The3DG

Knits & fabric · Test cube 16

Leather

A fine pebbled grain of small cells, like the back of a leather wallet.

Presented by SpoolYarn comes on a spool too. I feel very at home here.
× 1.00
0.7 mm
135°
  • Too fine for a 0.4 mm nozzle: the narrowest part is about 0.8 mm (under 1.2 mm). Make it bigger.

25 mm, with your size and depth. Prints upright, no supports. About 4 MB.

Good for

Cases, journal covers, a matte look that hides fingerprints.

Print notes

The finest texture in the library: the grain is under two nozzle widths, so it reads as a matte surface more than as cells. Scale it up (1.5 or more) to see the pebbles.

  • Depth 0.4 to 1.5 mm for a 0.4 mm nozzle (as written: 0.7 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 leather(U: number, V: number, amp = 0.7) {
  const { d1, d2 } = cells(U, V, 3.2, 9);
  return amp * (clamp((d2 - d1) / 0.25, 0, 1) ** 0.6 * (0.8 + 0.2 * fbm(U / 9, V / 9)));
}
The helpers it uses (clamp, fbm, noise, rnd, cells)
function clamp(x: number, lo: number, hi: number) {
  return Math.min(Math.max(x, lo), hi);
}
/** Three octaves of noise, 0..1. */
function fbm(x: number, y: number, o = 3) {
  let sum = 0;
  let norm = 0;
  for (let i = 0; i < o; i++) sum += noise(x * 2 ** i, y * 2 ** i) / 2 ** i;
  for (let i = 0; i < o; i++) norm += 1 / 2 ** i;
  return sum / norm;
}
/** Smooth value noise. */
function noise(x: number, y: number) {
  const xi = Math.floor(x);
  const yi = Math.floor(y);
  const xf = x - xi;
  const yf = y - yi;
  const u = xf * xf * (3 - 2 * xf);
  const v = yf * yf * (3 - 2 * yf);
  const a = rnd(xi, yi);
  const b = rnd(xi + 1, yi);
  const c = rnd(xi, yi + 1);
  const d = rnd(xi + 1, yi + 1);
  return a + (b - a) * u + (c - a) * v + (a - b - c + d) * u * v;
}
/** 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);
}
/** Jittered cells: distance to the nearest and second-nearest cell center (in cells), and the nearest cell's id. */
function cells(U: number, V: number, p: number, k = 1) {
  const x = U / p;
  const y = V / p;
  const xi = Math.floor(x);
  const yi = Math.floor(y);
  let d1 = 9;
  let d2 = 9;
  let id = 0;
  for (const dx of [-1, 0, 1])
    for (const dy of [-1, 0, 1]) {
      const ci = xi + dx;
      const cj = yi + dy;
      const cx = ci + 0.15 + 0.7 * rnd(ci, cj, k);
      const cy = cj + 0.15 + 0.7 * rnd(ci, cj, k + 1);
      const d = Math.hypot(x - cx, y - cy);
      if (d < d1) {
        d2 = d1;
        id = rnd(ci, cj, k + 2);
      } else d2 = Math.min(d2, d);
      d1 = Math.min(d1, d);
    }
  return { d1, d2, id };
}

Printed

Test cube 16 is waiting for the printer. Its photo goes here.