Petals

Good for

Vases, lamp shades and candle holders.

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 petals(U: number, V: number, w = 9.0, amp = 1.2) {
  const r = Math.floor(V / (w * 0.6));
  let h = 0;
  for (const dr of [0, 1]) {
    const rr = r + dr;
    const o = mod(rr, 2) * 0.5;
    const c = Math.floor(U / w - o);
    const s = U / w - o - c - 0.5;
    const t = rr - V / (w * 0.6);
    const d = Math.hypot(s / 0.5, (t - 0.05) / 1.0);
    h = Math.max(h, amp * Math.max(1 - d, 0) ** 0.5 * clamp(1.2 - t, 0, 1));
  }
  return h;
}

/** 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);
}

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

Printed