SimplexNoise.js

/**
 * A utility class providing noise functions.
 *
 * The code is based on [Simplex noise demystified]{@link https://web.archive.org/web/20210210162332/http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf}
 * by Stefan Gustavson, 2005.
 *
 * @three_import import { SimplexNoise } from 'three/addons/math/SimplexNoise.js';
 */
class SimplexNoise {

	/**
	 * Constructs a new simplex noise object.
	 *
	 * @param {Object} [r=Math] - A math utility class that holds a `random()` method. This makes it
	 * possible to pass in custom random number generator.
	 */
	constructor( r = Math ) {

		this.grad3 = [[ 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 ]];

		this.grad4 = [[ 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 ]];

		this.p = [];

		for ( let i = 0; i < 256; i ++ ) {

			this.p[ i ] = Math.floor( r.random() * 256 );

		}

		// To remove the need for index wrapping, double the permutation table length
		this.perm = [];

		for ( let i = 0; i < 512; i ++ ) {

			this.perm[ i ] = this.p[ i & 255 ];

		}

		// A lookup table to traverse the simplex around a given point in 4D.
		// Details can be found where this table is used, in the 4D noise method.
		this.simplex = [
			[ 0, 1, 2, 3 ], [ 0, 1, 3, 2 ], [ 0, 0, 0, 0 ], [ 0, 2, 3, 1 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 1, 2, 3, 0 ],
			[ 0, 2, 1, 3 ], [ 0, 0, 0, 0 ], [ 0, 3, 1, 2 ], [ 0, 3, 2, 1 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 1, 3, 2, 0 ],
			[ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ],
			[ 1, 2, 0, 3 ], [ 0, 0, 0, 0 ], [ 1, 3, 0, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 2, 3, 0, 1 ], [ 2, 3, 1, 0 ],
			[ 1, 0, 2, 3 ], [ 1, 0, 3, 2 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 2, 0, 3, 1 ], [ 0, 0, 0, 0 ], [ 2, 1, 3, 0 ],
			[ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ],
			[ 2, 0, 1, 3 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 3, 0, 1, 2 ], [ 3, 0, 2, 1 ], [ 0, 0, 0, 0 ], [ 3, 1, 2, 0 ],
			[ 2, 1, 0, 3 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 0, 0, 0, 0 ], [ 3, 1, 0, 2 ], [ 0, 0, 0, 0 ], [ 3, 2, 0, 1 ], [ 3, 2, 1, 0 ]];

	}

	/**
	 * A 2D simplex noise method.
	 *
	 * @param {number} xin - The x coordinate.
	 * @param {number} yin - The y coordinate.
	 * @return {number} The noise value.
	 */
	noise( xin, yin ) {

		let n0; // Noise contributions from the three corners
		let n1;
		let n2;
		// Skew the input space to determine which simplex cell we're in
		const F2 = 0.5 * ( Math.sqrt( 3.0 ) - 1.0 );
		const s = ( xin + yin ) * F2; // Hairy factor for 2D
		const i = Math.floor( xin + s );
		const j = Math.floor( yin + s );
		const G2 = ( 3.0 - Math.sqrt( 3.0 ) ) / 6.0;
		const t = ( i + j ) * G2;
		const X0 = i - t; // Unskew the cell origin back to (x,y) space
		const Y0 = j - t;
		const x0 = xin - X0; // The x,y distances from the cell origin
		const y0 = yin - Y0;

		// For the 2D case, the simplex shape is an equilateral triangle.
		// Determine which simplex we are in.
		let i1; // Offsets for second (middle) corner of simplex in (i,j) coords

		let j1;
		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 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
		const y2 = y0 - 1.0 + 2.0 * G2;
		// Work out the hashed gradient indices of the three simplex corners
		const ii = i & 255;
		const jj = j & 255;
		const gi0 = this.perm[ ii + this.perm[ jj ] ] % 12;
		const gi1 = this.perm[ ii + i1 + this.perm[ jj + j1 ] ] % 12;
		const gi2 = this.perm[ ii + 1 + this.perm[ jj + 1 ] ] % 12;
		// Calculate the contribution from the three corners
		let t0 = 0.5 - x0 * x0 - y0 * y0;
		if ( t0 < 0 ) n0 = 0.0;
		else {

			t0 *= t0;
			n0 = t0 * t0 * this._dot( this.grad3[ gi0 ], x0, y0 ); // (x,y) of grad3 used for 2D gradient

		}

		let t1 = 0.5 - x1 * x1 - y1 * y1;
		if ( t1 < 0 ) n1 = 0.0;
		else {

			t1 *= t1;
			n1 = t1 * t1 * this._dot( this.grad3[ gi1 ], x1, y1 );

		}

		let t2 = 0.5 - x2 * x2 - y2 * y2;
		if ( t2 < 0 ) n2 = 0.0;
		else {

			t2 *= t2;
			n2 = t2 * t2 * this._dot( this.grad3[ gi2 ], x2, 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 70.0 * ( n0 + n1 + n2 );

	}

	/**
	 * A 3D simplex noise method.
	 *
	 * @param {number} xin - The x coordinate.
	 * @param {number} yin - The y coordinate.
	 * @param {number} zin - The z coordinate.
	 * @return {number} The noise value.
	 */
	noise3d( xin, yin, zin ) {

		let n0; // Noise contributions from the four corners
		let n1;
		let n2;
		let n3;
		// Skew the input space to determine which simplex cell we're in
		const F3 = 1.0 / 3.0;
		const s = ( xin + yin + zin ) * F3; // Very nice and simple skew factor for 3D
		const i = Math.floor( xin + s );
		const j = Math.floor( yin + s );
		const k = Math.floor( zin + s );
		const G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
		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 = xin - X0; // The x,y,z distances from the cell origin
		const y0 = yin - Y0;
		const z0 = zin - Z0;

		// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
		// Determine which simplex we are in.
		let i1; // Offsets for second corner of simplex in (i,j,k) coords

		let j1;
		let k1;
		let i2; // Offsets for third corner of simplex in (i,j,k) coords
		let j2;
		let k2;
		if ( x0 >= y0 ) {

			if ( y0 >= z0 ) {

				i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0;

				// X Y Z order

			} else if ( x0 >= z0 ) {

				i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1;

				// X Z Y order

			} else {

				i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1;

			} // Z X Y order

		} else { // x0<y0

			if ( y0 < z0 ) {

				i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1;

				// Z Y X order

			} else if ( x0 < z0 ) {

				i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1;

				// Y Z X order

			} else {

				i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0;

			} // Y X Z order

		}

		// 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 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
		const y2 = y0 - j2 + 2.0 * G3;
		const z2 = z0 - k2 + 2.0 * G3;
		const x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
		const y3 = y0 - 1.0 + 3.0 * G3;
		const z3 = z0 - 1.0 + 3.0 * G3;
		// Work out the hashed gradient indices of the four simplex corners
		const ii = i & 255;
		const jj = j & 255;
		const kk = k & 255;
		const gi0 = this.perm[ ii + this.perm[ jj + this.perm[ kk ] ] ] % 12;
		const gi1 = this.perm[ ii + i1 + this.perm[ jj + j1 + this.perm[ kk + k1 ] ] ] % 12;
		const gi2 = this.perm[ ii + i2 + this.perm[ jj + j2 + this.perm[ kk + k2 ] ] ] % 12;
		const gi3 = this.perm[ ii + 1 + this.perm[ jj + 1 + this.perm[ kk + 1 ] ] ] % 12;
		// Calculate the contribution from the four corners
		let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
		if ( t0 < 0 ) n0 = 0.0;
		else {

			t0 *= t0;
			n0 = t0 * t0 * this._dot3( this.grad3[ gi0 ], x0, y0, z0 );

		}

		let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
		if ( t1 < 0 ) n1 = 0.0;
		else {

			t1 *= t1;
			n1 = t1 * t1 * this._dot3( this.grad3[ gi1 ], x1, y1, z1 );

		}

		let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
		if ( t2 < 0 ) n2 = 0.0;
		else {

			t2 *= t2;
			n2 = t2 * t2 * this._dot3( this.grad3[ gi2 ], x2, y2, z2 );

		}

		let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
		if ( t3 < 0 ) n3 = 0.0;
		else {

			t3 *= t3;
			n3 = t3 * t3 * this._dot3( this.grad3[ gi3 ], x3, y3, z3 );

		}

		// Add contributions from each corner to get the final noise value.
		// The result is scaled to stay just inside [-1,1]
		return 32.0 * ( n0 + n1 + n2 + n3 );

	}

	/**
	 * A 4D simplex noise method.
	 *
	 * @param {number} x - The x coordinate.
	 * @param {number} y - The y coordinate.
	 * @param {number} z - The z coordinate.
	 * @param {number} w - The w coordinate.
	 * @return {number} The noise value.
	 */
	noise4d( x, y, z, w ) {

		// For faster and easier lookups
		const grad4 = this.grad4;
		const simplex = this.simplex;
		const perm = this.perm;

		// The skewing and unskewing factors are hairy again for the 4D case
		const F4 = ( Math.sqrt( 5.0 ) - 1.0 ) / 4.0;
		const G4 = ( 5.0 - Math.sqrt( 5.0 ) ) / 20.0;
		let n0; // Noise contributions from the five corners
		let n1;
		let n2;
		let n3;
		let n4;
		// 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.
		// The method below is a good way of finding the ordering of x,y,z,w and
		// then find the correct traversal order for the simplex we’re in.
		// First, six pair-wise comparisons are performed between each possible pair
		// of the four coordinates, and the results are used to add up binary bits
		// for an integer index.
		const c1 = ( x0 > y0 ) ? 32 : 0;
		const c2 = ( x0 > z0 ) ? 16 : 0;
		const c3 = ( y0 > z0 ) ? 8 : 0;
		const c4 = ( x0 > w0 ) ? 4 : 0;
		const c5 = ( y0 > w0 ) ? 2 : 0;
		const c6 = ( z0 > w0 ) ? 1 : 0;
		const c = c1 + c2 + c3 + c4 + c5 + c6;

		// 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 number 3 in the "simplex" array is at the position of the largest coordinate.
		const i1 = simplex[ c ][ 0 ] >= 3 ? 1 : 0;
		const j1 = simplex[ c ][ 1 ] >= 3 ? 1 : 0;
		const k1 = simplex[ c ][ 2 ] >= 3 ? 1 : 0;
		const l1 = simplex[ c ][ 3 ] >= 3 ? 1 : 0;
		// The number 2 in the "simplex" array is at the second largest coordinate.
		const i2 = simplex[ c ][ 0 ] >= 2 ? 1 : 0;
		const j2 = simplex[ c ][ 1 ] >= 2 ? 1 : 0;
		const k2 = simplex[ c ][ 2 ] >= 2 ? 1 : 0;
		const l2 = simplex[ c ][ 3 ] >= 2 ? 1 : 0;
		// The number 1 in the "simplex" array is at the second smallest coordinate.
		const i3 = simplex[ c ][ 0 ] >= 1 ? 1 : 0;
		const j3 = simplex[ c ][ 1 ] >= 1 ? 1 : 0;
		const k3 = simplex[ c ][ 2 ] >= 1 ? 1 : 0;
		const l3 = simplex[ c ][ 3 ] >= 1 ? 1 : 0;
		// The fifth corner has all coordinate offsets = 1, so no need to look that up.
		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 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
		const y2 = y0 - j2 + 2.0 * G4;
		const z2 = z0 - k2 + 2.0 * G4;
		const w2 = w0 - l2 + 2.0 * G4;
		const x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
		const y3 = y0 - j3 + 3.0 * G4;
		const z3 = z0 - k3 + 3.0 * G4;
		const w3 = w0 - l3 + 3.0 * G4;
		const x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
		const y4 = y0 - 1.0 + 4.0 * G4;
		const z4 = z0 - 1.0 + 4.0 * G4;
		const w4 = w0 - 1.0 + 4.0 * G4;
		// Work out the hashed gradient indices of the five simplex corners
		const ii = i & 255;
		const jj = j & 255;
		const kk = k & 255;
		const ll = l & 255;
		const gi0 = perm[ ii + perm[ jj + perm[ kk + perm[ ll ] ] ] ] % 32;
		const gi1 = perm[ ii + i1 + perm[ jj + j1 + perm[ kk + k1 + perm[ ll + l1 ] ] ] ] % 32;
		const gi2 = perm[ ii + i2 + perm[ jj + j2 + perm[ kk + k2 + perm[ ll + l2 ] ] ] ] % 32;
		const gi3 = perm[ ii + i3 + perm[ jj + j3 + perm[ kk + k3 + perm[ ll + l3 ] ] ] ] % 32;
		const gi4 = perm[ ii + 1 + perm[ jj + 1 + perm[ kk + 1 + perm[ ll + 1 ] ] ] ] % 32;
		// Calculate the contribution from the five corners
		let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
		if ( t0 < 0 ) n0 = 0.0;
		else {

			t0 *= t0;
			n0 = t0 * t0 * this._dot4( grad4[ gi0 ], x0, y0, z0, w0 );

		}

		let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
		if ( t1 < 0 ) n1 = 0.0;
		else {

			t1 *= t1;
			n1 = t1 * t1 * this._dot4( grad4[ gi1 ], x1, y1, z1, w1 );

		}

		let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
		if ( t2 < 0 ) n2 = 0.0;
		else {

			t2 *= t2;
			n2 = t2 * t2 * this._dot4( grad4[ gi2 ], x2, y2, z2, w2 );

		}

		let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
		if ( t3 < 0 ) n3 = 0.0;
		else {

			t3 *= t3;
			n3 = t3 * t3 * this._dot4( grad4[ gi3 ], x3, y3, z3, w3 );

		}

		let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
		if ( t4 < 0 ) n4 = 0.0;
		else {

			t4 *= t4;
			n4 = t4 * t4 * this._dot4( grad4[ gi4 ], x4, y4, z4, w4 );

		}

		// Sum up and scale the result to cover the range [-1,1]
		return 27.0 * ( n0 + n1 + n2 + n3 + n4 );

	}

	// private

	_dot( g, x, y ) {

		return g[ 0 ] * x + g[ 1 ] * y;

	}

	_dot3( g, x, y, z ) {

		return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z;

	}

	_dot4( g, x, y, z, w ) {

		return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z + g[ 3 ] * w;

	}

}

export { SimplexNoise };