# Source: math/PerlinNoise.js

``````/**
*  @class PerlinNoise
*  @memberof SQR
*
*  @description <p>A speed-improved perlin and simplex noise algorithms for 2D.</p>
*
*	<p>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.</p>
*
*	<p>Version 2012-03-09</p>
*
*	<p>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.</p>
*
*	<p>This code below is copied from <a href='https://github.com/josephg/noisejs/blob/master/perlin.js'>perlin.js</a> and only slightly chnaged to  adapt for SQR API.</p>
*
*/
SQR.PerlinNoise = (function(){

var module = {};

this.x = x; this.y = y; this.z = z;
}

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 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);

// 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;
}
};

module.seed(0);

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

// 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;

/**
*	@method perlin2
*	@memberof SQR.PerlinNoise
*
*	@param {Number} x
*	@param {Number} y
*
*	@returns {Number} the noise value in -1 to 1 range
*/
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;
// 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);
};

/**
*	@method simplex3
*	@memberof SQR.PerlinNoise
*
*	@param {Number} x
*	@param {Number} y
*	@param {Number} z
*
*	@returns {Number} the noise value in -1 to 1 range
*/
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 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

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

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

/**
*	@method perlin2
*	@memberof SQR.PerlinNoise
*
*	@param {Number} x
*	@param {Number} y
*
*	@returns {Number} the noise value in -1 to 1 range
*/
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

// Compute the fade curve value for x

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

/**
*	@method perlin3
*	@memberof SQR.PerlinNoise
*
*	@param {Number} x
*	@param {Number} y
*	@param {Number} z
*
*	@returns {Number} the noise value in -1 to 1 range
*/
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

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

return module;

})();

``````