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@@ -10,415 +10,435 @@
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* You can pass in a random number generator object if you like.
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* It is assumed to have a random() method.
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*/
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-var SimplexNoise = function ( r ) {
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+class SimplexNoise {
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- if ( r == undefined ) r = Math;
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- this.grad3 = [[ 1, 1, 0 ], [ - 1, 1, 0 ], [ 1, - 1, 0 ], [ - 1, - 1, 0 ],
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- [ 1, 0, 1 ], [ - 1, 0, 1 ], [ 1, 0, - 1 ], [ - 1, 0, - 1 ],
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- [ 0, 1, 1 ], [ 0, - 1, 1 ], [ 0, 1, - 1 ], [ 0, - 1, - 1 ]];
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+ constructor( r = Math ) {
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- this.grad4 = [[ 0, 1, 1, 1 ], [ 0, 1, 1, - 1 ], [ 0, 1, - 1, 1 ], [ 0, 1, - 1, - 1 ],
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- [ 0, - 1, 1, 1 ], [ 0, - 1, 1, - 1 ], [ 0, - 1, - 1, 1 ], [ 0, - 1, - 1, - 1 ],
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- [ 1, 0, 1, 1 ], [ 1, 0, 1, - 1 ], [ 1, 0, - 1, 1 ], [ 1, 0, - 1, - 1 ],
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- [ - 1, 0, 1, 1 ], [ - 1, 0, 1, - 1 ], [ - 1, 0, - 1, 1 ], [ - 1, 0, - 1, - 1 ],
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- [ 1, 1, 0, 1 ], [ 1, 1, 0, - 1 ], [ 1, - 1, 0, 1 ], [ 1, - 1, 0, - 1 ],
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- [ - 1, 1, 0, 1 ], [ - 1, 1, 0, - 1 ], [ - 1, - 1, 0, 1 ], [ - 1, - 1, 0, - 1 ],
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- [ 1, 1, 1, 0 ], [ 1, 1, - 1, 0 ], [ 1, - 1, 1, 0 ], [ 1, - 1, - 1, 0 ],
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- [ - 1, 1, 1, 0 ], [ - 1, 1, - 1, 0 ], [ - 1, - 1, 1, 0 ], [ - 1, - 1, - 1, 0 ]];
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+ this.grad3 = [[ 1, 1, 0 ], [ - 1, 1, 0 ], [ 1, - 1, 0 ], [ - 1, - 1, 0 ],
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+ [ 1, 0, 1 ], [ - 1, 0, 1 ], [ 1, 0, - 1 ], [ - 1, 0, - 1 ],
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+ [ 0, 1, 1 ], [ 0, - 1, 1 ], [ 0, 1, - 1 ], [ 0, - 1, - 1 ]];
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- this.p = [];
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+ this.grad4 = [[ 0, 1, 1, 1 ], [ 0, 1, 1, - 1 ], [ 0, 1, - 1, 1 ], [ 0, 1, - 1, - 1 ],
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+ [ 0, - 1, 1, 1 ], [ 0, - 1, 1, - 1 ], [ 0, - 1, - 1, 1 ], [ 0, - 1, - 1, - 1 ],
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+ [ 1, 0, 1, 1 ], [ 1, 0, 1, - 1 ], [ 1, 0, - 1, 1 ], [ 1, 0, - 1, - 1 ],
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+ [ - 1, 0, 1, 1 ], [ - 1, 0, 1, - 1 ], [ - 1, 0, - 1, 1 ], [ - 1, 0, - 1, - 1 ],
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+ [ 1, 1, 0, 1 ], [ 1, 1, 0, - 1 ], [ 1, - 1, 0, 1 ], [ 1, - 1, 0, - 1 ],
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+ [ - 1, 1, 0, 1 ], [ - 1, 1, 0, - 1 ], [ - 1, - 1, 0, 1 ], [ - 1, - 1, 0, - 1 ],
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+ [ 1, 1, 1, 0 ], [ 1, 1, - 1, 0 ], [ 1, - 1, 1, 0 ], [ 1, - 1, - 1, 0 ],
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+ [ - 1, 1, 1, 0 ], [ - 1, 1, - 1, 0 ], [ - 1, - 1, 1, 0 ], [ - 1, - 1, - 1, 0 ]];
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- for ( var i = 0; i < 256; i ++ ) {
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+ this.p = [];
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- this.p[ i ] = Math.floor( r.random() * 256 );
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+ for ( let i = 0; i < 256; i ++ ) {
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- }
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-
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- // To remove the need for index wrapping, double the permutation table length
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- this.perm = [];
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-
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- for ( var i = 0; i < 512; i ++ ) {
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+ this.p[ i ] = Math.floor( r.random() * 256 );
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- this.perm[ i ] = this.p[ i & 255 ];
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+ }
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- }
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-
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- // A lookup table to traverse the simplex around a given point in 4D.
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- // Details can be found where this table is used, in the 4D noise method.
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- this.simplex = [
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- [ 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 ],
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- [ 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 ],
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- [ 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 ],
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- [ 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 ],
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- [ 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 ],
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- [ 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 ],
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- [ 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 ],
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- [ 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 ]];
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+ // To remove the need for index wrapping, double the permutation table length
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+ this.perm = [];
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-};
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+ for ( let i = 0; i < 512; i ++ ) {
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-SimplexNoise.prototype.dot = function ( g, x, y ) {
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+ this.perm[ i ] = this.p[ i & 255 ];
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- return g[ 0 ] * x + g[ 1 ] * y;
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+ }
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-};
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+ // A lookup table to traverse the simplex around a given point in 4D.
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+ // Details can be found where this table is used, in the 4D noise method.
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+ this.simplex = [
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+ [ 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 ],
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+ [ 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 ],
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+ [ 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 ],
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+ [ 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 ],
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+ [ 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 ],
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+ [ 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 ],
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+ [ 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 ],
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+ [ 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 ]];
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-SimplexNoise.prototype.dot3 = function ( g, x, y, z ) {
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+ }
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- return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z;
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+ dot( g, x, y ) {
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-};
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+ return g[ 0 ] * x + g[ 1 ] * y;
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-SimplexNoise.prototype.dot4 = function ( g, x, y, z, w ) {
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+ }
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- return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z + g[ 3 ] * w;
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+ dot3( g, x, y, z ) {
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-};
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+ return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z;
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-SimplexNoise.prototype.noise = function ( xin, yin ) {
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+ }
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- var n0, n1, n2; // Noise contributions from the three corners
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- // Skew the input space to determine which simplex cell we're in
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- var F2 = 0.5 * ( Math.sqrt( 3.0 ) - 1.0 );
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- var s = ( xin + yin ) * F2; // Hairy factor for 2D
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- var i = Math.floor( xin + s );
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- var j = Math.floor( yin + s );
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- var G2 = ( 3.0 - Math.sqrt( 3.0 ) ) / 6.0;
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- var t = ( i + j ) * G2;
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- var X0 = i - t; // Unskew the cell origin back to (x,y) space
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- var Y0 = j - t;
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- var x0 = xin - X0; // The x,y distances from the cell origin
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- var y0 = yin - Y0;
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- // For the 2D case, the simplex shape is an equilateral triangle.
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- // Determine which simplex we are in.
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- var i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
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- if ( x0 > y0 ) {
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+ dot4( g, x, y, z, w ) {
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- i1 = 1; j1 = 0;
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+ return g[ 0 ] * x + g[ 1 ] * y + g[ 2 ] * z + g[ 3 ] * w;
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- // lower triangle, XY order: (0,0)->(1,0)->(1,1)
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+ }
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- } else {
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+ noise( xin, yin ) {
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- i1 = 0; j1 = 1;
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+ let n0; // Noise contributions from the three corners
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+ let n1;
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+ let n2;
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+ // Skew the input space to determine which simplex cell we're in
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+ const F2 = 0.5 * ( Math.sqrt( 3.0 ) - 1.0 );
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+ const s = ( xin + yin ) * F2; // Hairy factor for 2D
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+ const i = Math.floor( xin + s );
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+ const j = Math.floor( yin + s );
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+ const G2 = ( 3.0 - Math.sqrt( 3.0 ) ) / 6.0;
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+ const t = ( i + j ) * G2;
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+ const X0 = i - t; // Unskew the cell origin back to (x,y) space
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+ const Y0 = j - t;
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+ const x0 = xin - X0; // The x,y distances from the cell origin
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+ const y0 = yin - Y0;
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- } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
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+ // For the 2D case, the simplex shape is an equilateral triangle.
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+ // Determine which simplex we are in.
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+ let i1; // Offsets for second (middle) corner of simplex in (i,j) coords
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- // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
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- // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
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- // c = (3-sqrt(3))/6
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- var x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
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- var y1 = y0 - j1 + G2;
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- var x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
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- var y2 = y0 - 1.0 + 2.0 * G2;
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- // Work out the hashed gradient indices of the three simplex corners
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- var ii = i & 255;
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- var jj = j & 255;
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- var gi0 = this.perm[ ii + this.perm[ jj ] ] % 12;
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- var gi1 = this.perm[ ii + i1 + this.perm[ jj + j1 ] ] % 12;
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- var gi2 = this.perm[ ii + 1 + this.perm[ jj + 1 ] ] % 12;
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- // Calculate the contribution from the three corners
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- var t0 = 0.5 - x0 * x0 - y0 * y0;
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- if ( t0 < 0 ) n0 = 0.0;
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- else {
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+ let j1;
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+ if ( x0 > y0 ) {
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- t0 *= t0;
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- n0 = t0 * t0 * this.dot( this.grad3[ gi0 ], x0, y0 ); // (x,y) of grad3 used for 2D gradient
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+ i1 = 1; j1 = 0;
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- }
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+ // lower triangle, XY order: (0,0)->(1,0)->(1,1)
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- var t1 = 0.5 - x1 * x1 - y1 * y1;
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- if ( t1 < 0 ) n1 = 0.0;
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- else {
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+ } else {
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- t1 *= t1;
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- n1 = t1 * t1 * this.dot( this.grad3[ gi1 ], x1, y1 );
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+ i1 = 0; j1 = 1;
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- }
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+ } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
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- var t2 = 0.5 - x2 * x2 - y2 * y2;
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- if ( t2 < 0 ) n2 = 0.0;
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- else {
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+ // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
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+ // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
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+ // c = (3-sqrt(3))/6
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+ const x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
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+ const y1 = y0 - j1 + G2;
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+ const x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords
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+ const y2 = y0 - 1.0 + 2.0 * G2;
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+ // Work out the hashed gradient indices of the three simplex corners
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+ const ii = i & 255;
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+ const jj = j & 255;
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+ const gi0 = this.perm[ ii + this.perm[ jj ] ] % 12;
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+ const gi1 = this.perm[ ii + i1 + this.perm[ jj + j1 ] ] % 12;
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+ const gi2 = this.perm[ ii + 1 + this.perm[ jj + 1 ] ] % 12;
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+ // Calculate the contribution from the three corners
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+ let t0 = 0.5 - x0 * x0 - y0 * y0;
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+ if ( t0 < 0 ) n0 = 0.0;
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+ else {
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- t2 *= t2;
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- n2 = t2 * t2 * this.dot( this.grad3[ gi2 ], x2, y2 );
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+ t0 *= t0;
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+ n0 = t0 * t0 * this.dot( this.grad3[ gi0 ], x0, y0 ); // (x,y) of grad3 used for 2D gradient
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- }
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+ }
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- // Add contributions from each corner to get the final noise value.
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- // The result is scaled to return values in the interval [-1,1].
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- return 70.0 * ( n0 + n1 + n2 );
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+ let t1 = 0.5 - x1 * x1 - y1 * y1;
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+ if ( t1 < 0 ) n1 = 0.0;
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+ else {
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-};
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+ t1 *= t1;
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+ n1 = t1 * t1 * this.dot( this.grad3[ gi1 ], x1, y1 );
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-// 3D simplex noise
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-SimplexNoise.prototype.noise3d = function ( xin, yin, zin ) {
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+ }
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- var n0, n1, n2, n3; // Noise contributions from the four corners
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- // Skew the input space to determine which simplex cell we're in
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- var F3 = 1.0 / 3.0;
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- var s = ( xin + yin + zin ) * F3; // Very nice and simple skew factor for 3D
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- var i = Math.floor( xin + s );
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- var j = Math.floor( yin + s );
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- var k = Math.floor( zin + s );
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- var G3 = 1.0 / 6.0; // Very nice and simple unskew factor, too
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- var t = ( i + j + k ) * G3;
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- var X0 = i - t; // Unskew the cell origin back to (x,y,z) space
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- var Y0 = j - t;
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- var Z0 = k - t;
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- var x0 = xin - X0; // The x,y,z distances from the cell origin
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- var y0 = yin - Y0;
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- var z0 = zin - Z0;
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- // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
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- // Determine which simplex we are in.
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- var i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
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- var i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
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- if ( x0 >= y0 ) {
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+ let t2 = 0.5 - x2 * x2 - y2 * y2;
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+ if ( t2 < 0 ) n2 = 0.0;
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+ else {
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- if ( y0 >= z0 ) {
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+ t2 *= t2;
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+ n2 = t2 * t2 * this.dot( this.grad3[ gi2 ], x2, y2 );
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- i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
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+ }
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- // X Y Z order
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+ // Add contributions from each corner to get the final noise value.
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+ // The result is scaled to return values in the interval [-1,1].
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+ return 70.0 * ( n0 + n1 + n2 );
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- } else if ( x0 >= z0 ) {
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+ }
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- i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1;
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+ // 3D simplex noise
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+ noise3d( xin, yin, zin ) {
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- // X Z Y order
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+ let n0; // Noise contributions from the four corners
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+ let n1;
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+ 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;
|
|
|
|
|
|
- } else {
|
|
|
+ // 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
|
|
|
|
|
|
- i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1;
|
|
|
+ let j1;
|
|
|
+ let k1;
|
|
|
+ let i2; // Offsets for third corner of simplex in (i,j,k) coords
|
|
|
+ let j2;
|
|
|
+ let k2;
|
|
|
+ if ( x0 >= y0 ) {
|
|
|
|
|
|
- } // Z X Y order
|
|
|
+ if ( y0 >= z0 ) {
|
|
|
|
|
|
- } else { // x0<y0
|
|
|
+ i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
|
|
|
|
|
|
- if ( y0 < z0 ) {
|
|
|
+ // X Y Z order
|
|
|
|
|
|
- i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1;
|
|
|
+ } else if ( x0 >= z0 ) {
|
|
|
|
|
|
- // Z Y X order
|
|
|
+ i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1;
|
|
|
|
|
|
- } else if ( x0 < z0 ) {
|
|
|
+ // X Z Y order
|
|
|
|
|
|
- i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1;
|
|
|
+ } else {
|
|
|
|
|
|
- // Y Z X order
|
|
|
+ i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1;
|
|
|
|
|
|
- } else {
|
|
|
+ } // Z X Y order
|
|
|
|
|
|
- i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
|
|
|
+ } else { // x0<y0
|
|
|
|
|
|
- } // Y X Z order
|
|
|
+ if ( y0 < z0 ) {
|
|
|
|
|
|
- }
|
|
|
+ i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1;
|
|
|
|
|
|
- // 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.dot3( this.grad3[ gi0 ], x0, y0, z0 );
|
|
|
+ // Z Y X order
|
|
|
|
|
|
- }
|
|
|
+ } else if ( x0 < z0 ) {
|
|
|
|
|
|
- var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
|
|
|
- if ( t1 < 0 ) n1 = 0.0;
|
|
|
- else {
|
|
|
+ i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1;
|
|
|
|
|
|
- t1 *= t1;
|
|
|
- n1 = t1 * t1 * this.dot3( this.grad3[ gi1 ], x1, y1, z1 );
|
|
|
+ // Y Z X order
|
|
|
|
|
|
- }
|
|
|
+ } else {
|
|
|
|
|
|
- var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
|
|
|
- if ( t2 < 0 ) n2 = 0.0;
|
|
|
- else {
|
|
|
+ i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0;
|
|
|
|
|
|
- t2 *= t2;
|
|
|
- n2 = t2 * t2 * this.dot3( this.grad3[ gi2 ], x2, y2, z2 );
|
|
|
+ } // Y X Z order
|
|
|
|
|
|
- }
|
|
|
+ }
|
|
|
|
|
|
- var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
|
|
|
- if ( t3 < 0 ) n3 = 0.0;
|
|
|
- else {
|
|
|
+ // 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 {
|
|
|
|
|
|
- t3 *= t3;
|
|
|
- n3 = t3 * t3 * this.dot3( this.grad3[ gi3 ], x3, y3, z3 );
|
|
|
+ t0 *= t0;
|
|
|
+ n0 = t0 * t0 * this.dot3( this.grad3[ gi0 ], x0, y0, z0 );
|
|
|
|
|
|
- }
|
|
|
+ }
|
|
|
|
|
|
- // 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
|
|
|
-SimplexNoise.prototype.noise4d = function ( x, y, z, w ) {
|
|
|
-
|
|
|
- // For faster and easier lookups
|
|
|
- var grad4 = this.grad4;
|
|
|
- var simplex = this.simplex;
|
|
|
- var perm = this.perm;
|
|
|
-
|
|
|
- // The skewing and unskewing factors are hairy again for the 4D case
|
|
|
- var F4 = ( Math.sqrt( 5.0 ) - 1.0 ) / 4.0;
|
|
|
- var G4 = ( 5.0 - Math.sqrt( 5.0 ) ) / 20.0;
|
|
|
- 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.
|
|
|
- // 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.
|
|
|
- var c1 = ( x0 > y0 ) ? 32 : 0;
|
|
|
- var c2 = ( x0 > z0 ) ? 16 : 0;
|
|
|
- var c3 = ( y0 > z0 ) ? 8 : 0;
|
|
|
- var c4 = ( x0 > w0 ) ? 4 : 0;
|
|
|
- var c5 = ( y0 > w0 ) ? 2 : 0;
|
|
|
- var c6 = ( z0 > w0 ) ? 1 : 0;
|
|
|
- var c = c1 + c2 + c3 + c4 + c5 + c6;
|
|
|
- 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.
|
|
|
- // The number 3 in the "simplex" array is at the position of the largest coordinate.
|
|
|
- i1 = simplex[ c ][ 0 ] >= 3 ? 1 : 0;
|
|
|
- j1 = simplex[ c ][ 1 ] >= 3 ? 1 : 0;
|
|
|
- k1 = simplex[ c ][ 2 ] >= 3 ? 1 : 0;
|
|
|
- l1 = simplex[ c ][ 3 ] >= 3 ? 1 : 0;
|
|
|
- // The number 2 in the "simplex" array is at the second largest coordinate.
|
|
|
- i2 = simplex[ c ][ 0 ] >= 2 ? 1 : 0;
|
|
|
- j2 = simplex[ c ][ 1 ] >= 2 ? 1 : 0; k2 = simplex[ c ][ 2 ] >= 2 ? 1 : 0;
|
|
|
- l2 = simplex[ c ][ 3 ] >= 2 ? 1 : 0;
|
|
|
- // The number 1 in the "simplex" array is at the second smallest coordinate.
|
|
|
- i3 = simplex[ c ][ 0 ] >= 1 ? 1 : 0;
|
|
|
- j3 = simplex[ c ][ 1 ] >= 1 ? 1 : 0;
|
|
|
- k3 = simplex[ c ][ 2 ] >= 1 ? 1 : 0;
|
|
|
- l3 = simplex[ c ][ 3 ] >= 1 ? 1 : 0;
|
|
|
- // The fifth corner has all coordinate offsets = 1, so no need to look that up.
|
|
|
- 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;
|
|
|
- var gi0 = perm[ ii + perm[ jj + perm[ kk + perm[ ll ] ] ] ] % 32;
|
|
|
- var gi1 = perm[ ii + i1 + perm[ jj + j1 + perm[ kk + k1 + perm[ ll + l1 ] ] ] ] % 32;
|
|
|
- var gi2 = perm[ ii + i2 + perm[ jj + j2 + perm[ kk + k2 + perm[ ll + l2 ] ] ] ] % 32;
|
|
|
- var gi3 = perm[ ii + i3 + perm[ jj + j3 + perm[ kk + k3 + perm[ ll + l3 ] ] ] ] % 32;
|
|
|
- var gi4 = perm[ ii + 1 + perm[ jj + 1 + perm[ kk + 1 + perm[ ll + 1 ] ] ] ] % 32;
|
|
|
- // 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 {
|
|
|
-
|
|
|
- t0 *= t0;
|
|
|
- n0 = t0 * t0 * this.dot4( grad4[ gi0 ], x0, y0, z0, w0 );
|
|
|
+ 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 );
|
|
|
|
|
|
- var 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;
|
|
|
+ if ( t2 < 0 ) n2 = 0.0;
|
|
|
+ else {
|
|
|
|
|
|
- }
|
|
|
+ t2 *= t2;
|
|
|
+ n2 = t2 * t2 * this.dot3( this.grad3[ gi2 ], x2, y2, z2 );
|
|
|
|
|
|
- var 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;
|
|
|
+ if ( t3 < 0 ) n3 = 0.0;
|
|
|
+ else {
|
|
|
|
|
|
- }
|
|
|
+ t3 *= t3;
|
|
|
+ n3 = t3 * t3 * this.dot3( this.grad3[ gi3 ], x3, y3, z3 );
|
|
|
|
|
|
- var 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 );
|
|
|
+ // 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 );
|
|
|
|
|
|
}
|
|
|
|
|
|
- var t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
|
|
|
- if ( t4 < 0 ) n4 = 0.0;
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- else {
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-
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- t4 *= t4;
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- n4 = t4 * t4 * this.dot4( grad4[ gi4 ], x4, y4, z4, w4 );
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+ // 4D simplex noise
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+ noise4d( x, y, z, w ) {
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+
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+ // For faster and easier lookups
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+ const grad4 = this.grad4;
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+ const simplex = this.simplex;
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+ const perm = this.perm;
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+
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+ // The skewing and unskewing factors are hairy again for the 4D case
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+ const F4 = ( Math.sqrt( 5.0 ) - 1.0 ) / 4.0;
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+ const G4 = ( 5.0 - Math.sqrt( 5.0 ) ) / 20.0;
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+ let n0; // Noise contributions from the five corners
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+ let n1;
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+ let n2;
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+ let n3;
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+ let n4;
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+ // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
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+ const s = ( x + y + z + w ) * F4; // Factor for 4D skewing
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+ const i = Math.floor( x + s );
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+ const j = Math.floor( y + s );
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+ const k = Math.floor( z + s );
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+ const l = Math.floor( w + s );
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+ const t = ( i + j + k + l ) * G4; // Factor for 4D unskewing
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+ const X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
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+ const Y0 = j - t;
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+ const Z0 = k - t;
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+ const W0 = l - t;
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+ const x0 = x - X0; // The x,y,z,w distances from the cell origin
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+ const y0 = y - Y0;
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+ const z0 = z - Z0;
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+ const w0 = w - W0;
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+
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+ // For the 4D case, the simplex is a 4D shape I won't even try to describe.
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+ // To find out which of the 24 possible simplices we're in, we need to
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+ // determine the magnitude ordering of x0, y0, z0 and w0.
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+ // The method below is a good way of finding the ordering of x,y,z,w and
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+ // then find the correct traversal order for the simplex we’re in.
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+ // First, six pair-wise comparisons are performed between each possible pair
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+ // of the four coordinates, and the results are used to add up binary bits
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+ // for an integer index.
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+ const c1 = ( x0 > y0 ) ? 32 : 0;
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+ const c2 = ( x0 > z0 ) ? 16 : 0;
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+ const c3 = ( y0 > z0 ) ? 8 : 0;
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+ const c4 = ( x0 > w0 ) ? 4 : 0;
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+ const c5 = ( y0 > w0 ) ? 2 : 0;
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+ const c6 = ( z0 > w0 ) ? 1 : 0;
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+ const c = c1 + c2 + c3 + c4 + c5 + c6;
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+
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+ // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
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+ // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
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+ // impossible. Only the 24 indices which have non-zero entries make any sense.
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+ // We use a thresholding to set the coordinates in turn from the largest magnitude.
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+ // The number 3 in the "simplex" array is at the position of the largest coordinate.
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+ const i1 = simplex[ c ][ 0 ] >= 3 ? 1 : 0;
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+ const j1 = simplex[ c ][ 1 ] >= 3 ? 1 : 0;
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+ const k1 = simplex[ c ][ 2 ] >= 3 ? 1 : 0;
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+ const l1 = simplex[ c ][ 3 ] >= 3 ? 1 : 0;
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+ // The number 2 in the "simplex" array is at the second largest coordinate.
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+ const i2 = simplex[ c ][ 0 ] >= 2 ? 1 : 0;
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+ const j2 = simplex[ c ][ 1 ] >= 2 ? 1 : 0;
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+ const k2 = simplex[ c ][ 2 ] >= 2 ? 1 : 0;
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+ const l2 = simplex[ c ][ 3 ] >= 2 ? 1 : 0;
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+ // The number 1 in the "simplex" array is at the second smallest coordinate.
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+ const i3 = simplex[ c ][ 0 ] >= 1 ? 1 : 0;
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+ const j3 = simplex[ c ][ 1 ] >= 1 ? 1 : 0;
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+ const k3 = simplex[ c ][ 2 ] >= 1 ? 1 : 0;
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+ const l3 = simplex[ c ][ 3 ] >= 1 ? 1 : 0;
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+ // The fifth corner has all coordinate offsets = 1, so no need to look that up.
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+ const x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
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+ const y1 = y0 - j1 + G4;
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+ const z1 = z0 - k1 + G4;
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+ const w1 = w0 - l1 + G4;
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+ const x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords
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+ const y2 = y0 - j2 + 2.0 * G4;
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+ const z2 = z0 - k2 + 2.0 * G4;
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+ const w2 = w0 - l2 + 2.0 * G4;
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+ const x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords
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+ const y3 = y0 - j3 + 3.0 * G4;
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+ const z3 = z0 - k3 + 3.0 * G4;
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+ const w3 = w0 - l3 + 3.0 * G4;
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+ const x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
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+ const y4 = y0 - 1.0 + 4.0 * G4;
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+ const z4 = z0 - 1.0 + 4.0 * G4;
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+ const w4 = w0 - 1.0 + 4.0 * G4;
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+ // Work out the hashed gradient indices of the five simplex corners
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+ const ii = i & 255;
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+ const jj = j & 255;
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+ const kk = k & 255;
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+ const ll = l & 255;
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+ const gi0 = perm[ ii + perm[ jj + perm[ kk + perm[ ll ] ] ] ] % 32;
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+ const gi1 = perm[ ii + i1 + perm[ jj + j1 + perm[ kk + k1 + perm[ ll + l1 ] ] ] ] % 32;
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+ const gi2 = perm[ ii + i2 + perm[ jj + j2 + perm[ kk + k2 + perm[ ll + l2 ] ] ] ] % 32;
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+ const gi3 = perm[ ii + i3 + perm[ jj + j3 + perm[ kk + k3 + perm[ ll + l3 ] ] ] ] % 32;
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+ const gi4 = perm[ ii + 1 + perm[ jj + 1 + perm[ kk + 1 + perm[ ll + 1 ] ] ] ] % 32;
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+ // Calculate the contribution from the five corners
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+ let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
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+ if ( t0 < 0 ) n0 = 0.0;
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+ else {
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+
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+ t0 *= t0;
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+ n0 = t0 * t0 * this.dot4( grad4[ gi0 ], x0, y0, z0, w0 );
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+
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+ }
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+
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+ let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
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+ if ( t1 < 0 ) n1 = 0.0;
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+ else {
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+
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+ t1 *= t1;
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+ n1 = t1 * t1 * this.dot4( grad4[ gi1 ], x1, y1, z1, w1 );
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+
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+ }
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+
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+ let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
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+ if ( t2 < 0 ) n2 = 0.0;
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+ else {
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+
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+ t2 *= t2;
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+ n2 = t2 * t2 * this.dot4( grad4[ gi2 ], x2, y2, z2, w2 );
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+
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+ }
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+
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+ let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
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+ if ( t3 < 0 ) n3 = 0.0;
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+ else {
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+
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+ t3 *= t3;
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+ n3 = t3 * t3 * this.dot4( grad4[ gi3 ], x3, y3, z3, w3 );
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+
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+ }
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+
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+ let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
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+ if ( t4 < 0 ) n4 = 0.0;
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+ else {
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+
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+ t4 *= t4;
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+ n4 = t4 * t4 * this.dot4( grad4[ gi4 ], x4, y4, z4, w4 );
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+
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+ }
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+
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+ // Sum up and scale the result to cover the range [-1,1]
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+ return 27.0 * ( n0 + n1 + n2 + n3 + n4 );
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}
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- // Sum up and scale the result to cover the range [-1,1]
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- return 27.0 * ( n0 + n1 + n2 + n3 + n4 );
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-
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-};
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+}
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export { SimplexNoise };
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Michael Herzog