Spaghetti

Good for

Inside jokes and gifts for anyone who has printed spaghetti.

Print notes

• Depth 0.4 to 1.5 mm for a 0.4 mm nozzle (as written: 1.1 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 spaghetti(U: number, V: number, amp = 1.1, n = 7) {
  let h = 0;
  for (let k = 0; k < n; k++) {
    const a = 3 + 2 * rnd(k, 1, 1);
    const b = 5 + 3 * rnd(k, 2, 1);
    const c = rnd(k, 3, 1) * 40;
    const y = c + 6 * Math.sin(U / a + k) + 4 * Math.sin((U / b) * 1.7 + 2 * k);
    const dv = Math.abs(frac((V - y) / 40 + 0.5) - 0.5) * 40;
    h = Math.max(h, amp * dome((dv / 1.0) ** 2));
  }
  return h;
}

/** 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);
}

/** A repeatable random number 0..1 for a cell (no Math.random: the same texture every time). */
function rnd(a: number, b: number, k = 0) {
  const x = Math.sin(a * 127.1 + b * 311.7 + k * 74.7) * 43758.5453;
  return x - Math.floor(x);
}

Printed