Truchet

Good for

Panels, boxes and anything that should look busy but calm.

Print notes

• Depth 0.4 to 1.5 mm for a 0.4 mm nozzle (as written: 1.0 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 truchet(U: number, V: number, p = 8.0, amp = 1.0) {
  const i = Math.floor(U / p);
  const j = Math.floor(V / p);
  let s = frac(U / p);
  const t = frac(V / p);
  if (rnd(i, j, 4) > 0.5) s = 1 - s; // flip half the tiles
  const d = Math.min(Math.abs(Math.hypot(s, t) - 0.5), Math.abs(Math.hypot(1 - s, 1 - t) - 0.5));
  return amp * dome((d / 0.17) ** 2);
}

/** 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