The3DG

Nature · Test cube 39

Dunes

Wind-blown sand ripples: a long gentle slope and a short drop.

Presented by FloNothing in nature repeats exactly. Neither do these. Relax into it.
× 1.00
1.2 mm
135°
  • Prints well with a 0.4 mm nozzle.

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

Good for

Sand-colored vases, desk pieces, lamp bases.

Print notes

  • Depth 0.4 to 1.5 mm for a 0.4 mm nozzle (as written: 1.2 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 dunes(U: number, V: number, amp = 1.2) {
  const x = V / 9 + 0.8 * Math.sin(U / 13) + 0.4 * fbm(U / 20, V / 20);
  return amp * frac(x) ** 1.8;
}
The helpers it uses (frac, fbm, noise, rnd)
/** The fractional part, 0..1. */
function frac(x: number) {
  return x - Math.floor(x);
}
/** 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);
}

Printed

Test cube 39 is waiting for the printer. Its photo goes here.