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3D Cloth Simulation. Eva Schiffer Aaron 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

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3d cloth simulation
3D Cloth Simulation
  • Eva Schiffer
  • Aaron Bryden
slide2
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
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

existing methods explicit integration
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
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
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
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.