Position based dynamics (PBD)

• PBD - Use symplectic integrator expressed using position only
• • - Velocity is computed implicitly as \((p^{k+1}-p^{k})/h\)
  • - Handle constraints using explicit projection of positions.
  • • - Interesting to handle non-linear/stiff constraints

PBD algorithm
For all k
    Integrate position (without constraints) p[k+1]=integrator(p[k],v[k],t)
    For all constraints
        Project p[k+1] on constraints
    Compute new speed v[k+1]=(p[k+1]-p[k])/h

• (+) Unconditionnaly stable even for stiff constraints
• (+) Simple to implement
• (-) Low accuracy, no energy preserving