Shingles

Good for

Little houses, bird feeders, roofs for anything.

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 shingles(U: number, V: number, w = 10.0, h = 6.0, amp = 1.3) {
  const r = Math.floor(V / h);
  const off = mod(r, 2) * 0.5 * w;
  const s = frac((U + off) / w);
  const t = frac(V / h);
  return amp * (1 - t) * clamp(Math.min(s, 1 - s) / 0.05, 0, 1);
}

/** 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);
}

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

Printed