📄 `SimplexNoise.js`¶

📊 Analysis Summary¶

Metric	Count
🔧 Functions	6
🧱 Classes	1
📊 Variables & Constants	134

📚 Table of Contents¶

Variables & Constants
Functions
Classes

🛠️ File Location:¶

📂 examples/jsm/math/SimplexNoise.js

Variables & Constants¶

Name	Type	Kind	Value	Exported
`n0`	`any`	let/var	`not shown`	✗
`n1`	`any`	let/var	`not shown`	✗
`n2`	`any`	let/var	`not shown`	✗
`F2`	`number`	let/var	`0.5 * ( Math.sqrt( 3.0 ) - 1.0 )`	✗
`s`	`number`	let/var	`( xin + yin ) * F2`	✗
`G2`	`number`	let/var	`( 3.0 - Math.sqrt( 3.0 ) ) / 6.0`	✗
`t`	`number`	let/var	`( i + j ) * G2`	✗
`X0`	`number`	let/var	`i - t`	✗
`Y0`	`number`	let/var	`j - t`	✗
`x0`	`number`	let/var	`xin - X0`	✗
`y0`	`number`	let/var	`yin - Y0`	✗
`i1`	`any`	let/var	`not shown`	✗
`j1`	`any`	let/var	`not shown`	✗
`x1`	`number`	let/var	`x0 - i1 + G2`	✗
`y1`	`number`	let/var	`y0 - j1 + G2`	✗
`x2`	`number`	let/var	`x0 - 1.0 + 2.0 * G2`	✗
`y2`	`number`	let/var	`y0 - 1.0 + 2.0 * G2`	✗
`ii`	`number`	let/var	`i & 255`	✗
`jj`	`number`	let/var	`j & 255`	✗
`gi0`	`number`	let/var	`this.perm[ ii + this.perm[ jj ] ] % 12`	✗
`gi1`	`number`	let/var	`this.perm[ ii + i1 + this.perm[ jj + j1 ] ] % 12`	✗
`gi2`	`number`	let/var	`this.perm[ ii + 1 + this.perm[ jj + 1 ] ] % 12`	✗
`t0`	`number`	let/var	`0.5 - x0 * x0 - y0 * y0`	✗
`t1`	`number`	let/var	`0.5 - x1 * x1 - y1 * y1`	✗
`t2`	`number`	let/var	`0.5 - x2 * x2 - y2 * y2`	✗
`n0`	`any`	let/var	`not shown`	✗
`n1`	`any`	let/var	`not shown`	✗
`n2`	`any`	let/var	`not shown`	✗
`n3`	`any`	let/var	`not shown`	✗
`F3`	`number`	let/var	`1.0 / 3.0`	✗
`s`	`number`	let/var	`( xin + yin + zin ) * F3`	✗
`G3`	`number`	let/var	`1.0 / 6.0`	✗
`t`	`number`	let/var	`( i + j + k ) * G3`	✗
`X0`	`number`	let/var	`i - t`	✗
`Y0`	`number`	let/var	`j - t`	✗
`Z0`	`number`	let/var	`k - t`	✗
`x0`	`number`	let/var	`xin - X0`	✗
`y0`	`number`	let/var	`yin - Y0`	✗
`z0`	`number`	let/var	`zin - Z0`	✗
`i1`	`any`	let/var	`not shown`	✗
`j1`	`any`	let/var	`not shown`	✗
`k1`	`any`	let/var	`not shown`	✗
`i2`	`any`	let/var	`not shown`	✗
`j2`	`any`	let/var	`not shown`	✗
`k2`	`any`	let/var	`not shown`	✗
`x1`	`number`	let/var	`x0 - i1 + G3`	✗
`y1`	`number`	let/var	`y0 - j1 + G3`	✗
`z1`	`number`	let/var	`z0 - k1 + G3`	✗
`x2`	`number`	let/var	`x0 - i2 + 2.0 * G3`	✗
`y2`	`number`	let/var	`y0 - j2 + 2.0 * G3`	✗
`z2`	`number`	let/var	`z0 - k2 + 2.0 * G3`	✗
`x3`	`number`	let/var	`x0 - 1.0 + 3.0 * G3`	✗
`y3`	`number`	let/var	`y0 - 1.0 + 3.0 * G3`	✗
`z3`	`number`	let/var	`z0 - 1.0 + 3.0 * G3`	✗
`ii`	`number`	let/var	`i & 255`	✗
`jj`	`number`	let/var	`j & 255`	✗
`kk`	`number`	let/var	`k & 255`	✗
`gi0`	`number`	let/var	`this.perm[ ii + this.perm[ jj + this.perm[ kk ] ] ] % 12`	✗
`gi1`	`number`	let/var	`this.perm[ ii + i1 + this.perm[ jj + j1 + this.perm[ kk + k1 ] ] ] % 12`	✗
`gi2`	`number`	let/var	`this.perm[ ii + i2 + this.perm[ jj + j2 + this.perm[ kk + k2 ] ] ] % 12`	✗
`gi3`	`number`	let/var	`this.perm[ ii + 1 + this.perm[ jj + 1 + this.perm[ kk + 1 ] ] ] % 12`	✗
`t0`	`number`	let/var	`0.6 - x0 * x0 - y0 * y0 - z0 * z0`	✗
`t1`	`number`	let/var	`0.6 - x1 * x1 - y1 * y1 - z1 * z1`	✗
`t2`	`number`	let/var	`0.6 - x2 * x2 - y2 * y2 - z2 * z2`	✗
`t3`	`number`	let/var	`0.6 - x3 * x3 - y3 * y3 - z3 * z3`	✗
`grad4`	`number[][]`	let/var	`this.grad4`	✗
`simplex`	`number[][]`	let/var	`this.simplex`	✗
`perm`	`number[]`	let/var	`this.perm`	✗
`F4`	`number`	let/var	`( Math.sqrt( 5.0 ) - 1.0 ) / 4.0`	✗
`G4`	`number`	let/var	`( 5.0 - Math.sqrt( 5.0 ) ) / 20.0`	✗
`n0`	`any`	let/var	`not shown`	✗
`n1`	`any`	let/var	`not shown`	✗
`n2`	`any`	let/var	`not shown`	✗
`n3`	`any`	let/var	`not shown`	✗
`n4`	`any`	let/var	`not shown`	✗
`s`	`number`	let/var	`( x + y + z + w ) * F4`	✗
`t`	`number`	let/var	`( i + j + k + l ) * G4`	✗
`X0`	`number`	let/var	`i - t`	✗
`Y0`	`number`	let/var	`j - t`	✗
`Z0`	`number`	let/var	`k - t`	✗
`W0`	`number`	let/var	`l - t`	✗
`x0`	`number`	let/var	`x - X0`	✗
`y0`	`number`	let/var	`y - Y0`	✗
`z0`	`number`	let/var	`z - Z0`	✗
`w0`	`number`	let/var	`w - W0`	✗
`c1`	`0 \\| 32`	let/var	`( x0 > y0 ) ? 32 : 0`	✗
`c2`	`0 \\| 16`	let/var	`( x0 > z0 ) ? 16 : 0`	✗
`c3`	`0 \\| 8`	let/var	`( y0 > z0 ) ? 8 : 0`	✗
`c4`	`4 \\| 0`	let/var	`( x0 > w0 ) ? 4 : 0`	✗
`c5`	`2 \\| 0`	let/var	`( y0 > w0 ) ? 2 : 0`	✗
`c6`	`1 \\| 0`	let/var	`( z0 > w0 ) ? 1 : 0`	✗
`c`	`number`	let/var	`c1 + c2 + c3 + c4 + c5 + c6`	✗
`i1`	`1 \\| 0`	let/var	`simplex[ c ][ 0 ] >= 3 ? 1 : 0`	✗
`j1`	`1 \\| 0`	let/var	`simplex[ c ][ 1 ] >= 3 ? 1 : 0`	✗
`k1`	`1 \\| 0`	let/var	`simplex[ c ][ 2 ] >= 3 ? 1 : 0`	✗
`l1`	`1 \\| 0`	let/var	`simplex[ c ][ 3 ] >= 3 ? 1 : 0`	✗
`i2`	`1 \\| 0`	let/var	`simplex[ c ][ 0 ] >= 2 ? 1 : 0`	✗
`j2`	`1 \\| 0`	let/var	`simplex[ c ][ 1 ] >= 2 ? 1 : 0`	✗
`k2`	`1 \\| 0`	let/var	`simplex[ c ][ 2 ] >= 2 ? 1 : 0`	✗
`l2`	`1 \\| 0`	let/var	`simplex[ c ][ 3 ] >= 2 ? 1 : 0`	✗
`i3`	`1 \\| 0`	let/var	`simplex[ c ][ 0 ] >= 1 ? 1 : 0`	✗
`j3`	`1 \\| 0`	let/var	`simplex[ c ][ 1 ] >= 1 ? 1 : 0`	✗
`k3`	`1 \\| 0`	let/var	`simplex[ c ][ 2 ] >= 1 ? 1 : 0`	✗
`l3`	`1 \\| 0`	let/var	`simplex[ c ][ 3 ] >= 1 ? 1 : 0`	✗
`x1`	`number`	let/var	`x0 - i1 + G4`	✗
`y1`	`number`	let/var	`y0 - j1 + G4`	✗
`z1`	`number`	let/var	`z0 - k1 + G4`	✗
`w1`	`number`	let/var	`w0 - l1 + G4`	✗
`x2`	`number`	let/var	`x0 - i2 + 2.0 * G4`	✗
`y2`	`number`	let/var	`y0 - j2 + 2.0 * G4`	✗
`z2`	`number`	let/var	`z0 - k2 + 2.0 * G4`	✗
`w2`	`number`	let/var	`w0 - l2 + 2.0 * G4`	✗
`x3`	`number`	let/var	`x0 - i3 + 3.0 * G4`	✗
`y3`	`number`	let/var	`y0 - j3 + 3.0 * G4`	✗
`z3`	`number`	let/var	`z0 - k3 + 3.0 * G4`	✗
`w3`	`number`	let/var	`w0 - l3 + 3.0 * G4`	✗
`x4`	`number`	let/var	`x0 - 1.0 + 4.0 * G4`	✗
`y4`	`number`	let/var	`y0 - 1.0 + 4.0 * G4`	✗
`z4`	`number`	let/var	`z0 - 1.0 + 4.0 * G4`	✗
`w4`	`number`	let/var	`w0 - 1.0 + 4.0 * G4`	✗
`ii`	`number`	let/var	`i & 255`	✗
`jj`	`number`	let/var	`j & 255`	✗
`kk`	`number`	let/var	`k & 255`	✗
`ll`	`number`	let/var	`l & 255`	✗
`gi0`	`number`	let/var	`perm[ ii + perm[ jj + perm[ kk + perm[ ll ] ] ] ] % 32`	✗
`gi1`	`number`	let/var	`perm[ ii + i1 + perm[ jj + j1 + perm[ kk + k1 + perm[ ll + l1 ] ] ] ] % 32`	✗
`gi2`	`number`	let/var	`perm[ ii + i2 + perm[ jj + j2 + perm[ kk + k2 + perm[ ll + l2 ] ] ] ] % 32`	✗
`gi3`	`number`	let/var	`perm[ ii + i3 + perm[ jj + j3 + perm[ kk + k3 + perm[ ll + l3 ] ] ] ] % 32`	✗
`gi4`	`number`	let/var	`perm[ ii + 1 + perm[ jj + 1 + perm[ kk + 1 + perm[ ll + 1 ] ] ] ] % 32`	✗
`t0`	`number`	let/var	`0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0`	✗
`t1`	`number`	let/var	`0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1`	✗
`t2`	`number`	let/var	`0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2`	✗
`t3`	`number`	let/var	`0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3`	✗
`t4`	`number`	let/var	`0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4`	✗

Functions¶

`SimplexNoise.noise(xin: number, yin: number): number`¶

JSDoc:

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

Parameters:

xin number
yin number

Returns: number

Calls:

Math.sqrt
Math.floor
this._dot

Internal Comments:

// Skew the input space to determine which simplex cell we're in (x2)
// For the 2D case, the simplex shape is an equilateral triangle. (x2)
// Determine which simplex we are in. (x2)
// A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and (x2)
// a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where (x2)
// c = (3-sqrt(3))/6 (x2)
// Work out the hashed gradient indices of the three simplex corners (x2)
// Calculate the contribution from the three corners (x2)
// Add contributions from each corner to get the final noise value.
// The result is scaled to return values in the interval [-1,1].

Code

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 );

    }

`SimplexNoise.noise3d(xin: number, yin: number, zin: number): number`¶

JSDoc:

/**
     * 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.
     */

Parameters:

xin number
yin number
zin number

Returns: number

Calls:

Math.floor
this._dot3

Internal Comments:

// Skew the input space to determine which simplex cell we're in (x2)
// For the 3D case, the simplex shape is a slightly irregular tetrahedron. (x2)
// Determine which simplex we are in. (x2)
// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), (x2)
// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and (x2)
// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where (x2)
// c = 1/6. (x2)
// Work out the hashed gradient indices of the four simplex corners (x2)
// Calculate the contribution from the four corners (x2)
// Add contributions from each corner to get the final noise value.
// The result is scaled to stay just inside [-1,1]

Code

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 );

    }

`SimplexNoise.noise4d(x: number, y: number, z: number, w: number): number`¶

JSDoc:

/**
     * 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.
     */

Parameters:

x number
y number
z number
w number

Returns: number

Calls:

Math.sqrt
Math.floor
this._dot4

Internal Comments:

// For faster and easier lookups (x2)
// The skewing and unskewing factors are hairy again for the 4D case (x2)
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in (x2)
// For the 4D case, the simplex is a 4D shape I won't even try to describe. (x2)
// To find out which of the 24 possible simplices we're in, we need to (x2)
// determine the magnitude ordering of x0, y0, z0 and w0. (x2)
// The method below is a good way of finding the ordering of x,y,z,w and (x2)
// then find the correct traversal order for the simplex we’re in. (x2)
// First, six pair-wise comparisons are performed between each possible pair (x2)
// of the four coordinates, and the results are used to add up binary bits (x2)
// for an integer index. (x2)
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. (x2)
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w (x2)
// impossible. Only the 24 indices which have non-zero entries make any sense. (x2)
// We use a thresholding to set the coordinates in turn from the largest magnitude. (x2)
// The number 3 in the "simplex" array is at the position of the largest coordinate. (x2)
// The number 2 in the "simplex" array is at the second largest coordinate. (x2)
// The number 1 in the "simplex" array is at the second smallest coordinate. (x2)
// The fifth corner has all coordinate offsets = 1, so no need to look that up. (x2)
// Work out the hashed gradient indices of the five simplex corners (x2)
// Calculate the contribution from the five corners (x2)
// Sum up and scale the result to cover the range [-1,1]

Code

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 );

    }

`SimplexNoise._dot(g: any, x: any, y: any): number`¶

Parameters:

g any
x any
y any

Returns: number

Code

_dot( g, x, y ) {

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

    }

`SimplexNoise._dot3(g: any, x: any, y: any, z: any): number`¶

Parameters:

g any
x any
y any
z any

Returns: number

Code

_dot3( g, x, y, z ) {

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

    }

`SimplexNoise._dot4(g: any, x: any, y: any, z: any, w: any): number`¶

Parameters:

g any
x any
y any
z any
w any

Returns: number

Code

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

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

    }

Classes¶

`SimplexNoise`¶

Class Code

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;

    }

}

Methods¶

`noise(xin: number, yin: number): number`¶

Code

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 );

    }

`noise3d(xin: number, yin: number, zin: number): number`¶

Code

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 );

    }

`noise4d(x: number, y: number, z: number, w: number): number`¶

Code

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 );

    }

`_dot(g: any, x: any, y: any): number`¶

Code

_dot( g, x, y ) {

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

    }

`_dot3(g: any, x: any, y: any, z: any): number`¶

Code

_dot3( g, x, y, z ) {

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

    }

`_dot4(g: any, x: any, y: any, z: any, w: any): number`¶

Code

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

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

    }

📄 SimplexNoise.js¶

📊 Analysis Summary¶

📚 Table of Contents¶

🛠️ File Location:¶

Variables & Constants¶

Functions¶

SimplexNoise.noise(xin: number, yin: number): number¶

SimplexNoise.noise3d(xin: number, yin: number, zin: number): number¶

SimplexNoise.noise4d(x: number, y: number, z: number, w: number): number¶

SimplexNoise._dot(g: any, x: any, y: any): number¶

SimplexNoise._dot3(g: any, x: any, y: any, z: any): number¶

SimplexNoise._dot4(g: any, x: any, y: any, z: any, w: any): number¶

Classes¶

SimplexNoise¶

Methods¶

noise(xin: number, yin: number): number¶

noise3d(xin: number, yin: number, zin: number): number¶

noise4d(x: number, y: number, z: number, w: number): number¶

_dot(g: any, x: any, y: any): number¶

_dot3(g: any, x: any, y: any, z: any): number¶

_dot4(g: any, x: any, y: any, z: any, w: any): number¶

📄 `SimplexNoise.js`¶

`SimplexNoise.noise(xin: number, yin: number): number`¶

`SimplexNoise.noise3d(xin: number, yin: number, zin: number): number`¶

`SimplexNoise.noise4d(x: number, y: number, z: number, w: number): number`¶

`SimplexNoise._dot(g: any, x: any, y: any): number`¶

`SimplexNoise._dot3(g: any, x: any, y: any, z: any): number`¶

`SimplexNoise._dot4(g: any, x: any, y: any, z: any, w: any): number`¶

`SimplexNoise`¶

`noise(xin: number, yin: number): number`¶

`noise3d(xin: number, yin: number, zin: number): number`¶

`noise4d(x: number, y: number, z: number, w: number): number`¶

`_dot(g: any, x: any, y: any): number`¶

`_dot3(g: any, x: any, y: any, z: any): number`¶

`_dot4(g: any, x: any, y: any, z: any, w: any): number`¶