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Created October 24, 2010 01:36
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// Ported from Stefan Gustavson's java implementation
// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
// Read Stefan's excellent paper for details on how this code works.
//
// Sean McCullough [email protected]
/**
* You can pass in a random number generator object if you like.
* It is assumed to have a random() method.
*/
var ClassicalNoise = function(r) { // Classic Perlin noise in 3D, for comparison
if (r == undefined) 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.p = [];
for (var 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(var i=0; i<512; i++) {
this.perm[i]=this.p[i & 255];
}
};
ClassicalNoise.prototype.dot = function(g, x, y, z) {
return g[0]*x + g[1]*y + g[2]*z;
};
ClassicalNoise.prototype.mix = function(a, b, t) {
return (1.0-t)*a + t*b;
};
ClassicalNoise.prototype.fade = function(t) {
return t*t*t*(t*(t*6.0-15.0)+10.0);
};
// Classic Perlin noise, 3D version
ClassicalNoise.prototype.noise = function(x, y, z) {
// Find unit grid cell containing point
var X = Math.floor(x);
var Y = Math.floor(y);
var 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 a set of eight hashed gradient indices
var gi000 = this.perm[X+this.perm[Y+this.perm[Z]]] % 12;
var gi001 = this.perm[X+this.perm[Y+this.perm[Z+1]]] % 12;
var gi010 = this.perm[X+this.perm[Y+1+this.perm[Z]]] % 12;
var gi011 = this.perm[X+this.perm[Y+1+this.perm[Z+1]]] % 12;
var gi100 = this.perm[X+1+this.perm[Y+this.perm[Z]]] % 12;
var gi101 = this.perm[X+1+this.perm[Y+this.perm[Z+1]]] % 12;
var gi110 = this.perm[X+1+this.perm[Y+1+this.perm[Z]]] % 12;
var gi111 = this.perm[X+1+this.perm[Y+1+this.perm[Z+1]]] % 12;
// The gradients of each corner are now:
// g000 = grad3[gi000];
// g001 = grad3[gi001];
// g010 = grad3[gi010];
// g011 = grad3[gi011];
// g100 = grad3[gi100];
// g101 = grad3[gi101];
// g110 = grad3[gi110];
// g111 = grad3[gi111];
// Calculate noise contributions from each of the eight corners
var n000= this.dot(this.grad3[gi000], x, y, z);
var n100= this.dot(this.grad3[gi100], x-1, y, z);
var n010= this.dot(this.grad3[gi010], x, y-1, z);
var n110= this.dot(this.grad3[gi110], x-1, y-1, z);
var n001= this.dot(this.grad3[gi001], x, y, z-1);
var n101= this.dot(this.grad3[gi101], x-1, y, z-1);
var n011= this.dot(this.grad3[gi011], x, y-1, z-1);
var n111= this.dot(this.grad3[gi111], x-1, y-1, z-1);
// Compute the fade curve value for each of x, y, z
var u = this.fade(x);
var v = this.fade(y);
var w = this.fade(z);
// Interpolate along x the contributions from each of the corners
var nx00 = this.mix(n000, n100, u);
var nx01 = this.mix(n001, n101, u);
var nx10 = this.mix(n010, n110, u);
var nx11 = this.mix(n011, n111, u);
// Interpolate the four results along y
var nxy0 = this.mix(nx00, nx10, v);
var nxy1 = this.mix(nx01, nx11, v);
// Interpolate the two last results along z
var nxyz = this.mix(nxy0, nxy1, w);
return nxyz;
};
// Ported from Stefan Gustavson's java implementation
// http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf
// Read Stefan's excellent paper for details on how this code works.
//
// Sean McCullough [email protected]
/**
* You can pass in a random number generator object if you like.
* It is assumed to have a random() method.
*/
var SimplexNoise = function(r) {
if (r == undefined) 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.p = [];
for (var 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(var 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]];
};
// This is the dot function for 2d
// SimplexNoise.prototype.dot = function(g, x, y) {
// return g[0]*x + g[1]*y;
// };
// This is the dot function for 3d
SimplexNoise.prototype.dot = function(g, x, y, z) {
return g[0]*x + g[1]*y + g[2]*z;
};
private static double dot(int g[], double x, double y, double z) { return g[0]*x + g[1]*y + g[2]*z; }
SimplexNoise.prototype.noise = 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 F2 = 0.5*(Math.sqrt(3.0)-1.0);
var s = (xin+yin)*F2; // Hairy factor for 2D
var i = Math.floor(xin+s);
var j = Math.floor(yin+s);
var G2 = (3.0-Math.sqrt(3.0))/6.0;
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;
var gi0 = this.perm[ii+this.perm[jj]] % 12;
var gi1 = this.perm[ii+i1+this.perm[jj+j1]] % 12;
var gi2 = this.perm[ii+1+this.perm[jj+1]] % 12;
// Calculate the contribution from the three corners
var 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
}
var 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);
}
var 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);
};
// 3D simplex noise
SimplexNoise.prototype.noise3d = 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 F3 = 1.0/3.0;
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 G3 = 1.0/6.0; // Very nice and simple unskew factor, too
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;
var gi0 = this.perm[ii+this.perm[jj+this.perm[kk]]] % 12;
var gi1 = this.perm[ii+i1+this.perm[jj+j1+this.perm[kk+k1]]] % 12;
var gi2 = this.perm[ii+i2+this.perm[jj+j2+this.perm[kk+k2]]] % 12;
var gi3 = this.perm[ii+1+this.perm[jj+1+this.perm[kk+1]]] % 12;
// Calculate the contribution from the four corners
var t0 = 0.6 - x0*x0 - y0*y0 - z0*z0;
if(t0<0) n0 = 0.0;
else {
t0 *= t0;
n0 = t0 * t0 * this.dot(this.grad3[gi0], x0, y0, z0);
}
var t1 = 0.6 - x1*x1 - y1*y1 - z1*z1;
if(t1<0) n1 = 0.0;
else {
t1 *= t1;
n1 = t1 * t1 * this.dot(this.grad3[gi1], x1, y1, z1);
}
var t2 = 0.6 - x2*x2 - y2*y2 - z2*z2;
if(t2<0) n2 = 0.0;
else {
t2 *= t2;
n2 = t2 * t2 * this.dot(this.grad3[gi2], x2, y2, z2);
}
var t3 = 0.6 - x3*x3 - y3*y3 - z3*z3;
if(t3<0) n3 = 0.0;
else {
t3 *= t3;
n3 = t3 * t3 * this.dot(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);
};
#include <math.h>
#include <stdio.h>
static int p[512];
static int permutation[] = { 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
};
/* Function declarations */
double fade(double t);
double lerp(double t, double a, double b);
double grad(int hash, double x, double y, double z);
void init();
double pnoise(double x, double y, double z);
void init()
{
int i;
for(i = 0; i < 256 ; i++)
p[256+i] = p[i] = permutation[i];
}
double pnoise(double x, double y, double z)
{
int X = (int)floor(x) & 255, /* FIND UNIT CUBE THAT */
Y = (int)floor(y) & 255, /* CONTAINS POINT. */
Z = (int)floor(z) & 255;
x -= floor(x); /* FIND RELATIVE X,Y,Z */
y -= floor(y); /* OF POINT IN CUBE. */
z -= floor(z);
double u = fade(x), /* COMPUTE FADE CURVES */
v = fade(y), /* FOR EACH OF X,Y,Z. */
w = fade(z);
int A = p[X]+Y,
AA = p[A]+Z,
AB = p[A+1]+Z, /* HASH COORDINATES OF */
B = p[X+1]+Y,
BA = p[B]+Z,
BB = p[B+1]+Z; /* THE 8 CUBE CORNERS, */
return lerp(w,lerp(v,lerp(u, grad(p[AA ], x, y, z), /* AND ADD */
grad(p[BA ], x-1, y, z)), /* BLENDED */
lerp(u, grad(p[AB ], x, y-1, z), /* RESULTS */
grad(p[BB ], x-1, y-1, z))), /* FROM 8 */
lerp(v, lerp(u, grad(p[AA+1], x, y, z-1 ),/* CORNERS */
grad(p[BA+1], x-1, y, z-1)), /* OF CUBE */
lerp(u, grad(p[AB+1], x, y-1, z-1),
grad(p[BB+1], x-1, y-1, z-1))));
}
double fade(double t){ return t * t * t * (t * (t * 6 - 15) + 10); }
double lerp(double t, double a, double b){ return a + t * (b - a); }
double grad(int hash, double x, double y, double z)
{
int h = hash & 15; /* CONVERT LO 4 BITS OF HASH CODE */
double u = h < 8 ? x : y, /* INTO 12 GRADIENT DIRECTIONS. */
v = h < 4 ? y : h==12||h==14 ? x : z;
return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v);
}
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