mc-beta-server/server/Generators/perlin.js

/**
 * A Perlin Noise library for JavaScript.
 * 
 * Based on implementations by Ken Perlin (Java, C) & Stefan Gustavson (C).
 * 
 * MIT License.
 * Copyright (c) 2018 Leonardo de S.L.F.
 * http://leodeslf.com/
 */

// Permutation table.

const p = [
	151, 160, 137, 91, 90, 15, 131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140,
	36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23, 190, 6, 148, 247, 120, 234,
	75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33, 88, 237,
	149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48,
	27, 166, 77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105,
	92, 41, 55, 46, 245, 40, 244, 102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73,
	209, 76, 132, 187, 208, 89, 18, 169, 200, 196, 135, 130, 116, 188, 159, 86,
	164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123, 5, 202, 38,
	147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189,
	28, 42, 223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153,
	101, 155, 167, 43, 172, 9, 129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224,
	232, 178, 185, 112, 104, 218, 246, 97, 228, 251, 34, 242, 193, 238, 210, 144,
	12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107, 49, 192, 214,
	31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150,
	254, 138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66,
	215, 61, 156, 180
];
const P = [...p, ...p];

// Utility functions.

function fade(t) {
	return t * t * t * (t * (t * 6 - 15) + 10);
}

function lerp(t, a, b) {
	return a + t * (b - a);
}

// Helper functions to find gradients for each vertex.

function gradient1D(hash, x) {
	return hash & 1 ? -x : x;
}

function gradient2D(hash, x, y) {
	const H = hash & 3;
	return (H < 2 ? x : -x) + (H === 0 || H === 2 ? y : -y);
}

function gradient3D(hash, x, y, z) {
	const
		H = hash & 15,
		U = H < 8 ? x : y,
		V = H < 4 ? y : H === 12 || H === 14 ? x : z;
	return ((H & 1) ? -U : U) + ((H & 2) ? -V : V);
}

function gradient4D(hash, x, y, z, t) {
	const
		H = hash & 31,
		U = H < 24 ? x : y,
		V = H < 16 ? y : z,
		W = H < 8 ? z : t;
	return ((H & 1) ? -U : U) + ((H & 2) ? -V : V) + ((H & 4) ? -W : W);
}

// Perlin Noise functions.

/**
 * Returns a one-dimensional noise value between -1 and 1.
 * @param {number} x A numeric expression.
 * @returns {number} Perlin Noise value.
 */
function perlin1D(x) {
	const
		FX = Math.floor(x),
		X = FX & 255;

	x = x - FX;

	return lerp(
		fade(x),
		gradient1D(P[P[X]], x),
		gradient1D(P[P[X + 1]], x - 1)
	);
}

/**
 * Returns a two-dimensional noise value between -1 and 1.
 * @param {number} x A numeric expression.
 * @param {number} y A numeric expression.
 * @returns {number} Perlin Noise value.
 */
function perlin2D(x = 0, y = 0) {
	// Hack to allow this to work with integer block coords
	x += 0.2;
	y += 0.2;
	
	const FX = Math.floor(x),
		  FY = Math.floor(y),
		  X = FX & 255,
		  Y = FY & 255,
		  A = P[X] + Y,
		  B = P[X + 1] + Y;

	x = x - FX;
	y = y - FY;

	const
		FDX = fade(x),
		x1 = x - 1,
		y1 = y - 1;

	return lerp(
		fade(y),
		lerp(
			FDX,
			gradient2D(P[A], x, y),
			gradient2D(P[B], x1, y)
		),
		lerp(
			FDX,
			gradient2D(P[A + 1], x, y1),
			gradient2D(P[B + 1], x1, y1)
		)
	);
}

/**
 * Returns a three-dimensional noise value between -1 and 1.
 * @param {number} x A numeric expression.
 * @param {number} y A numeric expression.
 * @param {number} z A numeric expression.
 * @returns {number} Perlin Noise value.
 */
function perlin3D(x, y, z) {
	const
		FX = Math.floor(x),
		FY = Math.floor(y),
		FZ = Math.floor(z),
		X = FX & 255,
		Y = FY & 255,
		Z = FZ & 255,
		A = P[X] + Y,
		B = P[X + 1] + Y,
		AA = P[A] + Z,
		BA = P[B] + Z,
		AB = P[A + 1] + Z,
		BB = P[B + 1] + Z;

	x = x - FX;
	y = y - FY;
	z = z - FZ;

	const
		FDX = fade(x),
		FDY = fade(y),
		x1 = x - 1,
		y1 = y - 1,
		z1 = z - 1;

	return lerp(
		fade(z),
		lerp(
			FDY,
			lerp(
				FDX,
				gradient3D(P[AA], x, y, z),
				gradient3D(P[BA], x1, y, z)
			),
			lerp(
				FDX,
				gradient3D(P[AB], x, y1, z),
				gradient3D(P[BB], x1, y1, z)
			)
		),
		lerp(
			FDY,
			lerp(
				FDX,
				gradient3D(P[AA + 1], x, y, z1),
				gradient3D(P[BA + 1], x1, y, z1)
			),
			lerp(
				FDX,
				gradient3D(P[AB + 1], x, y1, z1),
				gradient3D(P[BB + 1], x1, y1, z1)
			)
		)
	);
}

/**
 * Returns a four-dimensional noise value between -1 and 1.
 * @param {number} x A numeric expression.
 * @param {number} y A numeric expression.
 * @param {number} z A numeric expression.
 * @param {number} t A numeric expression.
 * @returns {number} Perlin Noise value.
 */
function perlin4D(x, y, z, t) {
	const
		FX = Math.floor(x),
		FY = Math.floor(y),
		FZ = Math.floor(z),
		FT = Math.floor(t),
		X = FX & 255,
		Y = FY & 255,
		Z = FZ & 255,
		T = FT & 255,
		A = P[X] + Y,
		B = P[X + 1] + Y,
		AA = P[A] + Z,
		BA = P[B] + Z,
		AB = P[A + 1] + Z,
		BB = P[B + 1] + Z,
		AAA = P[AA] + T,
		BAA = P[BA] + T,
		ABA = P[AB] + T,
		BBA = P[BB] + T,
		AAB = P[AA + 1] + T,
		BAB = P[BA + 1] + T,
		ABB = P[AB + 1] + T,
		BBB = P[BB + 1] + T;

	x = x - FX;
	y = y - FY;
	z = z - FZ;
	t = t - FT;

	const
		FDX = fade(x),
		FDY = fade(y),
		FDZ = fade(z),
		x1 = x - 1,
		y1 = y - 1,
		z1 = z - 1,
		t1 = t - 1;

	return lerp(
		fade(t),
		lerp(
			FDZ,
			lerp(
				FDY,
				lerp(
					FDX,
					gradient4D(P[AAA], x, y, z, t),
					gradient4D(P[BAA], x1, y, z, t)
				),
				lerp(
					FDX,
					gradient4D(P[ABA], x, y1, z, t),
					gradient4D(P[BBA], x1, y1, z, t)
				)
			),
			lerp(
				FDY,
				lerp(
					FDX,
					gradient4D(P[AAB], x, y, z1, t),
					gradient4D(P[BAB], x1, y, z1, t)
				),
				lerp(
					FDX,
					gradient4D(P[ABB], x, y1, z1, t),
					gradient4D(P[BBB], x1, y1, z1, t)
				)
			)
		),
		lerp(
			FDZ,
			lerp(
				FDY,
				lerp(
					FDX,
					gradient4D(P[AAA + 1], x, y, z, t1),
					gradient4D(P[BAA + 1], x1, y, z, t1)
				),
				lerp(
					FDX,
					gradient4D(P[ABA + 1], x, y1, z, t1),
					gradient4D(P[BBA + 1], x1, y1, z, t1)
				)
			),
			lerp(
				FDY,
				lerp(
					FDX,
					gradient4D(P[AAB + 1], x, y, z1, t1),
					gradient4D(P[BAB + 1], x1, y, z1, t1)
				),
				lerp(
					FDX,
					gradient4D(P[ABB + 1], x, y1, z1, t1),
					gradient4D(P[BBB + 1], x1, y1, z1, t1)
				)
			)
		)
	);
}

module.exports = { perlin1D, perlin2D, perlin3D, perlin4D };