Cloth

Internal Forces for a Cloth Particle

A particle of mass m at a point $\mathbf{P}$ connected to another particle at the point $\mathbf{Q}$ experiences the forces:

$\large{\mathbf{F}_{spring} = k_{spring}(\|\mathbf{Q} - \mathbf{P}\| - d)\frac{\mathbf{Q} - \mathbf{P}}{\|\mathbf{Q} - \mathbf{P}\|}}$

and

$\large{\mathbf{F}_{damper} = k_{damper}(\frac{d\mathbf{Q}}{dt} - \frac{d\mathbf{P}}{dt})}$

where $d$ is the rest length of the spring connecting them

External Forces for a Cloth Particle

A particle of mass m having a velocity $\mathbf{V}$ experiences the force

$\large{\mathbf{F}_{extern} = m\mathbf{g} + k_{wind}|(\mathbf{W} - \mathbf{V})\cdot\mathbf{N}|}$

where $\mathbf{g}$ is the acceleration of gravity, $\mathbf{W}$ is the velocity of the wind, and $\mathbf{N}$ is the surface normal at the particle's location

Summary

$\large{\mathbf{f} = \frac{\mathbf{X}_{j} - \mathbf{X}_{i}}{|\mathbf{X}_{j} - \mathbf{X}_{i}|}[k_{s}(|\mathbf{X}_{j} - \mathbf{X}_{i}| - l_{0}) + k_{d}(\mathbf{V}_{j} - \mathbf{V}_{i})\cdot\frac{\mathbf{X}_{j} - \mathbf{X}_{i}}{|\mathbf{X}_{j} - \mathbf{X}_{i}|}]}$