Simple Spring-Damper-Mass Mesh

• data structures
  • node
    • m: mass
    • p: position
    • v: velocity
    • f: force
  • spring
    • n1: node
    • n2: node
    • len: rest length
    • ks: spring constant
    • kd: damper constant
• functions
  • f = F(spring s) = spring_force - damping_force
    = (|s.n2.p - s.n1.p|-s.len)*s.ks - (s.n1.v-s.n2.v)⋅((s.n1.p-s.n2.p)/|s.n1.p-s.n2.p|)*s.kd
  • a = A(f,m)
  • v = V(v,a,dt) ; integration
  • p = P(p,v,dt) ; integration
• pseudo code

  // initialize nodes
  for each node, n
    initialize force: either clear it (n.f = 0) or 
                      initialize with global forces such as wind
  
  // compute the force due to the spring and add it to the attached nodes
  for each spring, s 
    f = F(s)
    n1.f +=  f
    n2.f += -f
  
  // move the nodes
  for each node, n
    a = A(n.f,n.m)
    if gravity, add gravitational acceleration to a
    n.v = V(n.v,a,dt)
    n.p = P(n.p,n.v,dt)
  
  display mesh
  

• NOTE: the tricky thing is balancing the masses, spring constants, damping constants, rest lengths, and time step to get a responsive but stable system under a variety of inputs (external forces)
• For a quick and easy implementation, you can code this up for just the 2D case and then let the user pick and drag one of the mass points and have the mesh react to it.