Polka dots

Good for

Fun, simple and easy to print anywhere.

Print notes

• Depth 0.4 to 1.5 mm for a 0.4 mm nozzle (as written: 1.2 mm).
• Best on walls, printed upright. On a flat top, use thin layers (0.12 mm or less).
• 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 polkaDots(U: number, V: number, p = 7.0, amp = 1.2) {
  const s = frac(U / p) - 0.5;
  const t = frac(V / p + 0.5 * mod(Math.floor(U / p), 2)) - 0.5;
  return amp * dome((s / 0.3) ** 2 + (t / 0.3) ** 2);
}

/** Python's floor modulo: the result has the sign of b (`-1 % 2` is 1, as in numpy). */
function mod(a: number, b: number) {
  return a - b * Math.floor(a / b);
}

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

/** A round bump: 1 in the middle (r2 = 0), 0 at the edge (r2 = 1). */
function dome(r2: number) {
  return Math.sqrt(clamp(1 - r2, 0, 1));
}

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

Printed