cloth simulation | tinf

learn some animation v2

md

marvelous designer: mass-spring model

$ x¨=M−1(−∂x∂E+F) $

$ F_net=m*a $

Symbol	Name	Meaning
$x$	Position vector	Stacked positions of all $n$ particles: $x \in R^{3 n}$
$\dot{x}$	Velocity	$\frac{d x}{d t}$ , first time derivative of position
$\ddot{x}$	Acceleration	$\frac{d^{2} x}{d t^{2}}$ , what we're solving for each timestep
$M$	Mass matrix	Diagonal $3 n \times 3 n$ matrix. Each particle $i$ contributes $m_{i} I_{3}$ on the diagonal
$M^{- 1}$	Inverse mass matrix	Trivial to compute since $M$ is diagonal: $diag (1 / m_{1}, 1 / m_{1}, 1 / m_{1}, \dots)$
$E (x)$	Internal elastic energy	Potential energy stored in cloth deformation (stretch, shear, bend)
$- \frac{\partial E}{\partial x}$	Internal elastic force	Negative gradient of energy = force that tries to restore cloth to rest shape
$F$	External forces	Gravity, wind, damping, collision response, etc.

MD

MD UI Parameter	Symbol	Where It Lives
Stretch (Weft/Warp)	$k_{s}$	$E_{stretch}$
Shear	$k_{s h}$	$E_{shear}$
Bending (Weft/Warp)	$k_{b}$	$E_{bend}$
Damping	$d$	$F_{damping}$
Air Damping	$c_{d}$	$F_{air}$
Density / Mass	$m_{i}$ (diagonal of $M$ )	Everywhere via $M^{- 1}$
Gravity	$g$	$F_{gravity}$
Simulation Quality	$1 / h$ (substep count)	Implicit Euler step size
Particle Distance	Mesh resolution	Determines $n$ , edge count, $L_{0}$ values

ue5 chaoscloth

PBD