noise.mjs

1	/**
2	* Deterministic value noise with fBm, wrapping on the y (theta) axis.
3	*
4	* The map is a cylinder: y wraps and x does not. Noise that ignores that leaves a
5	* visible seam down the map, so the lattice wraps at a caller-supplied period.
6	*/
7
8	/**
9	* 32-bit integer hash. Uses Math.imul throughout: the obvious float version
10	* silently loses precision on large products and leaves axis-aligned streaks
11	* across the terrain.
12	*/
13	function hash(x, y, seed) {
14	let h = Math.imul(x \| 0, 374761393) ^ Math.imul(y \| 0, 668265263) ^ Math.imul(seed \| 0, 1274126177)
15	h = Math.imul(h ^ (h >>> 15), 2246822519)
16	h = Math.imul(h ^ (h >>> 13), 3266489917)
17	return ((h ^ (h >>> 16)) >>> 0) / 4294967295
18	}
19
20	const smooth = (t) => t * t * (3 - 2 * t)
21
22	/** Value noise at (x, y) on a lattice, wrapping y every `wrapY` cells. */
23	function value(x, y, seed, wrapY) {
24	const xi = Math.floor(x)
25	const yi = Math.floor(y)
26	const xf = smooth(x - xi)
27	const yf = smooth(y - yi)
28	const wrap = (v) => (wrapY > 0 ? ((v % wrapY) + wrapY) % wrapY : v)
29	const y0 = wrap(yi)
30	const y1 = wrap(yi + 1)
31	const a = hash(xi, y0, seed)
32	const b = hash(xi + 1, y0, seed)
33	const c = hash(xi, y1, seed)
34	const d = hash(xi + 1, y1, seed)
35	return (a + (b - a) * xf) * (1 - yf) + (c + (d - c) * xf) * yf
36	}
37
38	/** Fractal Brownian motion in [0,1]. `wrapY` is the lattice period on the y axis. */
39	export function fbm(x, y, { octaves = 4, seed = 1, wrapY = 0, lacunarity = 2, gain = 0.5 } = {}) {
40	let sum = 0
41	let amp = 1
42	let norm = 0
43	let freq = 1
44	for (let o = 0; o < octaves; o++) {
45	sum += value(x * freq, y * freq, seed + o * 101, wrapY * freq) * amp
46	norm += amp
47	amp *= gain
48	freq *= lacunarity
49	}
50	return sum / norm
51	}
52
53	/** Ridged fBm — absolute-valued and inverted, which makes mountain crests. */
54	export function ridged(x, y, opts = {}) {
55	const { octaves = 4 } = opts
56	let sum = 0
57	let amp = 1
58	let norm = 0
59	let freq = 1
60	for (let o = 0; o < octaves; o++) {
61	const v = 1 - Math.abs(value(x * freq, y * freq, (opts.seed ?? 1) + o * 211, (opts.wrapY ?? 0) * freq) * 2 - 1)
62	sum += v * v * amp
63	norm += amp
64	amp *= 0.5
65	freq *= 2
66	}
67	return sum / norm
68	}