simple explicit integration with generative forces inspired by “Particle System Dynamics” from SIGRAPH 2003 course notes

Implicit Integration based on “Large Steps in Cloth Simulation” by Baraff and Witkin, 1998.

Extended particle system and wrote implicit integration based on Hamilton Chong’s Code. Specifically, using his modified conjugate gradient solver and his filling of the df_dx and df_dy matrices based on position and velocity to have the proper sparsity characteristics.

Results

Explicit is slow to calculate, due to requiring a very small time step, and requires tuning the time step depending on the spring constants and damping factors to keep it from degenerating into chaos

Implicit is fast and does not degenerate with as small of a timestep. Each step takes longer to calculate, but the degree to which large time steps may be taken results in a significant time reduction to simulate a certain amount of time.