Tire tread

Good for

Toy wheels, grippy bands, rugged desk pieces.

Print notes

• Depth 0.4 to 1.5 mm for a 0.4 mm nozzle (as written: 1.3 mm).
• It has an up and a down: print it on a wall the way it is drawn here (the top of the picture is up).
• Fade it out over the bottom 3 mm so the first layers are flat and stick to the plate.
• Not printed yet: these notes come from the geometry. The test cube will tell us more.

The formula

The real code this page runs: give it a point (U mm across, V mm up) and it returns the height there, in mm. Push the surface out by that much and the texture is real geometry.

function tireTread(U: number, V: number, p = 10.0, amp = 1.3) {
  const s = frac((V + 4 * tri(U / 20)) / p);
  const groove = Math.abs(frac(U / 20) - 0.5) > 0.04 ? 1 : 0; // a channel down the middle
  return amp * clamp(Math.min(s, 0.62 - s) / 0.08, 0, 1) * groove;
}

/** The fractional part, 0..1. */
function frac(x: number) {
  return x - Math.floor(x);
}

/** A triangle wave: 0..1..0. */
function tri(x: number) {
  return 1 - 2 * Math.abs(frac(x) - 0.5);
}

function clamp(x: number, lo: number, hi: number) {
  return Math.min(Math.max(x, lo), hi);
}

Printed