Simplex.ts

const GRAD_3 = [
	[1, 1, 0],
	[-1, 1, 0],
	[1, -1, 0],
	[-1, -1, 0],
	[1, 0, 1],
	[-1, 0, 1],
	[1, 0, -1],
	[-1, 0, -1],
	[0, 1, 1],
	[0, -1, 1],
	[0, 1, -1],
	[0, -1, -1],
];

const GRAD_4 = [
	[0, 1, 1, 1],
	[0, 1, 1, -1],
	[0, 1, -1, 1],
	[0, 1, -1, -1],
	[0, -1, 1, 1],
	[0, -1, 1, -1],
	[0, -1, -1, 1],
	[0, -1, -1, -1],
	[1, 0, 1, 1],
	[1, 0, 1, -1],
	[1, 0, -1, 1],
	[1, 0, -1, -1],
	[-1, 0, 1, 1],
	[-1, 0, 1, -1],
	[-1, 0, -1, 1],
	[-1, 0, -1, -1],
	[1, 1, 0, 1],
	[1, 1, 0, -1],
	[1, -1, 0, 1],
	[1, -1, 0, -1],
	[-1, 1, 0, 1],
	[-1, 1, 0, -1],
	[-1, -1, 0, 1],
	[-1, -1, 0, -1],
	[1, 1, 1, 0],
	[1, 1, -1, 0],
	[1, -1, 1, 0],
	[1, -1, -1, 0],
	[-1, 1, 1, 0],
	[-1, 1, -1, 0],
	[-1, -1, 1, 0],
	[-1, -1, -1, 0],
];

const F2 = (math.sqrt(3) - 1) / 2;
const G2 = (3 - math.sqrt(3)) / 6;
const F3 = 1 / 3;
const G3 = 1 / 6;
const F4 = (math.sqrt(5) - 1) / 4;
const G4 = (5 - math.sqrt(5)) / 20;

const newPerm = () => {
	const perm = new Array<number>(256);
	for (let index = 0; index < 256; index += 1) perm[index] = index;
	return perm;
};

export default class Simplex {
	private perm: Array<number>;
	private permMod12: Array<number>;

	/**
	 * Returns a Simplex generator with a state initialized by a random shuffle.
	 * @param {Array<number>?} perm An array to set as the `perm` entry in the class.
	 * @param {Array<number>?} permMod12 An array to set as the `permMod12` entry in the class.
	 */
	public constructor(perm?: Array<number>, permMod12?: Array<number>) {
		const randomLib = new Random((os.clock() % 1) * 1e7);
		const permutations = newPerm();
		for (let index = permutations.size(); index > 1; index -= 1) {
			const jndex = randomLib.NextInteger(1, index);
			const swap = permutations[index];
			permutations[index] = permutations[jndex];
			permutations[jndex] = swap;
		}

		const isPermUndefined = perm === undefined;
		const isPermMod12Undefined = permMod12 === undefined;

		if (isPermUndefined) {
			if (isPermMod12Undefined) {
				this.perm = new Array<number>(512);
				this.permMod12 = new Array<number>(512);

				for (let index = 0; index < 512; index += 1) {
					this.perm[index] = permutations[index % 256];
					this.permMod12[index] = this.perm[index] % 12;
				}
			} else {
				this.perm = new Array<number>(512);
				this.permMod12 = permMod12;
				for (let index = 0; index < 512; index += 1) this.perm[index] = permutations[index % 256];
			}
		} else {
			if (isPermMod12Undefined) {
				this.perm = perm;
				this.permMod12 = new Array<number>(512);
				for (let index = 0; index < 512; index += 1) this.permMod12[index] = this.perm[index] % 12;
			} else {
				this.perm = perm;
				this.permMod12 = permMod12;
			}
		}
	}

	/**
	 * Returns a Simplex generator with a state initialized by a table of permutations.
	 * @param {Array<number>} permutations An array containing some permutation of each integer between 0 and 255, inclusive.
	 * @returns {Simplex}
	 */
	public static FromArray(permutations: Array<number>): Simplex {
		const found = new Set<number>();
		for (let index = 0; index < 256; index += 1) {
			const value = permutations[index];
			if (value === undefined) error(`permutations missing index ${index}`, 2);
			found.add(value);
		}

		for (let index = 0; index < 256; index += 1)
			if (!found.has(index)) error(`permutations missing value ${index}`, 2);

		const perm = new Array<number>(512);
		const permMod12 = new Array<number>(512);

		for (let index = 0; index < 512; index += 1) {
			perm[index] = permutations[index % 256];
			permMod12[index] = perm[index] % 12;
		}

		return new Simplex(perm, permMod12);
	}

	/**
	 * Returns a Simplex generator with a state initialized by a random function.
	 * @param {(index: number) => number} generator A function that receives an integer, and returns an integer between 1 and the given value, inclusive. A generated array of permutations will be shuffled using this function. `math.random` is an example of such a function.
	 * @returns {Simplex}
	 */
	public static FromFunction(generator: (index: number) => number): Simplex {
		const permutations = newPerm();
		for (let index = permutations.size(); index > 1; index -= 1) {
			const jndex = generator(index);
			const swap = permutations[index];
			permutations[index] = permutations[jndex];
			permutations[jndex] = swap;
		}

		const perm = new Array<number>(512);
		const permMod12 = new Array<number>(512);

		for (let index = 0; index < 512; index += 1) {
			perm[index] = permutations[index % 256];
			permMod12[index] = perm[index] % 12;
		}

		return new Simplex(perm, permMod12);
	}

	/**
	 * Returns a Simplex generator with a state initialized by a seed for a random number generator.
	 * @param {number} seed A number, which is used as a random seed to shuffle a generated array of permutations.
	 * @returns {Simplex}
	 */
	public static FromSeed(seed: number): Simplex {
		const randomLib = new Random(seed);
		const permutations = newPerm();
		for (let index = permutations.size(); index > 1; index -= 1) {
			const jndex = randomLib.NextInteger(1, index);
			const swap = permutations[index];
			permutations[index] = permutations[jndex];
			permutations[jndex] = swap;
		}

		const perm = new Array<number>(512);
		const permMod12 = new Array<number>(512);

		for (let index = 0; index < 512; index += 1) {
			perm[index] = permutations[index % 256];
			permMod12[index] = perm[index] % 12;
		}

		return new Simplex(perm, permMod12);
	}

	/**
	 * Returns a Simplex generator with a state initialized by a Random source.
	 * @param randomLib A Random value, which is used to shuffle a generated array of permutations.
	 * @returns {Simplex}
	 */
	public static FromRandom(randomLib: Random): Simplex {
		const permutations = newPerm();
		for (let index = permutations.size(); index > 1; index -= 1) {
			const jndex = randomLib.NextInteger(1, index) - 1;
			const swap = permutations[index];
			permutations[index] = permutations[jndex];
			permutations[jndex] = swap;
		}

		const perm = new Array<number>(512);
		const permMod12 = new Array<number>(512);

		for (let index = 0; index < 512; index += 1) {
			perm[index] = permutations[index % 256];
			permMod12[index] = perm[index] % 12;
		}

		return new Simplex(perm, permMod12);
	}

	/**
	 * Returns a number in the interval [-1, 1] based on the given two-dimensional coordinates and the generator's permutation state.
	 * @param {number} x The X value to generate with.
	 * @param {number} y The Y value to generate with.
	 * @returns {number} The 2D noise value.
	 */
	public Noise2d(x: number, y: number): number {
		const perm = this.perm;
		const permMod12 = this.permMod12;
		let n0, n1, n2; // Noise contributions from the three corners

		// Skew the input space to determine which simplex cell we're in
		const s = (x + y) * F2; // Hairy factor for 2D
		const i = math.floor(x + s);
		const j = math.floor(y + s);
		const t = (i + j) * G2;

		let x0 = i - t; // Unskew the cell origin back to (x,y) space
		let y0 = j - t;
		x0 = x - x0; // The x,y distances from the cell origin
		y0 = y - y0;

		// For the 2D case, the simplex shape is an equilateral triangle.
		// Determine which simplex we are in.
		let i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
		if (x0 > y0) {
			i1 = 1;
			j1 = 0; // lower triangle, xy order: (0,0)->(1,0)->(1,1)
		} else {
			i1 = 0;
			j1 = 1; // upper triangle, yx order: (0,0)->(0,1)->(1,1)
		}

		// A step of (1,0) in (i,j) means a step of (1-c, -c) in (x,y), and
		// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
		// c = (3-sqrt(3))/6
		const x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
		const y1 = y0 - j1 + G2;
		const x2 = x0 - 1 + 2 * G2; // Offsets for last corner in (x,y) unskewed coords
		const y2 = y0 - 1 + 2 * G2;

		// Work out the hashed gradient indices of the three simplex corners
		const ii = i % 256;
		const jj = j % 256;

		// Calculate the contribution from the three corners
		let t0 = 0.5 - x0 * x0 - y0 * y0;
		if (t0 < 0) n0 = 0;
		else {
			t0 *= t0;
			const g = GRAD_3[permMod12[ii + perm[jj]]];
			n0 = t0 * t0 * (g[0] * x0 + g[1] * y0); // (x,y) of GRAD_3 used for 2D gradient
		}

		let t1 = 0.5 - x1 * x1 - y1 * y1;
		if (t1 < 0) n1 = 0;
		else {
			t1 *= t1;
			const g = GRAD_3[permMod12[ii + i1 + perm[jj + j1]]];
			n1 = t1 * t1 * (g[0] * x1 + g[1] * y1);
		}

		let t2 = 0.5 - x2 * x2 - y2 * y2;
		if (t2 < 0) n2 = 0;
		else {
			t2 *= t2;
			const g = GRAD_3[permMod12[ii + 1 + perm[1 + jj]]];
			n2 = t2 * t2 * (g[0] * x2 + g[1] * y2);
		}

		// Add contributions from each corner to get the final noise value.
		// The result is scaled to return values in the interval [-1,1].
		return 70 * (n0 + n1 + n2);
	}

	/**
	 * Returns a number in the interval [-1, 1] based on the given three-dimensional coordinates and the generator's permutation state.
	 * @param {number} x The X value to generate with.
	 * @param {number} y The Y value to generate with.
	 * @param {number} z The Z value to generate with.
	 * @returns {number} The 3D noise value.
	 */
	public Noise3d(x: number, y: number, z: number): number {
		const perm = this.perm;
		const permMod12 = this.permMod12;
		let n0, n1, n2, n3; // Noise contributions from the four corners

		// Skew the input space to determine which simplex cell we're in
		const s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
		const i = math.floor(x + s);
		const j = math.floor(y + s);
		const k = math.floor(z + s);
		const t = (i + j + k) * G3;
		const X0 = i - t; // Unskew the cell origin back to (x,y,z) space
		const Y0 = j - t;
		const Z0 = k - t;
		const x0 = x - X0; // The x,y,z distances from the cell origin
		const y0 = y - Y0;
		const z0 = z - Z0;

		// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
		// Determine which simplex we are in.
		let i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
		let i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
		if (x0 >= y0) {
			if (y0 >= z0) {
				// X Y Z order
				i1 = 1;
				j1 = 0;
				k1 = 0;
				i2 = 1;
				j2 = 1;
				k2 = 0;
			} else if (x0 >= z0) {
				// X Z Y order
				i1 = 1;
				j1 = 0;
				k1 = 0;
				i2 = 1;
				j2 = 0;
				k2 = 1;
			} else {
				// Z X Y order
				i1 = 0;
				j1 = 0;
				k1 = 1;
				i2 = 1;
				j2 = 0;
				k2 = 1;
			}
		} else {
			// x0 < y0
			if (y0 < z0) {
				// Z Y X order
				i1 = 0;
				j1 = 0;
				k1 = 1;
				i2 = 0;
				j2 = 1;
				k2 = 1;
			} else if (x0 < z0) {
				// Y Z X order
				i1 = 0;
				j1 = 1;
				k1 = 0;
				i2 = 0;
				j2 = 1;
				k2 = 1;
			} else {
				// Y X Z order
				i1 = 0;
				j1 = 1;
				k1 = 0;
				i2 = 1;
				j2 = 1;
				k2 = 0;
			}
		}

		// A step of (1,0,0) in (i,j,k) means a step of (1-c, -c, -c) in (x,y,z),
		// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c, -c) in (x,y,z), and
		// a step of (0,0,1) in (i,j,k) means a step of (-c, -c,1-c) in (x,y,z), where
		// c = 1/6.
		const x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
		const y1 = y0 - j1 + G3;
		const z1 = z0 - k1 + G3;
		const x2 = x0 - i2 + 2 * G3; // Offsets for third corner in (x,y,z) coords
		const y2 = y0 - j2 + 2 * G3;
		const z2 = z0 - k2 + 2 * G3;
		const x3 = x0 - 1 + 3 * G3; // Offsets for last corner in (x,y,z) coords
		const y3 = y0 - 1 + 3 * G3;
		const z3 = z0 - 1 + 3 * G3;

		// Work out the hashed gradient indices of the four simplex corners
		const ii = i % 256;
		const jj = j % 256;
		const kk = k % 256;

		// Calculate the contribution from the four corners
		let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
		if (t0 < 0) n0 = 0;
		else {
			t0 *= t0;
			const g = GRAD_3[permMod12[ii + perm[jj + perm[kk]]]];
			n0 = t0 * t0 * (g[0] * x0 + g[1] * y0 + g[2] * z0);
		}

		let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
		if (t1 < 0) n1 = 0;
		else {
			t1 *= t1;
			const g = GRAD_3[permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]]];
			n1 = t1 * t1 * (g[0] * x1 + g[1] * y1 + g[2] * z1);
		}

		let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
		if (t2 < 0) n2 = 0;
		else {
			t2 *= t2;
			const g = GRAD_3[permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]]];
			n2 = t2 * t2 * (g[0] * x2 + g[1] * y2 + g[2] * z2);
		}

		let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
		if (t3 < 0) n3 = 0;
		else {
			t3 *= t3;
			const g = GRAD_3[permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]]];
			n3 = t3 * t3 * (g[0] * x3 + g[1] * y3 + g[2] * z3);
		}

		// Add contributions from each corner to get the final noise value.
		// The result is scaled to stay just inside [-1,1]
		return 32 * (n0 + n1 + n2 + n3);
	}

	/**
	 * Returns a number in the interval [-1, 1] based on the given four-dimensional coordinates and the generator's permutation state.
	 * @param {number} x The X to generate with.
	 * @param {number} y The Y to generate with.
	 * @param {number} z The Z to generate with.
	 * @param {number} w The W to generate with.
	 * @returns {number} The 4D noise value.
	 */
	public Noise4d(x: number, y: number, z: number, w: number): number {
		const perm = this.perm;
		let n0, n1, n2, n3, n4; // Noise contributions from the five corners

		// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
		const s = (x + y + z + w) * F4; // Factor for 4D skewing
		const i = math.floor(x + s);
		const j = math.floor(y + s);
		const k = math.floor(z + s);
		const l = math.floor(w + s);
		const t = (i + j + k + l) * G4; // Factor for 4D unskewing
		const X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
		const Y0 = j - t;
		const Z0 = k - t;
		const W0 = l - t;
		const x0 = x - X0; // The x,y,z,w distances from the cell origin
		const y0 = y - Y0;
		const z0 = z - Z0;
		const w0 = w - W0;

		// For the 4D case, the simplex is a 4D shape I won't even try to describe.
		// To find out which of the 24 possible simplices we're in, we need to
		// determine the magnitude ordering of x0, y0, z0 and w0.
		// Six pair-wise comparisons are performed between each possible pair
		// of the four coordinates, and the results are used to rank the numbers.
		let rankx = 0;
		let ranky = 0;
		let rankz = 0;
		let rankw = 0;

		if (x0 > y0) rankx += 1;
		else ranky += 1;

		if (x0 > z0) rankx += 1;
		else rankz += 1;

		if (x0 > w0) rankx += 1;
		else rankw += 1;

		if (y0 > z0) ranky += 1;
		else rankz += 1;

		if (y0 > w0) ranky += 1;
		else rankw += 1;

		if (z0 > w0) rankz += 1;
		else rankw += 1;

		// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
		// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
		// impossible. Only the 24 indices which have non-zero entries make any sense.
		// We use a thresholding to set the coordinates in turn from the largest magnitude.

		// The integer offsets for the second simplex corner
		// Rank 3 denotes the largest coordinate.
		const i1 = rankx >= 3 ? 1 : 0;
		const j1 = ranky >= 3 ? 1 : 0;
		const k1 = rankz >= 3 ? 1 : 0;
		const l1 = rankw >= 3 ? 1 : 0;

		// The integer offsets for the third simplex corner
		// Rank 2 denotes the second largest coordinate.
		const i2 = rankx >= 2 ? 1 : 0;
		const j2 = ranky >= 2 ? 1 : 0;
		const k2 = rankz >= 2 ? 1 : 0;
		const l2 = rankw >= 2 ? 1 : 0;

		// The integer offsets for the fourth simplex corner
		// Rank 1 denotes the second smallest coordinate.
		const i3 = rankx >= 1 ? 1 : 0;
		const j3 = ranky >= 1 ? 1 : 0;
		const k3 = rankz >= 1 ? 1 : 0;
		const l3 = rankw >= 1 ? 1 : 0;

		// The fifth corner has all coordinate offsets = 1, so no need to compute that.
		const x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
		const y1 = y0 - j1 + G4;
		const z1 = z0 - k1 + G4;
		const w1 = w0 - l1 + G4;
		const x2 = x0 - i2 + 2 * G4; // Offsets for third corner in (x,y,z,w) coords
		const y2 = y0 - j2 + 2 * G4;
		const z2 = z0 - k2 + 2 * G4;
		const w2 = w0 - l2 + 2 * G4;
		const x3 = x0 - i3 + 3 * G4; // Offsets for fourth corner in (x,y,z,w) coords
		const y3 = y0 - j3 + 3 * G4;
		const z3 = z0 - k3 + 3 * G4;
		const w3 = w0 - l3 + 3 * G4;
		const x4 = x0 - 1 + 4 * G4; // Offsets for last corner in (x,y,z,w) coords
		const y4 = y0 - 1 + 4 * G4;
		const z4 = z0 - 1 + 4 * G4;
		const w4 = w0 - 1 + 4 * G4;

		// Work out the hashed gradient indices of the five simplex corners
		const ii = i % 256;
		const jj = j % 256;
		const kk = k % 256;
		const ll = l % 256;

		// Calculate the contribution from the five corners
		let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
		if (t0 < 0) n0 = 0;
		else {
			t0 *= t0;
			const g = GRAD_4[perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32];
			n0 = t0 * t0 * (g[0] * x0 + g[1] * y0 + g[2] * z0 + g[3] * w0);
		}

		let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
		if (t1 < 0) n1 = 0;
		else {
			t1 *= t1;
			const g = GRAD_4[perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32];
			n1 = t1 * t1 * (g[0] * x1 + g[1] * y1 + g[2] * z1 + g[3] * w1);
		}

		let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
		if (t2 < 0) n2 = 0;
		else {
			t2 *= t2;
			const g = GRAD_4[perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32];
			n2 = t2 * t2 * (g[0] * x2 + g[1] * y2 + g[2] * z2 + g[3] * w2);
		}

		let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
		if (t3 < 0) n3 = 0;
		else {
			t3 *= t3;
			const g = GRAD_4[perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32];
			n3 = t3 * t3 * (g[0] * x3 + g[1] * y3 + g[2] * z3 + g[3] * w3);
		}

		let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
		if (t4 < 0) n4 = 0;
		else {
			t4 *= t4;
			const g = GRAD_4[perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32];
			n4 = t4 * t4 * (g[0] * x4 + g[1] * y4 + g[2] * z4 + g[3] * w4);
		}

		// Sum up and scale the result to cover the range [-1,1]
		return 27 * (n0 + n1 + n2 + n3 + n4);
	}
}

const simplexMetatable = Simplex as LuaMetatable<Simplex>;
simplexMetatable.__call = (simplex, x, y, z, w) => {
	if (w !== undefined) return simplex.Noise4d(x as number, y as number, z as number, w as number);
	else if (z !== undefined) return simplex.Noise3d(x as number, y as number, z as number);
	else return simplex.Noise2d(x as number, y as number);
};

simplexMetatable.__tostring = () => "Simplex";

SimplexTs.ts

const GRAD_3 = [
	[1, 1, 0],
	[-1, 1, 0],
	[1, -1, 0],
	[-1, -1, 0],
	[1, 0, 1],
	[-1, 0, 1],
	[1, 0, -1],
	[-1, 0, -1],
	[0, 1, 1],
	[0, -1, 1],
	[0, 1, -1],
	[0, -1, -1],
];

const GRAD_4 = [
	[0, 1, 1, 1],
	[0, 1, 1, -1],
	[0, 1, -1, 1],
	[0, 1, -1, -1],
	[0, -1, 1, 1],
	[0, -1, 1, -1],
	[0, -1, -1, 1],
	[0, -1, -1, -1],
	[1, 0, 1, 1],
	[1, 0, 1, -1],
	[1, 0, -1, 1],
	[1, 0, -1, -1],
	[-1, 0, 1, 1],
	[-1, 0, 1, -1],
	[-1, 0, -1, 1],
	[-1, 0, -1, -1],
	[1, 1, 0, 1],
	[1, 1, 0, -1],
	[1, -1, 0, 1],
	[1, -1, 0, -1],
	[-1, 1, 0, 1],
	[-1, 1, 0, -1],
	[-1, -1, 0, 1],
	[-1, -1, 0, -1],
	[1, 1, 1, 0],
	[1, 1, -1, 0],
	[1, -1, 1, 0],
	[1, -1, -1, 0],
	[-1, 1, 1, 0],
	[-1, 1, -1, 0],
	[-1, -1, 1, 0],
	[-1, -1, -1, 0],
];

const F2 = (Math.sqrt(3) - 1) / 2;
const G2 = (3 - Math.sqrt(3)) / 6;
const F3 = 1 / 3;
const G3 = 1 / 6;
const F4 = (Math.sqrt(5) - 1) / 4;
const G4 = (5 - Math.sqrt(5)) / 20;

const newPerm = () => {
	const perm = new Array<number>(256);
	for (let index = 0; index < 256; index += 1) perm[index] = index;
	return perm;
};

const NextInteger = (min: number, max: number) => Math.floor(Math.random()*(max - min + 1)) + min;

export default class Simplex {
	private perm: Array<number>;
	private permMod12: Array<number>;

	/**
	 * Returns a Simplex generator with a state initialized by a random shuffle.
	 * @param {Array<number>?} perm An array to set as the `perm` entry in the class.
	 * @param {Array<number>?} permMod12 An array to set as the `permMod12` entry in the class.
	 */
	public constructor(perm?: Array<number>, permMod12?: Array<number>) {
		const permutations = newPerm();
		for (let index = permutations.length; index > 1; index -= 1) {
			const jndex = NextInteger(1, index);
			const swap = permutations[index];
			permutations[index] = permutations[jndex];
			permutations[jndex] = swap;
		}

		const isPermUndefined = perm === undefined;
		const isPermMod12Undefined = permMod12 === undefined;

		if (isPermUndefined) {
			if (isPermMod12Undefined) {
				this.perm = new Array<number>(512);
				this.permMod12 = new Array<number>(512);

				for (let index = 0; index < 512; index += 1) {
					this.perm[index] = permutations[index % 256];
					this.permMod12[index] = this.perm[index] % 12;
				}
			} else {
				this.perm = new Array<number>(512);
				this.permMod12 = permMod12;
				for (let index = 0; index < 512; index += 1) this.perm[index] = permutations[index % 256];
			}
		} else {
			if (isPermMod12Undefined) {
				this.perm = perm;
				this.permMod12 = new Array<number>(512);
				for (let index = 0; index < 512; index += 1) this.permMod12[index] = this.perm[index] % 12;
			} else {
				this.perm = perm;
				this.permMod12 = permMod12;
			}
		}
	}

	/**
	 * Returns a Simplex generator with a state initialized by a table of permutations.
	 * @param {Array<number>} permutations An array containing some permutation of each integer between 0 and 255, inclusive.
	 * @returns {Simplex}
	 */
	public static FromArray(permutations: Array<number>): Simplex {
		const found = new Set<number>();
		for (let index = 0; index < 256; index += 1) {
			const value = permutations[index];
			if (value === undefined) throw(`permutations missing index ${index}`);
			found.add(value);
		}

		for (let index = 0; index < 256; index += 1)
			if (!found.has(index)) throw(`permutations missing value ${index}`);

		const perm = new Array<number>(512);
		const permMod12 = new Array<number>(512);

		for (let index = 0; index < 512; index += 1) {
			perm[index] = permutations[index % 256];
			permMod12[index] = perm[index] % 12;
		}

		return new Simplex(perm, permMod12);
	}

	/**
	 * Returns a Simplex generator with a state initialized by a random function.
	 * @param {(index: number) => number} generator A function that receives an integer, and returns an integer between 1 and the given value, inclusive. A generated array of permutations will be shuffled using this function. `math.random` is an example of such a function.
	 * @returns {Simplex}
	 */
	public static FromFunction(generator: (index: number) => number): Simplex {
		const permutations = newPerm();
		for (let index = permutations.length; index > 1; index -= 1) {
			const jndex = generator(index);
			const swap = permutations[index];
			permutations[index] = permutations[jndex];
			permutations[jndex] = swap;
		}

		const perm = new Array<number>(512);
		const permMod12 = new Array<number>(512);

		for (let index = 0; index < 512; index += 1) {
			perm[index] = permutations[index % 256];
			permMod12[index] = perm[index] % 12;
		}

		return new Simplex(perm, permMod12);
	}

	/**
	 * Returns a number in the interval [-1, 1] based on the given two-dimensional coordinates and the generator's permutation state.
	 * @param {number} x The X value to generate with.
	 * @param {number} y The Y value to generate with.
	 * @returns {number} The 2D noise value.
	 */
	public Noise2d(x: number, y: number): number {
		const perm = this.perm;
		const permMod12 = this.permMod12;
		let n0, n1, n2; // Noise contributions from the three corners

		// Skew the input space to determine which simplex cell we're in
		const s = (x + y) * F2; // Hairy factor for 2D
		const i = Math.floor(x + s);
		const j = Math.floor(y + s);
		const t = (i + j) * G2;

		let x0 = i - t; // Unskew the cell origin back to (x,y) space
		let y0 = j - t;
		x0 = x - x0; // The x,y distances from the cell origin
		y0 = y - y0;

		// For the 2D case, the simplex shape is an equilateral triangle.
		// Determine which simplex we are in.
		let i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
		if (x0 > y0) {
			i1 = 1;
			j1 = 0; // lower triangle, xy order: (0,0)->(1,0)->(1,1)
		} else {
			i1 = 0;
			j1 = 1; // upper triangle, yx order: (0,0)->(0,1)->(1,1)
		}

		// A step of (1,0) in (i,j) means a step of (1-c, -c) in (x,y), and
		// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
		// c = (3-sqrt(3))/6
		const x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
		const y1 = y0 - j1 + G2;
		const x2 = x0 - 1 + 2 * G2; // Offsets for last corner in (x,y) unskewed coords
		const y2 = y0 - 1 + 2 * G2;

		// Work out the hashed gradient indices of the three simplex corners
		const ii = i % 256;
		const jj = j % 256;

		// Calculate the contribution from the three corners
		let t0 = 0.5 - x0 * x0 - y0 * y0;
		if (t0 < 0) n0 = 0;
		else {
			t0 *= t0;
			const g = GRAD_3[permMod12[ii + perm[jj]]];
			n0 = t0 * t0 * (g[0] * x0 + g[1] * y0); // (x,y) of GRAD_3 used for 2D gradient
		}

		let t1 = 0.5 - x1 * x1 - y1 * y1;
		if (t1 < 0) n1 = 0;
		else {
			t1 *= t1;
			const g = GRAD_3[permMod12[ii + i1 + perm[jj + j1]]];
			n1 = t1 * t1 * (g[0] * x1 + g[1] * y1);
		}

		let t2 = 0.5 - x2 * x2 - y2 * y2;
		if (t2 < 0) n2 = 0;
		else {
			t2 *= t2;
			const g = GRAD_3[permMod12[ii + 1 + perm[1 + jj]]];
			n2 = t2 * t2 * (g[0] * x2 + g[1] * y2);
		}

		// Add contributions from each corner to get the final noise value.
		// The result is scaled to return values in the interval [-1,1].
		return 70 * (n0 + n1 + n2);
	}

	/**
	 * Returns a number in the interval [-1, 1] based on the given three-dimensional coordinates and the generator's permutation state.
	 * @param {number} x The X value to generate with.
	 * @param {number} y The Y value to generate with.
	 * @param {number} z The Z value to generate with.
	 * @returns {number} The 3D noise value.
	 */
	public Noise3d(x: number, y: number, z: number): number {
		const perm = this.perm;
		const permMod12 = this.permMod12;
		let n0, n1, n2, n3; // Noise contributions from the four corners

		// Skew the input space to determine which simplex cell we're in
		const s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
		const i = Math.floor(x + s);
		const j = Math.floor(y + s);
		const k = Math.floor(z + s);
		const t = (i + j + k) * G3;
		const X0 = i - t; // Unskew the cell origin back to (x,y,z) space
		const Y0 = j - t;
		const Z0 = k - t;
		const x0 = x - X0; // The x,y,z distances from the cell origin
		const y0 = y - Y0;
		const z0 = z - Z0;

		// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
		// Determine which simplex we are in.
		let i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
		let i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
		if (x0 >= y0) {
			if (y0 >= z0) {
				// X Y Z order
				i1 = 1;
				j1 = 0;
				k1 = 0;
				i2 = 1;
				j2 = 1;
				k2 = 0;
			} else if (x0 >= z0) {
				// X Z Y order
				i1 = 1;
				j1 = 0;
				k1 = 0;
				i2 = 1;
				j2 = 0;
				k2 = 1;
			} else {
				// Z X Y order
				i1 = 0;
				j1 = 0;
				k1 = 1;
				i2 = 1;
				j2 = 0;
				k2 = 1;
			}
		} else {
			// x0 < y0
			if (y0 < z0) {
				// Z Y X order
				i1 = 0;
				j1 = 0;
				k1 = 1;
				i2 = 0;
				j2 = 1;
				k2 = 1;
			} else if (x0 < z0) {
				// Y Z X order
				i1 = 0;
				j1 = 1;
				k1 = 0;
				i2 = 0;
				j2 = 1;
				k2 = 1;
			} else {
				// Y X Z order
				i1 = 0;
				j1 = 1;
				k1 = 0;
				i2 = 1;
				j2 = 1;
				k2 = 0;
			}
		}

		// A step of (1,0,0) in (i,j,k) means a step of (1-c, -c, -c) in (x,y,z),
		// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c, -c) in (x,y,z), and
		// a step of (0,0,1) in (i,j,k) means a step of (-c, -c,1-c) in (x,y,z), where
		// c = 1/6.
		const x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
		const y1 = y0 - j1 + G3;
		const z1 = z0 - k1 + G3;
		const x2 = x0 - i2 + 2 * G3; // Offsets for third corner in (x,y,z) coords
		const y2 = y0 - j2 + 2 * G3;
		const z2 = z0 - k2 + 2 * G3;
		const x3 = x0 - 1 + 3 * G3; // Offsets for last corner in (x,y,z) coords
		const y3 = y0 - 1 + 3 * G3;
		const z3 = z0 - 1 + 3 * G3;

		// Work out the hashed gradient indices of the four simplex corners
		const ii = i % 256;
		const jj = j % 256;
		const kk = k % 256;

		// Calculate the contribution from the four corners
		let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
		if (t0 < 0) n0 = 0;
		else {
			t0 *= t0;
			const g = GRAD_3[permMod12[ii + perm[jj + perm[kk]]]];
			n0 = t0 * t0 * (g[0] * x0 + g[1] * y0 + g[2] * z0);
		}

		let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
		if (t1 < 0) n1 = 0;
		else {
			t1 *= t1;
			const g = GRAD_3[permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]]];
			n1 = t1 * t1 * (g[0] * x1 + g[1] * y1 + g[2] * z1);
		}

		let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
		if (t2 < 0) n2 = 0;
		else {
			t2 *= t2;
			const g = GRAD_3[permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]]];
			n2 = t2 * t2 * (g[0] * x2 + g[1] * y2 + g[2] * z2);
		}

		let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
		if (t3 < 0) n3 = 0;
		else {
			t3 *= t3;
			const g = GRAD_3[permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]]];
			n3 = t3 * t3 * (g[0] * x3 + g[1] * y3 + g[2] * z3);
		}

		// Add contributions from each corner to get the final noise value.
		// The result is scaled to stay just inside [-1,1]
		return 32 * (n0 + n1 + n2 + n3);
	}

	/**
	 * Returns a number in the interval [-1, 1] based on the given four-dimensional coordinates and the generator's permutation state.
	 * @param {number} x The X to generate with.
	 * @param {number} y The Y to generate with.
	 * @param {number} z The Z to generate with.
	 * @param {number} w The W to generate with.
	 * @returns {number} The 4D noise value.
	 */
	public Noise4d(x: number, y: number, z: number, w: number): number {
		const perm = this.perm;
		let n0, n1, n2, n3, n4; // Noise contributions from the five corners

		// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
		const s = (x + y + z + w) * F4; // Factor for 4D skewing
		const i = Math.floor(x + s);
		const j = Math.floor(y + s);
		const k = Math.floor(z + s);
		const l = Math.floor(w + s);
		const t = (i + j + k + l) * G4; // Factor for 4D unskewing
		const X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
		const Y0 = j - t;
		const Z0 = k - t;
		const W0 = l - t;
		const x0 = x - X0; // The x,y,z,w distances from the cell origin
		const y0 = y - Y0;
		const z0 = z - Z0;
		const w0 = w - W0;

		// For the 4D case, the simplex is a 4D shape I won't even try to describe.
		// To find out which of the 24 possible simplices we're in, we need to
		// determine the magnitude ordering of x0, y0, z0 and w0.
		// Six pair-wise comparisons are performed between each possible pair
		// of the four coordinates, and the results are used to rank the numbers.
		let rankx = 0;
		let ranky = 0;
		let rankz = 0;
		let rankw = 0;

		if (x0 > y0) rankx += 1;
		else ranky += 1;

		if (x0 > z0) rankx += 1;
		else rankz += 1;

		if (x0 > w0) rankx += 1;
		else rankw += 1;

		if (y0 > z0) ranky += 1;
		else rankz += 1;

		if (y0 > w0) ranky += 1;
		else rankw += 1;

		if (z0 > w0) rankz += 1;
		else rankw += 1;

		// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
		// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
		// impossible. Only the 24 indices which have non-zero entries make any sense.
		// We use a thresholding to set the coordinates in turn from the largest magnitude.

		// The integer offsets for the second simplex corner
		// Rank 3 denotes the largest coordinate.
		const i1 = rankx >= 3 ? 1 : 0;
		const j1 = ranky >= 3 ? 1 : 0;
		const k1 = rankz >= 3 ? 1 : 0;
		const l1 = rankw >= 3 ? 1 : 0;

		// The integer offsets for the third simplex corner
		// Rank 2 denotes the second largest coordinate.
		const i2 = rankx >= 2 ? 1 : 0;
		const j2 = ranky >= 2 ? 1 : 0;
		const k2 = rankz >= 2 ? 1 : 0;
		const l2 = rankw >= 2 ? 1 : 0;

		// The integer offsets for the fourth simplex corner
		// Rank 1 denotes the second smallest coordinate.
		const i3 = rankx >= 1 ? 1 : 0;
		const j3 = ranky >= 1 ? 1 : 0;
		const k3 = rankz >= 1 ? 1 : 0;
		const l3 = rankw >= 1 ? 1 : 0;

		// The fifth corner has all coordinate offsets = 1, so no need to compute that.
		const x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
		const y1 = y0 - j1 + G4;
		const z1 = z0 - k1 + G4;
		const w1 = w0 - l1 + G4;
		const x2 = x0 - i2 + 2 * G4; // Offsets for third corner in (x,y,z,w) coords
		const y2 = y0 - j2 + 2 * G4;
		const z2 = z0 - k2 + 2 * G4;
		const w2 = w0 - l2 + 2 * G4;
		const x3 = x0 - i3 + 3 * G4; // Offsets for fourth corner in (x,y,z,w) coords
		const y3 = y0 - j3 + 3 * G4;
		const z3 = z0 - k3 + 3 * G4;
		const w3 = w0 - l3 + 3 * G4;
		const x4 = x0 - 1 + 4 * G4; // Offsets for last corner in (x,y,z,w) coords
		const y4 = y0 - 1 + 4 * G4;
		const z4 = z0 - 1 + 4 * G4;
		const w4 = w0 - 1 + 4 * G4;

		// Work out the hashed gradient indices of the five simplex corners
		const ii = i % 256;
		const jj = j % 256;
		const kk = k % 256;
		const ll = l % 256;

		// Calculate the contribution from the five corners
		let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
		if (t0 < 0) n0 = 0;
		else {
			t0 *= t0;
			const g = GRAD_4[perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32];
			n0 = t0 * t0 * (g[0] * x0 + g[1] * y0 + g[2] * z0 + g[3] * w0);
		}

		let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
		if (t1 < 0) n1 = 0;
		else {
			t1 *= t1;
			const g = GRAD_4[perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32];
			n1 = t1 * t1 * (g[0] * x1 + g[1] * y1 + g[2] * z1 + g[3] * w1);
		}

		let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
		if (t2 < 0) n2 = 0;
		else {
			t2 *= t2;
			const g = GRAD_4[perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32];
			n2 = t2 * t2 * (g[0] * x2 + g[1] * y2 + g[2] * z2 + g[3] * w2);
		}

		let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
		if (t3 < 0) n3 = 0;
		else {
			t3 *= t3;
			const g = GRAD_4[perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32];
			n3 = t3 * t3 * (g[0] * x3 + g[1] * y3 + g[2] * z3 + g[3] * w3);
		}

		let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
		if (t4 < 0) n4 = 0;
		else {
			t4 *= t4;
			const g = GRAD_4[perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32];
			n4 = t4 * t4 * (g[0] * x4 + g[1] * y4 + g[2] * z4 + g[3] * w4);
		}

		// Sum up and scale the result to cover the range [-1,1]
		return 27 * (n0 + n1 + n2 + n3 + n4);
	}
}