1. 3D Cloth Simulation • Eva Schiffer • Aaron Bryden

2. 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

3. 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 Equations from Steve RotenBerg’s Class’s notes

4. 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”

5. 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.

6. 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.

7. 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.