experiment 032 · classical mechanics

Cloth Simulation

A grid of point masses connected by structural springs, integrated using Verlet integration. This provides an incredibly stable and fast numerical method for simulating soft bodies and fabrics. Drag the fabric with your pointer to tear constraints or observe the dynamic rippling of the mesh.

Verlet Integration

Unlike standard Euler integration which stores position and velocity, Verlet integration infers velocity from the difference between the current and previous positions:

$$ x_{t+\Delta t} = 2x_t - x_{t-\Delta t} + a_t \Delta t^2 $$

This approach offers phenomenal numerical stability, essential for constraint-based physics systems like cloth where many interconnected springs might otherwise accumulate catastrophic energy errors.

Distance Constraints

The cloth is constructed as a grid of discrete point masses. Each adjacent pair is constrained to maintain a resting distance $d$. If the current distance $l$ diverges from $d$, the points are pushed along their axis by a corrective factor proportional to the difference:

$$ \Delta x = \frac{l - d}{l} \times 0.5 \times (x_2 - x_1) $$

By iterating this constraint solver multiple times per frame (relaxation), the grid globally stiffens into a cohesive fabric.

← back to workshop