noise.js

/*
 * A speed-improved perlin and simplex noise algorithms for 2D.
 *
 * Based on example code by Stefan Gustavson (stegu@itn.liu.se).
 * Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
 * Better rank ordering method by Stefan Gustavson in 2012.
 * Converted to Javascript by Joseph Gentle.
 *
 * Version 2012-03-09
 *
 * This code was placed in the public domain by its original author,
 * Stefan Gustavson. You may use it as you see fit, but
 * attribution is appreciated.
 *
 */

(function(global) {
    var module = global.noise = {};

    function Grad(x, y, z) {
        this.x = x;
        this.y = y;
        this.z = z;
    }

    Grad.prototype.dot2 = function(x, y) {
        return this.x * x + this.y * y;
    };

    Grad.prototype.dot3 = function(x, y, z) {
        return this.x * x + this.y * y + this.z * z;
    };

    var grad3 = [new Grad(1, 1, 0), new Grad(-1, 1, 0), new Grad(1, -1, 0), new Grad(-1, -1, 0),
        new Grad(1, 0, 1), new Grad(-1, 0, 1), new Grad(1, 0, -1), new Grad(-1, 0, -1),
        new Grad(0, 1, 1), new Grad(0, -1, 1), new Grad(0, 1, -1), new Grad(0, -1, -1)
    ];

    var p = [151, 160, 137, 91, 90, 15,
        131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23,
        190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33,
        88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166,
        77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244,
        102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196,
        135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123,
        5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42,
        223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9,
        129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228,
        251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107,
        49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254,
        138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180
    ];
    // To remove the need for index wrapping, double the permutation table length
    var perm = new Array(512);
    var gradP = new Array(512);

    // This isn't a very good seeding function, but it works ok. It supports 2^16
    // different seed values. Write something better if you need more seeds.
    module.seed = function(seed) {
        if (seed > 0 && seed < 1) {
            // Scale the seed out
            seed *= 65536;
        }

        seed = Math.floor(seed);
        if (seed < 256) {
            seed |= seed << 8;
        }

        for (var i = 0; i < 256; i++) {
            var v;
            if (i & 1) {
                v = p[i] ^ (seed & 255);
            } else {
                v = p[i] ^ ((seed >> 8) & 255);
            }

            perm[i] = perm[i + 256] = v;
            gradP[i] = gradP[i + 256] = grad3[v % 12];
        }
    };

    module.seed(0);

    /*
    for(var i=0; i<256; i++) {
      perm[i] = perm[i + 256] = p[i];
      gradP[i] = gradP[i + 256] = grad3[perm[i] % 12];
    }*/

    // Skewing and unskewing factors for 2, 3, and 4 dimensions
    var F2 = 0.5 * (Math.sqrt(3) - 1);
    var G2 = (3 - Math.sqrt(3)) / 6;

    var F3 = 1 / 3;
    var G3 = 1 / 6;

    // 2D simplex noise
    module.simplex2 = function(xin, yin) {
        var n0, n1, n2; // 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 = xin - i + t; // The x,y distances from the cell origin, unskewed.
        var y0 = yin - j + t;
        // 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) { // lower triangle, XY order: (0,0)->(1,0)->(1,1)
            i1 = 1;
            j1 = 0;
        } else { // upper triangle, YX order: (0,0)->(0,1)->(1,1)
            i1 = 0;
            j1 = 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 + 2 * G2; // Offsets for last corner in (x,y) unskewed coords
        var y2 = y0 - 1 + 2 * G2;
        // Work out the hashed gradient indices of the three simplex corners
        i &= 255;
        j &= 255;
        var gi0 = gradP[i + perm[j]];
        var gi1 = gradP[i + i1 + perm[j + j1]];
        var gi2 = gradP[i + 1 + perm[j + 1]];
        // Calculate the contribution from the three corners
        var t0 = 0.5 - x0 * x0 - y0 * y0;
        if (t0 < 0) {
            n0 = 0;
        } else {
            t0 *= t0;
            n0 = t0 * t0 * gi0.dot2(x0, y0); // (x,y) of grad3 used for 2D gradient
        }
        var t1 = 0.5 - x1 * x1 - y1 * y1;
        if (t1 < 0) {
            n1 = 0;
        } else {
            t1 *= t1;
            n1 = t1 * t1 * gi1.dot2(x1, y1);
        }
        var t2 = 0.5 - x2 * x2 - y2 * y2;
        if (t2 < 0) {
            n2 = 0;
        } else {
            t2 *= t2;
            n2 = t2 * t2 * gi2.dot2(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 * (n0 + n1 + n2);
    };

    // 3D simplex noise
    module.simplex3 = function(xin, yin, zin) {
        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; // Hairy factor for 2D
        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 = xin - i + t; // The x,y distances from the cell origin, unskewed.
        var y0 = yin - j + t;
        var z0 = zin - k + t;

        // 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;
            } else if (x0 >= z0) {
                i1 = 1;
                j1 = 0;
                k1 = 0;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            } else {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 1;
                j2 = 0;
                k2 = 1;
            }
        } else {
            if (y0 < z0) {
                i1 = 0;
                j1 = 0;
                k1 = 1;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } else if (x0 < z0) {
                i1 = 0;
                j1 = 1;
                k1 = 0;
                i2 = 0;
                j2 = 1;
                k2 = 1;
            } else {
                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.
        var x1 = x0 - i1 + G3; // Offsets for second corner
        var y1 = y0 - j1 + G3;
        var z1 = z0 - k1 + G3;

        var x2 = x0 - i2 + 2 * G3; // Offsets for third corner
        var y2 = y0 - j2 + 2 * G3;
        var z2 = z0 - k2 + 2 * G3;

        var x3 = x0 - 1 + 3 * G3; // Offsets for fourth corner
        var y3 = y0 - 1 + 3 * G3;
        var z3 = z0 - 1 + 3 * G3;

        // Work out the hashed gradient indices of the four simplex corners
        i &= 255;
        j &= 255;
        k &= 255;
        var gi0 = gradP[i + perm[j + perm[k]]];
        var gi1 = gradP[i + i1 + perm[j + j1 + perm[k + k1]]];
        var gi2 = gradP[i + i2 + perm[j + j2 + perm[k + k2]]];
        var gi3 = gradP[i + 1 + perm[j + 1 + perm[k + 1]]];

        // Calculate the contribution from the four corners
        var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
        if (t0 < 0) {
            n0 = 0;
        } else {
            t0 *= t0;
            n0 = t0 * t0 * gi0.dot3(x0, y0, z0); // (x,y) of grad3 used for 2D gradient
        }
        var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
        if (t1 < 0) {
            n1 = 0;
        } else {
            t1 *= t1;
            n1 = t1 * t1 * gi1.dot3(x1, y1, z1);
        }
        var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
        if (t2 < 0) {
            n2 = 0;
        } else {
            t2 *= t2;
            n2 = t2 * t2 * gi2.dot3(x2, y2, z2);
        }
        var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
        if (t3 < 0) {
            n3 = 0;
        } else {
            t3 *= t3;
            n3 = t3 * t3 * gi3.dot3(x3, y3, z3);
        }
        // Add contributions from each corner to get the final noise value.
        // The result is scaled to return values in the interval [-1,1].
        return 32 * (n0 + n1 + n2 + n3);

    };

    // ##### Perlin noise stuff

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

    function lerp(a, b, t) {
        return (1 - t) * a + t * b;
    }

    // 2D Perlin Noise
    module.perlin2 = function(x, y) {
        // Find unit grid cell containing point
        var X = Math.floor(x),
            Y = Math.floor(y);
        // Get relative xy coordinates of point within that cell
        x = x - X;
        y = y - Y;
        // Wrap the integer cells at 255 (smaller integer period can be introduced here)
        X = X & 255;
        Y = Y & 255;

        // Calculate noise contributions from each of the four corners
        var n00 = gradP[X + perm[Y]].dot2(x, y);
        var n01 = gradP[X + perm[Y + 1]].dot2(x, y - 1);
        var n10 = gradP[X + 1 + perm[Y]].dot2(x - 1, y);
        var n11 = gradP[X + 1 + perm[Y + 1]].dot2(x - 1, y - 1);

        // Compute the fade curve value for x
        var u = fade(x);

        // Interpolate the four results
        return lerp(
            lerp(n00, n10, u),
            lerp(n01, n11, u),
            fade(y));
    };

    // 3D Perlin Noise
    module.perlin3 = function(x, y, z) {
        // Find unit grid cell containing point
        var X = Math.floor(x),
            Y = Math.floor(y),
            Z = Math.floor(z);
        // Get relative xyz coordinates of point within that cell
        x = x - X;
        y = y - Y;
        z = z - Z;
        // Wrap the integer cells at 255 (smaller integer period can be introduced here)
        X = X & 255;
        Y = Y & 255;
        Z = Z & 255;

        // Calculate noise contributions from each of the eight corners
        var n000 = gradP[X + perm[Y + perm[Z]]].dot3(x, y, z);
        var n001 = gradP[X + perm[Y + perm[Z + 1]]].dot3(x, y, z - 1);
        var n010 = gradP[X + perm[Y + 1 + perm[Z]]].dot3(x, y - 1, z);
        var n011 = gradP[X + perm[Y + 1 + perm[Z + 1]]].dot3(x, y - 1, z - 1);
        var n100 = gradP[X + 1 + perm[Y + perm[Z]]].dot3(x - 1, y, z);
        var n101 = gradP[X + 1 + perm[Y + perm[Z + 1]]].dot3(x - 1, y, z - 1);
        var n110 = gradP[X + 1 + perm[Y + 1 + perm[Z]]].dot3(x - 1, y - 1, z);
        var n111 = gradP[X + 1 + perm[Y + 1 + perm[Z + 1]]].dot3(x - 1, y - 1, z - 1);

        // Compute the fade curve value for x, y, z
        var u = fade(x);
        var v = fade(y);
        var w = fade(z);

        // Interpolate
        return lerp(
            lerp(
                lerp(n000, n100, u),
                lerp(n001, n101, u), w),
            lerp(
                lerp(n010, n110, u),
                lerp(n011, n111, u), w),
            v);
    };

})(this);