3D Cloth Simulation

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3D Cloth Simulation

• Eva Schiffer
• Aaron Bryden

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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

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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 RotenBergs Classs notes
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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

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Existing methods, implicit integration

• use state(t s) state(t) s
  forces(state(ts), ts) 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.

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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 Chongs 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.

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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.