simplex-noise.js

/*
 * A fast javascript implementation of simplex noise by Jonas Wagner
 *
 * Based on a speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
 * Which is based on example code by Stefan Gustavson (stegu@itn.liu.se).
 * With Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
 * Better rank ordering method by Stefan Gustavson in 2012.
 *
 *
 * Copyright (C) 2012 Jonas Wagner
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 */
(function () {

var F2 = 0.5 * (Math.sqrt(3.0) - 1.0),
    G2 = (3.0 - Math.sqrt(3.0)) / 6.0,
    F3 = 1.0 / 3.0,
    G3 = 1.0 / 6.0,
    F4 = (Math.sqrt(5.0) - 1.0) / 4.0,
    G4 = (5.0 - Math.sqrt(5.0)) / 20.0;


function SimplexNoise(random) {
    if (!random) random = Math.random;
    this.p = new Uint8Array(256);
    this.perm = new Uint8Array(512);
    this.permMod12 = new Uint8Array(512);
    for (var i = 0; i < 256; i++) {
        this.p[i] = random() * 256;
    }
    for (i = 0; i < 512; i++) {
        this.perm[i] = this.p[i & 255];
        this.permMod12[i] = this.perm[i] % 12;
    }

}
SimplexNoise.prototype = {
    grad3: new Float32Array([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]),
    grad4: new Float32Array([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]),
    noise2D: function (xin, yin) {
        var permMod12 = this.permMod12,
            perm = this.perm,
            grad3 = this.grad3;
        var n0=0, n1=0, n2=0; // Noise contributions from the three corners
        // Skew the input space to determine which simplex cell we're in
        var s = (xin + yin) * F2; // Hairy factor for 2D
        var i = Math.floor(xin + s);
        var j = Math.floor(yin + s);
        var t = (i + j) * G2;
        var X0 = i - t; // Unskew the cell origin back to (x,y) space
        var Y0 = j - t;
        var x0 = xin - X0; // The x,y distances from the cell origin
        var y0 = yin - Y0;
        // For the 2D case, the simplex shape is an equilateral triangle.
        // Determine which simplex we are in.
        var 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
        var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
        var y1 = y0 - j1 + G2;
        var x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
        var y2 = y0 - 1.0 + 2.0 * G2;
        // Work out the hashed gradient indices of the three simplex corners
        var ii = i & 255;
        var jj = j & 255;
        // Calculate the contribution from the three corners
        var t0 = 0.5 - x0 * x0 - y0 * y0;
        if (t0 >= 0) {
            var gi0 = permMod12[ii + perm[jj]] * 3;
            t0 *= t0;
            n0 = t0 * t0 * (grad3[gi0] * x0 + grad3[gi0 + 1] * y0); // (x,y) of grad3 used for 2D gradient
        }
        var t1 = 0.5 - x1 * x1 - y1 * y1;
        if (t1 >= 0) {
            var gi1 = permMod12[ii + i1 + perm[jj + j1]] * 3;
            t1 *= t1;
            n1 = t1 * t1 * (grad3[gi1] * x1 + grad3[gi1 + 1] * y1);
        }
        var t2 = 0.5 - x2 * x2 - y2 * y2;
        if (t2 >= 0) {
            var gi2 = permMod12[ii + 1 + perm[jj + 1]] * 3;
            t2 *= t2;
            n2 = t2 * t2 * (grad3[gi2] * x2 + grad3[gi2 + 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 70.0 * (n0 + n1 + n2);
    },
    // 3D simplex noise
    noise3D: function (xin, yin, zin) {
        var permMod12 = this.permMod12,
            perm = this.perm,
            grad3 = this.grad3;
        var n0, n1, n2, n3; // Noise contributions from the four corners
        // Skew the input space to determine which simplex cell we're in
        var s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
        var i = Math.floor(xin + s);
        var j = Math.floor(yin + s);
        var k = Math.floor(zin + s);
        var t = (i + j + k) * G3;
        var X0 = i - t; // Unskew the cell origin back to (x,y,z) space
        var Y0 = j - t;
        var Z0 = k - t;
        var x0 = xin - X0; // The x,y,z distances from the cell origin
        var y0 = yin - Y0;
        var z0 = zin - Z0;
        // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
        // Determine which simplex we are in.
        var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
        var i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
        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.
        var x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
        var y1 = y0 - j1 + G3;
        var z1 = z0 - k1 + G3;
        var x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
        var y2 = y0 - j2 + 2.0 * G3;
        var z2 = z0 - k2 + 2.0 * G3;
        var x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
        var y3 = y0 - 1.0 + 3.0 * G3;
        var z3 = z0 - 1.0 + 3.0 * G3;
        // Work out the hashed gradient indices of the four simplex corners
        var ii = i & 255;
        var jj = j & 255;
        var kk = k & 255;
        // Calculate the contribution from the four corners
        var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
        if (t0 < 0) n0 = 0.0;
        else {
            var gi0 = permMod12[ii + perm[jj + perm[kk]]] * 3;
            t0 *= t0;
            n0 = t0 * t0 * (grad3[gi0] * x0 + grad3[gi0 + 1] * y0 + grad3[gi0 + 2] * z0);
        }
        var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
        if (t1 < 0) n1 = 0.0;
        else {
            var gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]] * 3;
            t1 *= t1;
            n1 = t1 * t1 * (grad3[gi1] * x1 + grad3[gi1 + 1] * y1 + grad3[gi1 + 2] * z1);
        }
        var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
        if (t2 < 0) n2 = 0.0;
        else {
            var gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]] * 3;
            t2 *= t2;
            n2 = t2 * t2 * (grad3[gi2] * x2 + grad3[gi2 + 1] * y2 + grad3[gi2 + 2] * z2);
        }
        var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
        if (t3 < 0) n3 = 0.0;
        else {
            var gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]] * 3;
            t3 *= t3;
            n3 = t3 * t3 * (grad3[gi3] * x3 + grad3[gi3 + 1] * y3 + grad3[gi3 + 2] * z3);
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to stay just inside [-1,1]
        return 32.0 * (n0 + n1 + n2 + n3);
    },
    // 4D simplex noise, better simplex rank ordering method 2012-03-09
    noise4D: function (x, y, z, w) {
        var permMod12 = this.permMod12,
            perm = this.perm,
            grad4 = this.grad4;

        var 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
        var s = (x + y + z + w) * F4; // Factor for 4D skewing
        var i = Math.floor(x + s);
        var j = Math.floor(y + s);
        var k = Math.floor(z + s);
        var l = Math.floor(w + s);
        var t = (i + j + k + l) * G4; // Factor for 4D unskewing
        var X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
        var Y0 = j - t;
        var Z0 = k - t;
        var W0 = l - t;
        var x0 = x - X0; // The x,y,z,w distances from the cell origin
        var y0 = y - Y0;
        var z0 = z - Z0;
        var 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.
        var rankx = 0;
        var ranky = 0;
        var rankz = 0;
        var rankw = 0;
        if (x0 > y0) rankx++;
        else ranky++;
        if (x0 > z0) rankx++;
        else rankz++;
        if (x0 > w0) rankx++;
        else rankw++;
        if (y0 > z0) ranky++;
        else rankz++;
        if (y0 > w0) ranky++;
        else rankw++;
        if (z0 > w0) rankz++;
        else rankw++;
        var i1, j1, k1, l1; // The integer offsets for the second simplex corner
        var i2, j2, k2, l2; // The integer offsets for the third simplex corner
        var i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
        // 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.
        // Rank 3 denotes the largest coordinate.
        i1 = rankx >= 3 ? 1 : 0;
        j1 = ranky >= 3 ? 1 : 0;
        k1 = rankz >= 3 ? 1 : 0;
        l1 = rankw >= 3 ? 1 : 0;
        // Rank 2 denotes the second largest coordinate.
        i2 = rankx >= 2 ? 1 : 0;
        j2 = ranky >= 2 ? 1 : 0;
        k2 = rankz >= 2 ? 1 : 0;
        l2 = rankw >= 2 ? 1 : 0;
        // Rank 1 denotes the second smallest coordinate.
        i3 = rankx >= 1 ? 1 : 0;
        j3 = ranky >= 1 ? 1 : 0;
        k3 = rankz >= 1 ? 1 : 0;
        l3 = rankw >= 1 ? 1 : 0;
        // The fifth corner has all coordinate offsets = 1, so no need to compute that.
        var x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
        var y1 = y0 - j1 + G4;
        var z1 = z0 - k1 + G4;
        var w1 = w0 - l1 + G4;
        var x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
        var y2 = y0 - j2 + 2.0 * G4;
        var z2 = z0 - k2 + 2.0 * G4;
        var w2 = w0 - l2 + 2.0 * G4;
        var x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
        var y3 = y0 - j3 + 3.0 * G4;
        var z3 = z0 - k3 + 3.0 * G4;
        var w3 = w0 - l3 + 3.0 * G4;
        var x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
        var y4 = y0 - 1.0 + 4.0 * G4;
        var z4 = z0 - 1.0 + 4.0 * G4;
        var w4 = w0 - 1.0 + 4.0 * G4;
        // Work out the hashed gradient indices of the five simplex corners
        var ii = i & 255;
        var jj = j & 255;
        var kk = k & 255;
        var ll = l & 255;
        // Calculate the contribution from the five corners
        var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
        if (t0 < 0) n0 = 0.0;
        else {
            var gi0 = (perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32) * 4;
            t0 *= t0;
            n0 = t0 * t0 * (grad4[gi0] * x0 + grad4[gi0 + 1] * y0 + grad4[gi0 + 2] * z0 + grad4[gi0 + 3] * w0);
        }
        var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
        if (t1 < 0) n1 = 0.0;
        else {
            var gi1 = (perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32) * 4;
            t1 *= t1;
            n1 = t1 * t1 * (grad4[gi1] * x1 + grad4[gi1 + 1] * y1 + grad4[gi1 + 2] * z1 + grad4[gi1 + 3] * w1);
        }
        var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
        if (t2 < 0) n2 = 0.0;
        else {
            var gi2 = (perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32) * 4;
            t2 *= t2;
            n2 = t2 * t2 * (grad4[gi2] * x2 + grad4[gi2 + 1] * y2 + grad4[gi2 + 2] * z2 + grad4[gi2 + 3] * w2);
        }
        var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
        if (t3 < 0) n3 = 0.0;
        else {
            var gi3 = (perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32) * 4;
            t3 *= t3;
            n3 = t3 * t3 * (grad4[gi3] * x3 + grad4[gi3 + 1] * y3 + grad4[gi3 + 2] * z3 + grad4[gi3 + 3] * w3);
        }
        var t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
        if (t4 < 0) n4 = 0.0;
        else {
            var gi4 = (perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32) * 4;
            t4 *= t4;
            n4 = t4 * t4 * (grad4[gi4] * x4 + grad4[gi4 + 1] * y4 + grad4[gi4 + 2] * z4 + grad4[gi4 + 3] * w4);
        }
        // Sum up and scale the result to cover the range [-1,1]
        return 27.0 * (n0 + n1 + n2 + n3 + n4);
    }


};

// amd
if (typeof define !== 'undefined' && define.amd) define(function(){return SimplexNoise;});
//common js
if (typeof exports !== 'undefined') exports.SimplexNoise = SimplexNoise;
// browser
else if (typeof navigator !== 'undefined') this.SimplexNoise = SimplexNoise;
// nodejs
if (typeof module !== 'undefined') {
    module.exports = SimplexNoise;
}

})();