Cross-stitch

Good for

Sewing boxes, hoops and anything crafty.

Print notes

Thin crossing lines: right at the limit of a 0.4 mm nozzle. Keep the size at 1.0 or above.

• 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 crossStitch(U: number, V: number, p = 5.0, amp = 1.0) {
  const s = frac(U / p) - 0.5;
  const t = frac(V / p) - 0.5;
  const d = Math.min(Math.abs(s - t), Math.abs(s + t)) / Math.sqrt(2);
  return amp * dome((d / 0.12) ** 2) * (Math.max(Math.abs(s), Math.abs(t)) < 0.42 ? 1 : 0);
}

/** 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