Jakobsen constraints
Velum.
— THE CLOTH · THE VEIL · THE SAIL —
PROJECT LAVOS · VERLET INTEGRATION · 17 ROWS · 32 COLUMNS · TONE.JS PLUCK · MMXXVI
A piece of cloth, hanging from its top edge, simulated with Verlet integration —
points that remember where they were a frame ago and use that memory to know how to move.
Every row is one plate of The Studies, dyed into the warp.
Drag the fabric. Where you tug, the cloth pulls;
where the cloth swings past a threshold, the row plays its plate's pitch through a
Tone.PluckSynth. Velum. The cloth holds the wind. Wave it, and the chord plays.
Jakobsen constraints
~544 points
D3 — F♯5
Karplus–Strong
The Verlet integration scheme was published in 1791 by Jean Baptiste Delambre and rediscovered by Loup Verlet in 1967 for molecular dynamics. It is the simplest possible physics that doesn't drift apart. Each particle stores only its current position and the position it had one step ago; the difference between the two is the implicit velocity. To advance, you take twice the current minus the previous, plus acceleration times time-squared. That's it. No velocity vector to track. No rotational state. Constraints are satisfied by relaxation: shorten or lengthen each spring by half the error, applied to both ends, repeated a few times per frame.
Cloth is the canonical Verlet example because cloth is what you can see physics doing. Every fold, every drape, every swing of the corner under tug — that is the integration scheme made visible. Each row of this cloth is one of the seventeen plate colors of The Studies. Each row is also one note of the seventeen-note D-major voicing. The chord is dyed into the warp. Wave the cloth, and the chord plays.
The pulse. The score. The étude. The molt. The loom. The cloth. Drag a corner. Let it swing.