500 lines
18 KiB
TypeScript
500 lines
18 KiB
TypeScript
/*
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* A fast javascript implementation of simplex noise by Jonas Wagner
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Based on a speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.
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Which is based on example code by Stefan Gustavson (stegu@itn.liu.se).
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With Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
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Better rank ordering method by Stefan Gustavson in 2012.
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Copyright (c) 2024 Jonas Wagner
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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// these __PURE__ comments help uglifyjs with dead code removal
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//
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const SQRT3 = /*#__PURE__*/ Math.sqrt(3.0);
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const SQRT5 = /*#__PURE__*/ Math.sqrt(5.0);
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const F2 = 0.5 * (SQRT3 - 1.0);
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const G2 = (3.0 - SQRT3) / 6.0;
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const F3 = 1.0 / 3.0;
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const G3 = 1.0 / 6.0;
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const F4 = (SQRT5 - 1.0) / 4.0;
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const G4 = (5.0 - SQRT5) / 20.0;
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// I'm really not sure why this | 0 (basically a coercion to int)
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// is making this faster but I get ~5 million ops/sec more on the
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// benchmarks across the board or a ~10% speedup.
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const fastFloor = (x: number) => Math.floor(x) | 0;
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const grad2 = /*#__PURE__*/ new Float64Array([1, 1,
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-1, 1,
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1, -1,
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-1, -1,
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1, 0,
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-1, 0,
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1, 0,
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-1, 0,
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0, 1,
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0, -1,
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0, 1,
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0, -1]);
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// double seems to be faster than single or int's
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// probably because most operations are in double precision
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const grad3 = /*#__PURE__*/ new Float64Array([1, 1, 0,
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-1, 1, 0,
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1, -1, 0,
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-1, -1, 0,
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1, 0, 1,
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-1, 0, 1,
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1, 0, -1,
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-1, 0, -1,
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0, 1, 1,
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0, -1, 1,
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0, 1, -1,
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0, -1, -1]);
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// double is a bit quicker here as well
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const grad4 = /*#__PURE__*/ new Float64Array([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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/**
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* A random() function, must return a number in the interval [0,1), just like Math.random().
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*/
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export type RandomFn = () => number;
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/**
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* Samples the noise field in two dimensions
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*
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* Coordinates should be finite, bigger than -2^31 and smaller than 2^31.
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* @param x
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* @param y
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* @returns a number in the interval [-1, 1]
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*/
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export type NoiseFunction2D = (x: number, y: number) => number;
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/**
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* Creates a 2D noise function
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* @param random the random function that will be used to build the permutation table
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* @returns {NoiseFunction2D}
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*/
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export function createNoise2D(random: RandomFn = Math.random): NoiseFunction2D {
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const perm = buildPermutationTable(random);
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// precalculating this yields a little ~3% performance improvement.
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const permGrad2x = new Float64Array(perm).map(v => grad2[(v % 12) * 2]);
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const permGrad2y = new Float64Array(perm).map(v => grad2[(v % 12) * 2 + 1]);
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return function noise2D(x: number, y: number): number {
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// if(!isFinite(x) || !isFinite(y)) return 0;
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let n0 = 0; // Noise contributions from the three corners
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let n1 = 0;
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let n2 = 0;
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// Skew the input space to determine which simplex cell we're in
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const s = (x + y) * F2; // Hairy factor for 2D
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const i = fastFloor(x + s);
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const j = fastFloor(y + s);
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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 = x - X0; // The x,y distances from the cell origin
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const y0 = y - 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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let i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
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if (x0 > y0) {
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i1 = 1;
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j1 = 0;
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} // lower triangle, XY order: (0,0)->(1,0)->(1,1)
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else {
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i1 = 0;
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j1 = 1;
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} // upper triangle, YX order: (0,0)->(0,1)->(1,1)
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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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// 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) {
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const gi0 = ii + perm[jj];
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const g0x = permGrad2x[gi0];
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const g0y = permGrad2y[gi0];
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t0 *= t0;
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// n0 = t0 * t0 * (grad2[gi0] * x0 + grad2[gi0 + 1] * y0); // (x,y) of grad3 used for 2D gradient
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n0 = t0 * t0 * (g0x * x0 + g0y * y0);
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}
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let t1 = 0.5 - x1 * x1 - y1 * y1;
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if (t1 >= 0) {
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const gi1 = ii + i1 + perm[jj + j1];
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const g1x = permGrad2x[gi1];
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const g1y = permGrad2y[gi1];
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t1 *= t1;
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// n1 = t1 * t1 * (grad2[gi1] * x1 + grad2[gi1 + 1] * y1);
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n1 = t1 * t1 * (g1x * x1 + g1y * y1);
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}
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let t2 = 0.5 - x2 * x2 - y2 * y2;
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if (t2 >= 0) {
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const gi2 = ii + 1 + perm[jj + 1];
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const g2x = permGrad2x[gi2];
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const g2y = permGrad2y[gi2];
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t2 *= t2;
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// n2 = t2 * t2 * (grad2[gi2] * x2 + grad2[gi2 + 1] * y2);
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n2 = t2 * t2 * (g2x * x2 + g2y * y2);
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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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};
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}
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/**
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* Samples the noise field in three dimensions
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*
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* Coordinates should be finite, bigger than -2^31 and smaller than 2^31.
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* @param x
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* @param y
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* @param z
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* @returns a number in the interval [-1, 1]
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*/
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export type NoiseFunction3D = (x: number, y: number, z: number) => number;
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/**
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* Creates a 3D noise function
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* @param random the random function that will be used to build the permutation table
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* @returns {NoiseFunction3D}
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*/
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export function createNoise3D(random: RandomFn = Math.random): NoiseFunction3D {
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const perm = buildPermutationTable(random);
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// precalculating these seems to yield a speedup of over 15%
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const permGrad3x = new Float64Array(perm).map(v => grad3[(v % 12) * 3]);
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const permGrad3y = new Float64Array(perm).map(v => grad3[(v % 12) * 3 + 1]);
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const permGrad3z = new Float64Array(perm).map(v => grad3[(v % 12) * 3 + 2]);
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return function noise3D(x: number, y: number, z: number): number {
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let 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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const s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
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const i = fastFloor(x + s);
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const j = fastFloor(y + s);
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const k = fastFloor(z + s);
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const t = (i + j + k) * G3;
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const X0 = i - t; // Unskew the cell origin back to (x,y,z) space
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const Y0 = j - t;
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const Z0 = k - t;
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const x0 = x - X0; // The x,y,z 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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// 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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let i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
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let 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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if (y0 >= z0) {
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i1 = 1;
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j1 = 0;
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k1 = 0;
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i2 = 1;
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j2 = 1;
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k2 = 0;
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} // X Y Z order
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else if (x0 >= z0) {
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i1 = 1;
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j1 = 0;
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k1 = 0;
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i2 = 1;
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j2 = 0;
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k2 = 1;
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} // X Z Y order
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else {
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i1 = 0;
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j1 = 0;
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k1 = 1;
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i2 = 1;
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j2 = 0;
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k2 = 1;
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} // Z X Y order
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}
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else { // x0<y0
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if (y0 < z0) {
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i1 = 0;
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j1 = 0;
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k1 = 1;
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i2 = 0;
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j2 = 1;
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k2 = 1;
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} // Z Y X order
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else if (x0 < z0) {
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i1 = 0;
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j1 = 1;
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k1 = 0;
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i2 = 0;
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j2 = 1;
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k2 = 1;
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} // Y Z X order
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else {
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i1 = 0;
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j1 = 1;
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k1 = 0;
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i2 = 1;
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j2 = 1;
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k2 = 0;
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} // Y X Z order
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}
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// A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
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// a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
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// a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
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// c = 1/6.
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const x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
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const y1 = y0 - j1 + G3;
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const z1 = z0 - k1 + G3;
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const x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
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const y2 = y0 - j2 + 2.0 * G3;
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const z2 = z0 - k2 + 2.0 * G3;
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const x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
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const y3 = y0 - 1.0 + 3.0 * G3;
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const z3 = z0 - 1.0 + 3.0 * G3;
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// Work out the hashed gradient indices of the four 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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// Calculate the contribution from the four corners
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let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
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if (t0 < 0) n0 = 0.0;
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else {
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const gi0 = ii + perm[jj + perm[kk]];
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t0 *= t0;
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n0 = t0 * t0 * (permGrad3x[gi0] * x0 + permGrad3y[gi0] * y0 + permGrad3z[gi0] * z0);
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}
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let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
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if (t1 < 0) n1 = 0.0;
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else {
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const gi1 = ii + i1 + perm[jj + j1 + perm[kk + k1]];
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t1 *= t1;
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n1 = t1 * t1 * (permGrad3x[gi1] * x1 + permGrad3y[gi1] * y1 + permGrad3z[gi1] * z1);
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}
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let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
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if (t2 < 0) n2 = 0.0;
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else {
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const gi2 = ii + i2 + perm[jj + j2 + perm[kk + k2]];
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t2 *= t2;
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n2 = t2 * t2 * (permGrad3x[gi2] * x2 + permGrad3y[gi2] * y2 + permGrad3z[gi2] * z2);
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}
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let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
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if (t3 < 0) n3 = 0.0;
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else {
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const gi3 = ii + 1 + perm[jj + 1 + perm[kk + 1]];
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t3 *= t3;
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n3 = t3 * t3 * (permGrad3x[gi3] * x3 + permGrad3y[gi3] * y3 + permGrad3z[gi3] * z3);
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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 stay just inside [-1,1]
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return 32.0 * (n0 + n1 + n2 + n3);
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};
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}
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/**
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* Samples the noise field in four dimensions
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*
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* Coordinates should be finite, bigger than -2^31 and smaller than 2^31.
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* @param x
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* @param y
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* @param z
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* @param w
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* @returns a number in the interval [-1, 1]
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*/
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export type NoiseFunction4D = (x: number, y: number, z: number, w: number) => number;
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/**
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* Creates a 4D noise function
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* @param random the random function that will be used to build the permutation table
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* @returns {NoiseFunction4D}
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*/
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export function createNoise4D(random: RandomFn = Math.random): NoiseFunction4D {
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const perm = buildPermutationTable(random);
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// precalculating these leads to a ~10% speedup
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const permGrad4x = new Float64Array(perm).map(v => grad4[(v % 32) * 4]);
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const permGrad4y = new Float64Array(perm).map(v => grad4[(v % 32) * 4 + 1]);
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const permGrad4z = new Float64Array(perm).map(v => grad4[(v % 32) * 4 + 2]);
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const permGrad4w = new Float64Array(perm).map(v => grad4[(v % 32) * 4 + 3]);
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return function noise4D(x: number, y: number, z: number, w: number): number {
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let n0, n1, n2, n3, n4; // Noise contributions from the five corners
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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 = fastFloor(x + s);
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const j = fastFloor(y + s);
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const k = fastFloor(z + s);
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const l = fastFloor(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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// 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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// Six pair-wise comparisons are performed between each possible pair
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// of the four coordinates, and the results are used to rank the numbers.
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let rankx = 0;
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let ranky = 0;
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let rankz = 0;
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let rankw = 0;
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if (x0 > y0) rankx++;
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else ranky++;
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if (x0 > z0) rankx++;
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else rankz++;
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if (x0 > w0) rankx++;
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else rankw++;
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if (y0 > z0) ranky++;
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else rankz++;
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if (y0 > w0) ranky++;
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else rankw++;
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if (z0 > w0) rankz++;
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else rankw++;
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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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// Rank 3 denotes the largest coordinate.
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// Rank 2 denotes the second largest coordinate.
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// Rank 1 denotes the second smallest coordinate.
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// The integer offsets for the second simplex corner
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const i1 = rankx >= 3 ? 1 : 0;
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const j1 = ranky >= 3 ? 1 : 0;
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const k1 = rankz >= 3 ? 1 : 0;
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const l1 = rankw >= 3 ? 1 : 0;
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// The integer offsets for the third simplex corner
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const i2 = rankx >= 2 ? 1 : 0;
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const j2 = ranky >= 2 ? 1 : 0;
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const k2 = rankz >= 2 ? 1 : 0;
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const l2 = rankw >= 2 ? 1 : 0;
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|
|
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// The integer offsets for the fourth simplex corner
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const i3 = rankx >= 1 ? 1 : 0;
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const j3 = ranky >= 1 ? 1 : 0;
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const k3 = rankz >= 1 ? 1 : 0;
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const l3 = rankw >= 1 ? 1 : 0;
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// The fifth corner has all coordinate offsets = 1, so no need to compute that.
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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
|
|
const y3 = y0 - j3 + 3.0 * G4;
|
|
const z3 = z0 - k3 + 3.0 * G4;
|
|
const w3 = w0 - l3 + 3.0 * G4;
|
|
const x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords
|
|
const y4 = y0 - 1.0 + 4.0 * G4;
|
|
const z4 = z0 - 1.0 + 4.0 * G4;
|
|
const w4 = w0 - 1.0 + 4.0 * G4;
|
|
// Work out the hashed gradient indices of the five simplex corners
|
|
const ii = i & 255;
|
|
const jj = j & 255;
|
|
const kk = k & 255;
|
|
const ll = l & 255;
|
|
// Calculate the contribution from the five corners
|
|
let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
|
|
if (t0 < 0) n0 = 0.0;
|
|
else {
|
|
const gi0 = ii + perm[jj + perm[kk + perm[ll]]];
|
|
t0 *= t0;
|
|
n0 = t0 * t0 * (permGrad4x[gi0] * x0 + permGrad4y[gi0] * y0 + permGrad4z[gi0] * z0 + permGrad4w[gi0] * w0);
|
|
}
|
|
let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
|
|
if (t1 < 0) n1 = 0.0;
|
|
else {
|
|
const gi1 = ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]];
|
|
t1 *= t1;
|
|
n1 = t1 * t1 * (permGrad4x[gi1] * x1 + permGrad4y[gi1] * y1 + permGrad4z[gi1] * z1 + permGrad4w[gi1] * w1);
|
|
}
|
|
let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
|
|
if (t2 < 0) n2 = 0.0;
|
|
else {
|
|
const gi2 = ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]];
|
|
t2 *= t2;
|
|
n2 = t2 * t2 * (permGrad4x[gi2] * x2 + permGrad4y[gi2] * y2 + permGrad4z[gi2] * z2 + permGrad4w[gi2] * w2);
|
|
}
|
|
let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
|
|
if (t3 < 0) n3 = 0.0;
|
|
else {
|
|
const gi3 = ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]];
|
|
t3 *= t3;
|
|
n3 = t3 * t3 * (permGrad4x[gi3] * x3 + permGrad4y[gi3] * y3 + permGrad4z[gi3] * z3 + permGrad4w[gi3] * w3);
|
|
}
|
|
let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
|
|
if (t4 < 0) n4 = 0.0;
|
|
else {
|
|
const gi4 = ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]];
|
|
t4 *= t4;
|
|
n4 = t4 * t4 * (permGrad4x[gi4] * x4 + permGrad4y[gi4] * y4 + permGrad4z[gi4] * z4 + permGrad4w[gi4] * w4);
|
|
}
|
|
// Sum up and scale the result to cover the range [-1,1]
|
|
return 27.0 * (n0 + n1 + n2 + n3 + n4);
|
|
};
|
|
}
|
|
|
|
/**
|
|
* Builds a random permutation table.
|
|
* This is exported only for (internal) testing purposes.
|
|
* Do not rely on this export.
|
|
* @private
|
|
*/
|
|
export function buildPermutationTable(random: RandomFn): Uint8Array {
|
|
const tableSize = 512;
|
|
const p = new Uint8Array(tableSize);
|
|
for (let i = 0; i < tableSize / 2; i++) {
|
|
p[i] = i;
|
|
}
|
|
for (let i = 0; i < tableSize / 2 - 1; i++) {
|
|
const r = i + ~~(random() * (256 - i));
|
|
const aux = p[i];
|
|
p[i] = p[r];
|
|
p[r] = aux;
|
|
}
|
|
for (let i = 256; i < tableSize; i++) {
|
|
p[i] = p[i - 256];
|
|
}
|
|
return p;
|
|
} |