{"version":3,"file":"uber-noise.cjs","sources":["../src/simplex-noise/simplex-noise.ts","../src/alea/alea.ts","../src/uber-noise.ts"],"sourcesContent":["/*\n * A fast javascript implementation of simplex noise by Jonas Wagner\n\nBased on a speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.\nWhich is based on example code by Stefan Gustavson (stegu@itn.liu.se).\nWith Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).\nBetter rank ordering method by Stefan Gustavson in 2012.\n\n Copyright (c) 2024 Jonas Wagner\n\n Permission is hereby granted, free of charge, to any person obtaining a copy\n of this software and associated documentation files (the \"Software\"), to deal\n in the Software without restriction, including without limitation the rights\n to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n copies of the Software, and to permit persons to whom the Software is\n furnished to do so, subject to the following conditions:\n\n The above copyright notice and this permission notice shall be included in all\n copies or substantial portions of the Software.\n\n THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\n SOFTWARE.\n */\n\n// these __PURE__ comments help uglifyjs with dead code removal\n//\nconst SQRT3 = /*#__PURE__*/ Math.sqrt(3.0);\nconst SQRT5 = /*#__PURE__*/ Math.sqrt(5.0);\nconst F2 = 0.5 * (SQRT3 - 1.0);\nconst G2 = (3.0 - SQRT3) / 6.0;\nconst F3 = 1.0 / 3.0;\nconst G3 = 1.0 / 6.0;\nconst F4 = (SQRT5 - 1.0) / 4.0;\nconst G4 = (5.0 - SQRT5) / 20.0;\n\n// I'm really not sure why this | 0 (basically a coercion to int)\n// is making this faster but I get ~5 million ops/sec more on the\n// benchmarks across the board or a ~10% speedup.\nconst fastFloor = (x: number) => Math.floor(x) | 0;\n\nconst grad2 = /*#__PURE__*/ new Float64Array([\n 1, 1, -1, 1, 1, -1,\n\n -1, -1, 1, 0, -1, 0,\n\n 1, 0, -1, 0, 0, 1,\n\n 0, -1, 0, 1, 0, -1,\n]);\n\n// double seems to be faster than single or int's\n// probably because most operations are in double precision\nconst grad3 = /*#__PURE__*/ new Float64Array([\n 1, 1, 0, -1, 1, 0, 1, -1, 0,\n\n -1, -1, 0, 1, 0, 1, -1, 0, 1,\n\n 1, 0, -1, -1, 0, -1, 0, 1, 1,\n\n 0, -1, 1, 0, 1, -1, 0, -1, -1,\n]);\n\n// double is a bit quicker here as well\nconst grad4 = /*#__PURE__*/ new Float64Array([\n 0, 1, 1, 1, 0, 1, 1, -1, 0, 1, -1, 1, 0, 1, -1, -1, 0, -1, 1, 1, 0, -1, 1, -1,\n 0, -1, -1, 1, 0, -1, -1, -1, 1, 0, 1, 1, 1, 0, 1, -1, 1, 0, -1, 1, 1, 0, -1,\n -1, -1, 0, 1, 1, -1, 0, 1, -1, -1, 0, -1, 1, -1, 0, -1, -1, 1, 1, 0, 1, 1, 1,\n 0, -1, 1, -1, 0, 1, 1, -1, 0, -1, -1, 1, 0, 1, -1, 1, 0, -1, -1, -1, 0, 1, -1,\n -1, 0, -1, 1, 1, 1, 0, 1, 1, -1, 0, 1, -1, 1, 0, 1, -1, -1, 0, -1, 1, 1, 0,\n -1, 1, -1, 0, -1, -1, 1, 0, -1, -1, -1, 0,\n]);\n\n/**\n * A random() function, must return a number in the interval [0,1), just like Math.random().\n */\nexport type RandomFn = () => number;\n\n/**\n * Samples the noise field in two dimensions\n *\n * Coordinates should be finite, bigger than -2^31 and smaller than 2^31.\n * @param x\n * @param y\n * @returns a number in the interval [-1, 1]\n */\nexport type NoiseFunction2D = (x: number, y: number) => number;\n\n/**\n * Creates a 2D noise function\n * @param random the random function that will be used to build the permutation table\n * @returns {NoiseFunction2D}\n */\nexport function createNoise2D(random: RandomFn = Math.random): NoiseFunction2D {\n const perm = buildPermutationTable(random);\n // precalculating this yields a little ~3% performance improvement.\n const permGrad2x = new Float64Array(perm).map((v) => grad2[(v % 12) * 2]);\n const permGrad2y = new Float64Array(perm).map((v) => grad2[(v % 12) * 2 + 1]);\n return function noise2D(x: number, y: number): number {\n // if(!isFinite(x) || !isFinite(y)) return 0;\n let n0 = 0; // Noise contributions from the three corners\n let n1 = 0;\n let n2 = 0;\n // Skew the input space to determine which simplex cell we're in\n const s = (x + y) * F2; // Hairy factor for 2D\n const i = fastFloor(x + s);\n const j = fastFloor(y + s);\n const t = (i + j) * G2;\n const X0 = i - t; // Unskew the cell origin back to (x,y) space\n const Y0 = j - t;\n const x0 = x - X0; // The x,y distances from the cell origin\n const y0 = y - Y0;\n // For the 2D case, the simplex shape is an equilateral triangle.\n // Determine which simplex we are in.\n let i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords\n if (x0 > y0) {\n i1 = 1;\n j1 = 0;\n } // lower triangle, XY order: (0,0)->(1,0)->(1,1)\n else {\n i1 = 0;\n j1 = 1;\n } // upper triangle, YX order: (0,0)->(0,1)->(1,1)\n // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and\n // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where\n // c = (3-sqrt(3))/6\n const x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords\n const y1 = y0 - j1 + G2;\n const x2 = x0 - 1.0 + 2.0 * G2; // Offsets for last corner in (x,y) unskewed coords\n const y2 = y0 - 1.0 + 2.0 * G2;\n // Work out the hashed gradient indices of the three simplex corners\n const ii = i & 255;\n const jj = j & 255;\n // Calculate the contribution from the three corners\n let t0 = 0.5 - x0 * x0 - y0 * y0;\n if (t0 >= 0) {\n const gi0 = ii + perm[jj];\n const g0x = permGrad2x[gi0];\n const g0y = permGrad2y[gi0];\n t0 *= t0;\n // n0 = t0 * t0 * (grad2[gi0] * x0 + grad2[gi0 + 1] * y0); // (x,y) of grad3 used for 2D gradient\n n0 = t0 * t0 * (g0x * x0 + g0y * y0);\n }\n let t1 = 0.5 - x1 * x1 - y1 * y1;\n if (t1 >= 0) {\n const gi1 = ii + i1 + perm[jj + j1];\n const g1x = permGrad2x[gi1];\n const g1y = permGrad2y[gi1];\n t1 *= t1;\n // n1 = t1 * t1 * (grad2[gi1] * x1 + grad2[gi1 + 1] * y1);\n n1 = t1 * t1 * (g1x * x1 + g1y * y1);\n }\n let t2 = 0.5 - x2 * x2 - y2 * y2;\n if (t2 >= 0) {\n const gi2 = ii + 1 + perm[jj + 1];\n const g2x = permGrad2x[gi2];\n const g2y = permGrad2y[gi2];\n t2 *= t2;\n // n2 = t2 * t2 * (grad2[gi2] * x2 + grad2[gi2 + 1] * y2);\n n2 = t2 * t2 * (g2x * x2 + g2y * y2);\n }\n // Add contributions from each corner to get the final noise value.\n // The result is scaled to return values in the interval [-1,1].\n return 70.0 * (n0 + n1 + n2);\n };\n}\n\n/**\n * Samples the noise field in three dimensions\n *\n * Coordinates should be finite, bigger than -2^31 and smaller than 2^31.\n * @param x\n * @param y\n * @param z\n * @returns a number in the interval [-1, 1]\n */\nexport type NoiseFunction3D = (x: number, y: number, z: number) => number;\n\n/**\n * Creates a 3D noise function\n * @param random the random function that will be used to build the permutation table\n * @returns {NoiseFunction3D}\n */\nexport function createNoise3D(random: RandomFn = Math.random): NoiseFunction3D {\n const perm = buildPermutationTable(random);\n // precalculating these seems to yield a speedup of over 15%\n const permGrad3x = new Float64Array(perm).map((v) => grad3[(v % 12) * 3]);\n const permGrad3y = new Float64Array(perm).map((v) => grad3[(v % 12) * 3 + 1]);\n const permGrad3z = new Float64Array(perm).map((v) => grad3[(v % 12) * 3 + 2]);\n return function noise3D(x: number, y: number, z: number): number {\n let n0, n1, n2, n3; // Noise contributions from the four corners\n // Skew the input space to determine which simplex cell we're in\n const s = (x + y + z) * F3; // Very nice and simple skew factor for 3D\n const i = fastFloor(x + s);\n const j = fastFloor(y + s);\n const k = fastFloor(z + s);\n const t = (i + j + k) * G3;\n const X0 = i - t; // Unskew the cell origin back to (x,y,z) space\n const Y0 = j - t;\n const Z0 = k - t;\n const x0 = x - X0; // The x,y,z distances from the cell origin\n const y0 = y - Y0;\n const z0 = z - Z0;\n // For the 3D case, the simplex shape is a slightly irregular tetrahedron.\n // Determine which simplex we are in.\n let i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords\n let i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords\n if (x0 >= y0) {\n if (y0 >= z0) {\n i1 = 1;\n j1 = 0;\n k1 = 0;\n i2 = 1;\n j2 = 1;\n k2 = 0;\n } // X Y Z order\n else if (x0 >= z0) {\n i1 = 1;\n j1 = 0;\n k1 = 0;\n i2 = 1;\n j2 = 0;\n k2 = 1;\n } // X Z Y order\n else {\n i1 = 0;\n j1 = 0;\n k1 = 1;\n i2 = 1;\n j2 = 0;\n k2 = 1;\n } // Z X Y order\n } else {\n // x0 number;\n\n/**\n * Creates a 4D noise function\n * @param random the random function that will be used to build the permutation table\n * @returns {NoiseFunction4D}\n */\nexport function createNoise4D(random: RandomFn = Math.random): NoiseFunction4D {\n const perm = buildPermutationTable(random);\n // precalculating these leads to a ~10% speedup\n const permGrad4x = new Float64Array(perm).map((v) => grad4[(v % 32) * 4]);\n const permGrad4y = new Float64Array(perm).map((v) => grad4[(v % 32) * 4 + 1]);\n const permGrad4z = new Float64Array(perm).map((v) => grad4[(v % 32) * 4 + 2]);\n const permGrad4w = new Float64Array(perm).map((v) => grad4[(v % 32) * 4 + 3]);\n return function noise4D(x: number, y: number, z: number, w: number): number {\n let n0, n1, n2, n3, n4; // Noise contributions from the five corners\n // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in\n const s = (x + y + z + w) * F4; // Factor for 4D skewing\n const i = fastFloor(x + s);\n const j = fastFloor(y + s);\n const k = fastFloor(z + s);\n const l = fastFloor(w + s);\n const t = (i + j + k + l) * G4; // Factor for 4D unskewing\n const X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space\n const Y0 = j - t;\n const Z0 = k - t;\n const W0 = l - t;\n const x0 = x - X0; // The x,y,z,w distances from the cell origin\n const y0 = y - Y0;\n const z0 = z - Z0;\n const w0 = w - W0;\n // For the 4D case, the simplex is a 4D shape I won't even try to describe.\n // To find out which of the 24 possible simplices we're in, we need to\n // determine the magnitude ordering of x0, y0, z0 and w0.\n // Six pair-wise comparisons are performed between each possible pair\n // of the four coordinates, and the results are used to rank the numbers.\n let rankx = 0;\n let ranky = 0;\n let rankz = 0;\n let rankw = 0;\n if (x0 > y0) rankx++;\n else ranky++;\n if (x0 > z0) rankx++;\n else rankz++;\n if (x0 > w0) rankx++;\n else rankw++;\n if (y0 > z0) ranky++;\n else rankz++;\n if (y0 > w0) ranky++;\n else rankw++;\n if (z0 > w0) rankz++;\n else rankw++;\n // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.\n // Many values of c will never occur, since e.g. x>y>z>w makes x= 3 ? 1 : 0;\n const j1 = ranky >= 3 ? 1 : 0;\n const k1 = rankz >= 3 ? 1 : 0;\n const l1 = rankw >= 3 ? 1 : 0;\n // The integer offsets for the third simplex corner\n const i2 = rankx >= 2 ? 1 : 0;\n const j2 = ranky >= 2 ? 1 : 0;\n const k2 = rankz >= 2 ? 1 : 0;\n const l2 = rankw >= 2 ? 1 : 0;\n\n // The integer offsets for the fourth simplex corner\n const i3 = rankx >= 1 ? 1 : 0;\n const j3 = ranky >= 1 ? 1 : 0;\n const k3 = rankz >= 1 ? 1 : 0;\n const l3 = rankw >= 1 ? 1 : 0;\n // The fifth corner has all coordinate offsets = 1, so no need to compute that.\n const x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords\n const y1 = y0 - j1 + G4;\n const z1 = z0 - k1 + G4;\n const w1 = w0 - l1 + G4;\n const x2 = x0 - i2 + 2.0 * G4; // Offsets for third corner in (x,y,z,w) coords\n const y2 = y0 - j2 + 2.0 * G4;\n const z2 = z0 - k2 + 2.0 * G4;\n const w2 = w0 - l2 + 2.0 * G4;\n const x3 = x0 - i3 + 3.0 * G4; // Offsets for fourth corner in (x,y,z,w) coords\n const y3 = y0 - j3 + 3.0 * G4;\n const z3 = z0 - k3 + 3.0 * G4;\n const w3 = w0 - l3 + 3.0 * G4;\n const x4 = x0 - 1.0 + 4.0 * G4; // Offsets for last corner in (x,y,z,w) coords\n const y4 = y0 - 1.0 + 4.0 * G4;\n const z4 = z0 - 1.0 + 4.0 * G4;\n const w4 = w0 - 1.0 + 4.0 * G4;\n // Work out the hashed gradient indices of the five simplex corners\n const ii = i & 255;\n const jj = j & 255;\n const kk = k & 255;\n const ll = l & 255;\n // Calculate the contribution from the five corners\n let t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;\n if (t0 < 0) n0 = 0.0;\n else {\n const gi0 = ii + perm[jj + perm[kk + perm[ll]]];\n t0 *= t0;\n n0 =\n t0 *\n t0 *\n (permGrad4x[gi0] * x0 +\n permGrad4y[gi0] * y0 +\n permGrad4z[gi0] * z0 +\n permGrad4w[gi0] * w0);\n }\n let t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;\n if (t1 < 0) n1 = 0.0;\n else {\n const gi1 = ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]];\n t1 *= t1;\n n1 =\n t1 *\n t1 *\n (permGrad4x[gi1] * x1 +\n permGrad4y[gi1] * y1 +\n permGrad4z[gi1] * z1 +\n permGrad4w[gi1] * w1);\n }\n let t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;\n if (t2 < 0) n2 = 0.0;\n else {\n const gi2 = ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]];\n t2 *= t2;\n n2 =\n t2 *\n t2 *\n (permGrad4x[gi2] * x2 +\n permGrad4y[gi2] * y2 +\n permGrad4z[gi2] * z2 +\n permGrad4w[gi2] * w2);\n }\n let t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;\n if (t3 < 0) n3 = 0.0;\n else {\n const gi3 = ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]];\n t3 *= t3;\n n3 =\n t3 *\n t3 *\n (permGrad4x[gi3] * x3 +\n permGrad4y[gi3] * y3 +\n permGrad4z[gi3] * z3 +\n permGrad4w[gi3] * w3);\n }\n let t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;\n if (t4 < 0) n4 = 0.0;\n else {\n const gi4 = ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]];\n t4 *= t4;\n n4 =\n t4 *\n t4 *\n (permGrad4x[gi4] * x4 +\n permGrad4y[gi4] * y4 +\n permGrad4z[gi4] * z4 +\n permGrad4w[gi4] * w4);\n }\n // Sum up and scale the result to cover the range [-1,1]\n return 27.0 * (n0 + n1 + n2 + n3 + n4);\n };\n}\n\n/**\n * Builds a random permutation table.\n * This is exported only for (internal) testing purposes.\n * Do not rely on this export.\n * @private\n */\nexport function buildPermutationTable(random: RandomFn): Uint8Array {\n const tableSize = 512;\n const p = new Uint8Array(tableSize);\n for (let i = 0; i < tableSize / 2; i++) {\n p[i] = i;\n }\n for (let i = 0; i < tableSize / 2 - 1; i++) {\n const r = i + ~~(random() * (256 - i));\n const aux = p[i];\n p[i] = p[r];\n p[r] = aux;\n }\n for (let i = 256; i < tableSize; i++) {\n p[i] = p[i - 256];\n }\n return p;\n}\n\n/**\n * The output of the noise function with derivatives\n *\n * @property value the noise value in the interval [-1, 1]\n * @property dx the partial derivative with respect to x\n * @property dy the partial derivative with respect to y\n */\nexport type NoiseDeriv2DOutput = {\n value: number;\n dx: number;\n dy: number;\n};\n\n/**\n * Samples the noise field in two dimensions and returns the partial derivatives (dx, dy).\n *\n * Coordinates should be finite, bigger than -2^31 and smaller than 2^31.\n * @param x\n * @param y\n * @param output optional output object to store the result, if not provided, a new one will be created\n * @returns {NoiseDeriv2DOutput}\n */\nexport type NoiseDerivFunction2D = (\n x: number,\n y: number,\n output?: NoiseDeriv2DOutput,\n) => NoiseDeriv2DOutput;\n\n/**\n * Creates a 2D noise function with derivatives\n *\n * @param random the random function that will be used to build the permutation table\n * @returns {NoiseDerivFunction2D}\n */\nexport function createNoise2DWithDerivatives(\n random: RandomFn = Math.random,\n): NoiseDerivFunction2D {\n const perm = buildPermutationTable(random);\n // Precompute the x/y gradients for each possible permutation value\n const permGrad2x = new Float64Array(perm).map((v) => grad2[(v % 12) * 2]);\n const permGrad2y = new Float64Array(perm).map((v) => grad2[(v % 12) * 2 + 1]);\n\n return function noise2DWithDerivatives(\n x: number,\n y: number,\n output?: NoiseDeriv2DOutput,\n ): NoiseDeriv2DOutput {\n // Noise and derivatives that we'll accumulate\n let value = 0;\n let dx = 0;\n let dy = 0;\n\n // Skew the input space to determine which simplex cell we're in\n const s = (x + y) * F2;\n const i = fastFloor(x + s);\n const j = fastFloor(y + s);\n const t = (i + j) * G2;\n const X0 = i - t;\n const Y0 = j - t;\n\n // Unskewed distances from the cell origin\n const x0 = x - X0;\n const y0 = y - Y0;\n\n // Determine which simplex triangle we are in\n let i1, j1;\n if (x0 > y0) {\n i1 = 1;\n j1 = 0;\n } else {\n i1 = 0;\n j1 = 1;\n }\n\n // Offsets for the other two corners\n const x1 = x0 - i1 + G2;\n const y1 = y0 - j1 + G2;\n const x2 = x0 - 1.0 + 2.0 * G2;\n const y2 = y0 - 1.0 + 2.0 * G2;\n\n // Work out the hashed gradient indices of the three corners\n const ii = i & 255;\n const jj = j & 255;\n\n // -- Corner 0\n const t0 = 0.5 - x0 * x0 - y0 * y0;\n if (t0 > 0) {\n // Precompute the gradient index and the actual gradient\n const gi0 = ii + perm[jj];\n const g0x = permGrad2x[gi0];\n const g0y = permGrad2y[gi0];\n\n // Contribution (the usual simplex noise formula)\n const t0sq = t0 * t0; // t0^2\n const t0p4 = t0sq * t0sq; // t0^4\n const dot0 = g0x * x0 + g0y * y0;\n const n0 = t0p4 * dot0;\n\n // Derivatives:\n //\n // t0 = 0.5 - x0^2 - y0^2\n // dt0/dx = -2 * x0\n // dt0/dy = -2 * y0\n //\n // ∂n0/∂x = ∂/∂x [ t0^4 * (g0x*x0 + g0y*y0) ]\n // = (4 * t0^3 * dt0/dx) * (g0x*x0 + g0y*y0)\n // + t0^4 * g0x * (∂x0/∂x)\n // Since x0 = x - X0, (∂x0/∂x) = 1\n //\n // Putting it together:\n const t0cubic = t0sq * t0; // t0^3\n const dT0dx = -2.0 * x0;\n const dT0dy = -2.0 * y0;\n\n const dn0dx = 4.0 * t0cubic * dT0dx * dot0 + t0p4 * g0x;\n const dn0dy = 4.0 * t0cubic * dT0dy * dot0 + t0p4 * g0y;\n\n // Accumulate\n value += n0;\n dx += dn0dx;\n dy += dn0dy;\n }\n\n // -- Corner 1\n const t1 = 0.5 - x1 * x1 - y1 * y1;\n if (t1 > 0) {\n const gi1 = ii + i1 + perm[jj + j1];\n const g1x = permGrad2x[gi1];\n const g1y = permGrad2y[gi1];\n\n const t1sq = t1 * t1;\n const t1p4 = t1sq * t1sq;\n const dot1 = g1x * x1 + g1y * y1;\n const n1 = t1p4 * dot1;\n\n const t1cubic = t1sq * t1;\n const dT1dx = -2.0 * x1; // because x1 depends on x\n const dT1dy = -2.0 * y1; // because y1 depends on y\n\n const dn1dx = 4.0 * t1cubic * dT1dx * dot1 + t1p4 * g1x;\n const dn1dy = 4.0 * t1cubic * dT1dy * dot1 + t1p4 * g1y;\n\n value += n1;\n dx += dn1dx;\n dy += dn1dy;\n }\n\n // -- Corner 2\n const t2 = 0.5 - x2 * x2 - y2 * y2;\n if (t2 > 0) {\n const gi2 = ii + 1 + perm[jj + 1];\n const g2x = permGrad2x[gi2];\n const g2y = permGrad2y[gi2];\n\n const t2sq = t2 * t2;\n const t2p4 = t2sq * t2sq;\n const dot2 = g2x * x2 + g2y * y2;\n const n2 = t2p4 * dot2;\n\n const t2cubic = t2sq * t2;\n const dT2dx = -2.0 * x2;\n const dT2dy = -2.0 * y2;\n\n const dn2dx = 4.0 * t2cubic * dT2dx * dot2 + t2p4 * g2x;\n const dn2dy = 4.0 * t2cubic * dT2dy * dot2 + t2p4 * g2y;\n\n value += n2;\n dx += dn2dx;\n dy += dn2dy;\n }\n\n // Scale the final result (the same factor 70 used in standard 2D simplex)\n value *= 70.0;\n dx *= 70.0;\n dy *= 70.0;\n\n if (output) {\n output.value = value;\n output.dx = dx;\n output.dy = dy;\n return output;\n }\n\n return { value, dx, dy };\n };\n}\n\n/**\n * The output of the noise function with derivatives\n *\n * @property value the noise value in the interval [-1, 1]\n * @property dx the partial derivative with respect to x\n * @property dy the partial derivative with respect to y\n * @property dz the partial derivative with respect to z\n */\nexport type NoiseDeriv3DOutput = {\n value: number;\n dx: number;\n dy: number;\n dz: number;\n};\n\n/**\n * Samples the noise field in three dimensions and returns the partial derivatives (dx, dy, dz).\n *\n * Coordinates should be finite, bigger than -2^31 and smaller than 2^31.\n * @param x\n * @param y\n * @param z\n * @param output\n * @returns a number in the interval [-1, 1]\n */\nexport type NoiseDerivFunction3D = (\n x: number,\n y: number,\n z: number,\n output?: NoiseDeriv3DOutput,\n) => NoiseDeriv3DOutput;\n\n/**\n * Creates a 3D Simplex noise function that also returns partial derivatives (dx, dy, dz).\n *\n * The final noise value is scaled to ~[-1, 1], just like `createNoise3D`.\n * The derivatives match that same scaling.\n *\n * @param random the random function that will be used to build the permutation table\n * @returns {NoiseDerivFunction3D}\n */\nexport function createNoise3DWithDerivatives(\n random: RandomFn = Math.random,\n): NoiseDerivFunction3D {\n // Build the permutation table\n const perm = buildPermutationTable(random);\n\n // Precompute the 3D gradients for each possible perm value\n // i.e. permGrad3x[i] = grad3[(perm[i] % 12)*3 + 0]\n const permGrad3x = new Float64Array(512);\n const permGrad3y = new Float64Array(512);\n const permGrad3z = new Float64Array(512);\n for (let i = 0; i < 512; i++) {\n const gIndex = (perm[i] % 12) * 3;\n permGrad3x[i] = grad3[gIndex + 0];\n permGrad3y[i] = grad3[gIndex + 1];\n permGrad3z[i] = grad3[gIndex + 2];\n }\n\n return function noise3DWithDerivatives(\n x: number,\n y: number,\n z: number,\n output?: NoiseDeriv3DOutput,\n ): NoiseDeriv3DOutput {\n // Skew the input space\n const s = (x + y + z) * F3;\n const i = fastFloor(x + s);\n const j = fastFloor(y + s);\n const k = fastFloor(z + s);\n\n const t = (i + j + k) * G3;\n // Unskew\n const X0 = i - t;\n const Y0 = j - t;\n const Z0 = k - t;\n\n // Distances from cell origin\n const x0 = x - X0;\n const y0 = y - Y0;\n const z0 = z - Z0;\n\n // Determine simplex region\n let i1, j1, k1;\n let i2, j2, k2;\n\n if (x0 >= y0) {\n if (y0 >= z0) {\n // X Y Z order\n i1 = 1;\n j1 = 0;\n k1 = 0;\n i2 = 1;\n j2 = 1;\n k2 = 0;\n } else if (x0 >= z0) {\n // X Z Y order\n i1 = 1;\n j1 = 0;\n k1 = 0;\n i2 = 1;\n j2 = 0;\n k2 = 1;\n } else {\n // Z X Y order\n i1 = 0;\n j1 = 0;\n k1 = 1;\n i2 = 1;\n j2 = 0;\n k2 = 1;\n }\n } else {\n // x0 < y0\n if (y0 < z0) {\n // Z Y X order\n i1 = 0;\n j1 = 0;\n k1 = 1;\n i2 = 0;\n j2 = 1;\n k2 = 1;\n } else if (x0 < z0) {\n // Y Z X order\n i1 = 0;\n j1 = 1;\n k1 = 0;\n i2 = 0;\n j2 = 1;\n k2 = 1;\n } else {\n // Y X Z order\n i1 = 0;\n j1 = 1;\n k1 = 0;\n i2 = 1;\n j2 = 1;\n k2 = 0;\n }\n }\n\n // Offsets for second corner\n const x1 = x0 - i1 + G3;\n const y1 = y0 - j1 + G3;\n const z1 = z0 - k1 + G3;\n // Offsets for third corner\n const x2 = x0 - i2 + 2.0 * G3;\n const y2 = y0 - j2 + 2.0 * G3;\n const z2 = z0 - k2 + 2.0 * G3;\n // Offsets for last corner\n const x3 = x0 - 1.0 + 3.0 * G3;\n const y3 = y0 - 1.0 + 3.0 * G3;\n const z3 = z0 - 1.0 + 3.0 * G3;\n\n // Hashed gradient indices\n const ii = i & 255;\n const jj = j & 255;\n const kk = k & 255;\n\n // Contribution accumulators\n let n0 = 0,\n n1 = 0,\n n2 = 0,\n n3 = 0;\n let dx0 = 0,\n dy0 = 0,\n dz0 = 0;\n let dx1 = 0,\n dy1 = 0,\n dz1 = 0;\n let dx2 = 0,\n dy2 = 0,\n dz2 = 0;\n let dx3 = 0,\n dy3 = 0,\n dz3 = 0;\n\n // For each corner, we compute t_i, the gradient dot, and the derivatives\n\n // Corner 0\n {\n const t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;\n if (t0 > 0) {\n const gi0 = ii + perm[jj + perm[kk]];\n const gx0 = permGrad3x[gi0];\n const gy0 = permGrad3y[gi0];\n const gz0 = permGrad3z[gi0];\n\n const gDot0 = gx0 * x0 + gy0 * y0 + gz0 * z0;\n const t0Sq = t0 * t0;\n const t0Pow4 = t0Sq * t0Sq; // t0^4\n\n n0 = t0Pow4 * gDot0;\n\n // Derivative of (t0^4 * (g·(x,y,z))) w.r.t x:\n // d/dx [t0^4 * gDot0] = (d/dx t0^4)*gDot0 + t0^4*gx0\n // where t0 = 0.6 - (x^2 + y^2 + z^2),\n // d/dx t0^4 = 4 * t0^3 * d/dx t0 = 4*t0^3*(-2*x) = -8*t0^3*x\n // => partial_x = -8*t0^3*x0*gDot0 + t0^4*gx0\n const t0Cub = t0Sq * t0; // t0^3\n const coeff = -8.0 * t0Cub; // factor for x*gDot\n dx0 = coeff * x0 * gDot0 + t0Pow4 * gx0;\n dy0 = coeff * y0 * gDot0 + t0Pow4 * gy0;\n dz0 = coeff * z0 * gDot0 + t0Pow4 * gz0;\n }\n }\n\n // Corner 1\n {\n const t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;\n if (t1 > 0) {\n const gi1 = ii + i1 + perm[jj + j1 + perm[kk + k1]];\n const gx1 = permGrad3x[gi1];\n const gy1 = permGrad3y[gi1];\n const gz1 = permGrad3z[gi1];\n\n const gDot1 = gx1 * x1 + gy1 * y1 + gz1 * z1;\n const t1Sq = t1 * t1;\n const t1Pow4 = t1Sq * t1Sq;\n\n n1 = t1Pow4 * gDot1;\n\n const t1Cub = t1Sq * t1;\n const coeff = -8.0 * t1Cub;\n dx1 = coeff * x1 * gDot1 + t1Pow4 * gx1;\n dy1 = coeff * y1 * gDot1 + t1Pow4 * gy1;\n dz1 = coeff * z1 * gDot1 + t1Pow4 * gz1;\n }\n }\n\n // Corner 2\n {\n const t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;\n if (t2 > 0) {\n const gi2 = ii + i2 + perm[jj + j2 + perm[kk + k2]];\n const gx2 = permGrad3x[gi2];\n const gy2 = permGrad3y[gi2];\n const gz2 = permGrad3z[gi2];\n\n const gDot2 = gx2 * x2 + gy2 * y2 + gz2 * z2;\n const t2Sq = t2 * t2;\n const t2Pow4 = t2Sq * t2Sq;\n\n n2 = t2Pow4 * gDot2;\n\n const t2Cub = t2Sq * t2;\n const coeff = -8.0 * t2Cub;\n dx2 = coeff * x2 * gDot2 + t2Pow4 * gx2;\n dy2 = coeff * y2 * gDot2 + t2Pow4 * gy2;\n dz2 = coeff * z2 * gDot2 + t2Pow4 * gz2;\n }\n }\n\n // Corner 3\n {\n const t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;\n if (t3 > 0) {\n const gi3 = ii + 1 + perm[jj + 1 + perm[kk + 1]];\n const gx3 = permGrad3x[gi3];\n const gy3 = permGrad3y[gi3];\n const gz3 = permGrad3z[gi3];\n\n const gDot3 = gx3 * x3 + gy3 * y3 + gz3 * z3;\n const t3Sq = t3 * t3;\n const t3Pow4 = t3Sq * t3Sq;\n\n n3 = t3Pow4 * gDot3;\n\n const t3Cub = t3Sq * t3;\n const coeff = -8.0 * t3Cub;\n dx3 = coeff * x3 * gDot3 + t3Pow4 * gx3;\n dy3 = coeff * y3 * gDot3 + t3Pow4 * gy3;\n dz3 = coeff * z3 * gDot3 + t3Pow4 * gz3;\n }\n }\n\n // Sum up contributions\n const value = n0 + n1 + n2 + n3;\n const dx = dx0 + dx1 + dx2 + dx3;\n const dy = dy0 + dy1 + dy2 + dy3;\n const dz = dz0 + dz1 + dz2 + dz3;\n\n // The original 3D simplex scaling factor is 32.0 in this library\n // (makes final output ~in [-1,1]).\n const scale = 32.0;\n\n if (output) {\n output.value = scale * value;\n output.dx = scale * dx;\n output.dy = scale * dy;\n output.dz = scale * dz;\n return output;\n }\n\n return {\n value: scale * value,\n dx: scale * dx,\n dy: scale * dy,\n dz: scale * dz,\n };\n };\n}\n\n/**\n * The output of the noise function with derivatives\n *\n * @property value the noise value in the interval [-1, 1]\n * @property dx the partial derivative with respect to x\n * @property dy the partial derivative with respect to y\n * @property dz the partial derivative with respect to z\n * @property dw the partial derivative with respect to w\n */\nexport type NoiseDeriv4DOutput = {\n value: number;\n dx: number;\n dy: number;\n dz: number;\n dw: number;\n};\n\n/**\n * Samples the noise field in four dimensions and returns the partial derivatives (dx, dy, dz, dw).\n *\n * Coordinates should be finite, bigger than -2^31 and smaller than 2^31.\n * @param x\n * @param y\n * @param z\n * @param w\n * @param output (optional) an object to re-use for the result, so as to avoid allocations\n * @returns {NoiseDeriv4DOutput}\n */\nexport type NoiseDerivFunction4D = (\n x: number,\n y: number,\n z: number,\n w: number,\n output?: NoiseDeriv4DOutput,\n) => NoiseDeriv4DOutput;\n\n/**\n * Creates a 4D Simplex noise function that also computes its analytical partial derivatives.\n *\n * @param random the random function that will be used to build the permutation table\n * @returns {NoiseDerivFunction4D}\n */\nexport function createNoise4DWithDerivatives(\n random: RandomFn = Math.random,\n): NoiseDerivFunction4D {\n // Build the standard permutation table\n const perm = buildPermutationTable(random);\n\n // Precompute gradient indices for each possible value in `perm` (0..511).\n // Because the default grad4 array has 32 different grad vectors for 4D, we do `perm[i] % 32`.\n const permGrad4x = new Float64Array(512);\n const permGrad4y = new Float64Array(512);\n const permGrad4z = new Float64Array(512);\n const permGrad4w = new Float64Array(512);\n for (let i = 0; i < 512; i++) {\n const gi = (perm[i] % 32) * 4;\n permGrad4x[i] = grad4[gi + 0];\n permGrad4y[i] = grad4[gi + 1];\n permGrad4z[i] = grad4[gi + 2];\n permGrad4w[i] = grad4[gi + 3];\n }\n\n return function noise4DWithDerivatives(\n x: number,\n y: number,\n z: number,\n w: number,\n output?: NoiseDeriv4DOutput,\n ): NoiseDeriv4DOutput {\n // Skew the (x,y,z,w) space\n const s = (x + y + z + w) * F4;\n const i = fastFloor(x + s);\n const j = fastFloor(y + s);\n const k = fastFloor(z + s);\n const l = fastFloor(w + s);\n\n // Unskew\n const t = (i + j + k + l) * G4;\n const X0 = i - t;\n const Y0 = j - t;\n const Z0 = k - t;\n const W0 = l - t;\n\n // Distances from cell origin\n const x0 = x - X0;\n const y0 = y - Y0;\n const z0 = z - Z0;\n const w0 = w - W0;\n\n // 4D simplex region rank ordering\n let rankx = 0;\n let ranky = 0;\n let rankz = 0;\n let rankw = 0;\n if (x0 > y0) rankx++;\n else ranky++;\n if (x0 > z0) rankx++;\n else rankz++;\n if (x0 > w0) rankx++;\n else rankw++;\n if (y0 > z0) ranky++;\n else rankz++;\n if (y0 > w0) ranky++;\n else rankw++;\n if (z0 > w0) rankz++;\n else rankw++;\n\n // Offsets for each corner\n const i1 = rankx >= 3 ? 1 : 0;\n const j1 = ranky >= 3 ? 1 : 0;\n const k1 = rankz >= 3 ? 1 : 0;\n const l1 = rankw >= 3 ? 1 : 0;\n\n const i2 = rankx >= 2 ? 1 : 0;\n const j2 = ranky >= 2 ? 1 : 0;\n const k2 = rankz >= 2 ? 1 : 0;\n const l2 = rankw >= 2 ? 1 : 0;\n\n const i3 = rankx >= 1 ? 1 : 0;\n const j3 = ranky >= 1 ? 1 : 0;\n const k3 = rankz >= 1 ? 1 : 0;\n const l3 = rankw >= 1 ? 1 : 0;\n\n // Position deltas for each corner\n const x1 = x0 - i1 + G4;\n const y1 = y0 - j1 + G4;\n const z1 = z0 - k1 + G4;\n const w1 = w0 - l1 + G4;\n\n const x2 = x0 - i2 + 2.0 * G4;\n const y2 = y0 - j2 + 2.0 * G4;\n const z2 = z0 - k2 + 2.0 * G4;\n const w2 = w0 - l2 + 2.0 * G4;\n\n const x3 = x0 - i3 + 3.0 * G4;\n const y3 = y0 - j3 + 3.0 * G4;\n const z3 = z0 - k3 + 3.0 * G4;\n const w3 = w0 - l3 + 3.0 * G4;\n\n const x4 = x0 - 1.0 + 4.0 * G4;\n const y4 = y0 - 1.0 + 4.0 * G4;\n const z4 = z0 - 1.0 + 4.0 * G4;\n const w4 = w0 - 1.0 + 4.0 * G4;\n\n // Hashed gradient indices\n const ii = i & 255;\n const jj = j & 255;\n const kk = k & 255;\n const ll = l & 255;\n\n // Corner accumulators\n let n0 = 0,\n n1 = 0,\n n2 = 0,\n n3 = 0,\n n4 = 0;\n let dx0 = 0,\n dx1 = 0,\n dx2 = 0,\n dx3 = 0,\n dx4 = 0;\n let dy0 = 0,\n dy1 = 0,\n dy2 = 0,\n dy3 = 0,\n dy4 = 0;\n let dz0 = 0,\n dz1 = 0,\n dz2 = 0,\n dz3 = 0,\n dz4 = 0;\n let dw0 = 0,\n dw1 = 0,\n dw2 = 0,\n dw3 = 0,\n dw4 = 0;\n\n // A small helper to do the repeated derivative logic\n function cornerContribution(\n tx: number,\n ty: number,\n tz: number,\n tw: number,\n cornerIdx: number,\n ) {\n // t = 0.6 - sum of squares\n const tVal = 0.6 - (tx * tx + ty * ty + tz * tz + tw * tw);\n if (tVal <= 0) {\n return {\n n: 0,\n dx: 0,\n dy: 0,\n dz: 0,\n dw: 0,\n };\n }\n // Hashed gradient\n const gx = permGrad4x[cornerIdx];\n const gy = permGrad4y[cornerIdx];\n const gz = permGrad4z[cornerIdx];\n const gw = permGrad4w[cornerIdx];\n\n // Gradient dot\n const gDot = gx * tx + gy * ty + gz * tz + gw * tw;\n\n // t^2, t^3, t^4\n const t2 = tVal * tVal;\n const t4 = t2 * t2; // t^4\n const t3 = t2 * tVal; // t^3\n\n // Contribution\n const n = t4 * gDot;\n\n // Derivatives:\n // dn/d(tx) = ∂/∂(tx) [ t^4 * (grad·(tx,ty,tz,tw)) ]\n // = (4 * t^3 * d(t)/d(tx)) * gDot + t^4 * gx\n // where d(t)/d(tx) = -2*tx\n const factor = -8.0 * t3; // 4 * t^3 * -2\n const dx = factor * tx * gDot + t4 * gx;\n const dy = factor * ty * gDot + t4 * gy;\n const dz = factor * tz * gDot + t4 * gz;\n const dw = factor * tw * gDot + t4 * gw;\n\n return { n, dx, dy, dz, dw };\n }\n\n // Evaluate each corner's contribution\n {\n // Corner 0\n const gi0 = ii + perm[jj + perm[kk + perm[ll]]];\n const c0 = cornerContribution(x0, y0, z0, w0, gi0);\n n0 = c0.n;\n dx0 = c0.dx;\n dy0 = c0.dy;\n dz0 = c0.dz;\n dw0 = c0.dw;\n }\n {\n // Corner 1\n const gi1 = ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]];\n const c1 = cornerContribution(x1, y1, z1, w1, gi1);\n n1 = c1.n;\n dx1 = c1.dx;\n dy1 = c1.dy;\n dz1 = c1.dz;\n dw1 = c1.dw;\n }\n {\n // Corner 2\n const gi2 = ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]];\n const c2 = cornerContribution(x2, y2, z2, w2, gi2);\n n2 = c2.n;\n dx2 = c2.dx;\n dy2 = c2.dy;\n dz2 = c2.dz;\n dw2 = c2.dw;\n }\n {\n // Corner 3\n const gi3 = ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]];\n const c3 = cornerContribution(x3, y3, z3, w3, gi3);\n n3 = c3.n;\n dx3 = c3.dx;\n dy3 = c3.dy;\n dz3 = c3.dz;\n dw3 = c3.dw;\n }\n {\n // Corner 4\n const gi4 = ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]];\n const c4 = cornerContribution(x4, y4, z4, w4, gi4);\n n4 = c4.n;\n dx4 = c4.dx;\n dy4 = c4.dy;\n dz4 = c4.dz;\n dw4 = c4.dw;\n }\n\n // Sum contributions\n let value = n0 + n1 + n2 + n3 + n4;\n let dx = dx0 + dx1 + dx2 + dx3 + dx4;\n let dy = dy0 + dy1 + dy2 + dy3 + dy4;\n let dz = dz0 + dz1 + dz2 + dz3 + dz4;\n let dw = dw0 + dw1 + dw2 + dw3 + dw4;\n\n // Scale it to ~[-1, 1], consistent with createNoise4D\n const scale = 27.0;\n value *= scale;\n dx *= scale;\n dy *= scale;\n dz *= scale;\n dw *= scale;\n\n if (!output) {\n return { value, dx, dy, dz, dw };\n }\n // Re-use the output object\n output.value = value;\n output.dx = dx;\n output.dy = dy;\n output.dz = dz;\n output.dw = dw;\n return output;\n };\n}\n","// -----------------------------------------------------\n// \t\t\t\t\t\t Alea\n//\n//\tA port of an algorithm by Johannes Baagøe , 2010\n//\thttp://baagoe.com/en/RandomMusings/javascript/\n//\n//\tOriginal work is under MIT license -\n//\n//\tCopyright (C) 2010 by Johannes Baagøe \n//\n//\tPermission is hereby granted, free of charge, to any person obtaining a copy\n//\tof this software and associated documentation files (the \"Software\"), to deal\n//\tin the Software without restriction, including without limitation the rights\n//\tto use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n//\tcopies of the Software, and to permit persons to whom the Software is\n//\tfurnished to do so, subject to the following conditions:\n//\n//\tThe above copyright notice and this permission notice shall be included in\n//\tall copies or substantial portions of the Software.\n//\n//\tTHE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n//\tIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n//\tFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\n//\tAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n//\tLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n//\tOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n//\tTHE SOFTWARE.\n// -----------------------------------------------------\n\nconst _mashMagicNumber = 0.025_196_032_824_169_38;\nconst _fractionalFix = Number.EPSILON / 2;\n\n/**\n * Equivalent to 2^32\n *\n * @private\n */\nconst _twoPow32 = 0x1_00_00_00_00;\n/**\n * Equivalent to 2^-32\n *\n * @private\n */\nconst _twoPowNegative32 = 2 ** -32;\n\n/**\n * Mash factory\n * returns an alea mash function\n *\n * @private\n * @returns a stateful hash function\n */\nconst _aleaMash = () => {\n\tlet _state = 0xef_c8_24_9d;\n\t/**\n\t * Mash\n\t *\n\t * hash used in alea\n\t *\n\t * @param input - a value to mash\n\t * @returns a hashed version of the input\n\t */\n\tconst _mash = (input: { toString: () => string }): number => {\n\t\tconst inputString = input.toString();\n\t\tfor (var index = 0; index < inputString.length; index++) {\n\t\t\t_state += inputString.charCodeAt(index);\n\t\t\tvar h = _mashMagicNumber * _state;\n\t\t\t_state = h >>> 0;\n\t\t\th -= _state;\n\t\t\th *= _state;\n\t\t\t_state = h >>> 0;\n\t\t\th -= _state;\n\t\t\t_state += h * _twoPow32; // 2^32\n\t\t}\n\t\treturn (_state >>> 0) * _twoPowNegative32; // 2^-32\n\t};\n\n\treturn _mash;\n};\n\n/**\n * aleaState\n *\n * the three 32 bit seeds of alea and a dynamic integration constant\n */\ninterface aleaState {\n\tseed0: number;\n\tseed1: number;\n\tseed2: number;\n\tconstant: number;\n}\n\n/**\n * aleaType\n *\n * The required functions of an alea implementation\n */\nexport interface aleaType {\n\t/**\n\t * @returns a 32 bit number between `[0,1)` like Math.random\n\t */\n\trandom(): number;\n\t/**\n\t * @returns an integer `[0, 2^32)`\n\t */\n\tuint32(): number;\n\t/**\n\t * @returns a pseudo-random 53-bit number between `[0, 1)`, higher precision than random()\n\t */\n\tfract53(): number;\n\t/** @returns Exports the current state of the alea prng*/\n\texportState(): aleaState;\n\t/**\n\t * Imports the current state of the alea prng\n\t *\n\t * @param state - the new state to change the prng to\n\t */\n\timportState(state: Readonly): void;\n}\n\n/**\n * aleaFactory\n *\n * creates a seedable pseduo random number generator\n *\n * @param seed - the seed for the pseudo random generations\n * @returns a pseduo random number generator\n */\nexport const aleaFactory = (\n\tseed = `${Date.now()}` as { toString: () => string }\n): aleaType => {\n\tconst _mash = _aleaMash();\n\n\tconst _state = [_mash(' '), _mash(' '), _mash(' '), 1];\n\n\t_state[0] -= _mash(seed);\n\tif (_state[0] < 0) _state[0] += 1;\n\n\t_state[1] -= _mash(seed);\n\tif (_state[1] < 0) _state[1] += 1;\n\n\t_state[2] -= _mash(seed);\n\tif (_state[2] < 0) _state[2] += 1;\n\n\tconst aleaObject = {\n\t\trandom: () => {\n\t\t\tconst _temporary =\n\t\t\t\t2_091_639 * _state[0] + _state[3] * _twoPowNegative32;\n\t\t\t_state[0] = _state[1];\n\t\t\t_state[1] = _state[2];\n\t\t\treturn (_state[2] =\n\t\t\t\t_temporary - (_state[3] = Math.floor(_temporary)));\n\t\t},\n\t\tuint32: () => aleaObject.random() * _twoPow32,\n\t\tfract53: () => {\n\t\t\treturn (\n\t\t\t\taleaObject.random() +\n\t\t\t\tMath.trunc(aleaObject.random() * 0x20_00_00) * _fractionalFix\n\t\t\t);\n\t\t},\n\t\texportState: (): aleaState => ({\n\t\t\tseed0: _state[0],\n\t\t\tseed1: _state[1],\n\t\t\tseed2: _state[2],\n\t\t\tconstant: _state[3],\n\t\t}),\n\t\timportState: (inputState: Readonly): void => {\n\t\t\t[_state[0], _state[1], _state[2], _state[3]] = [\n\t\t\t\tinputState.seed0,\n\t\t\t\tinputState.seed1,\n\t\t\t\tinputState.seed2,\n\t\t\t\tinputState.constant,\n\t\t\t];\n\t\t},\n\t};\n\treturn aleaObject;\n};\n\nexport const alea = aleaFactory().random;","import {\n type NoiseDerivFunction2D,\n type NoiseDerivFunction3D,\n type NoiseDerivFunction4D,\n NoiseFunction2D,\n NoiseFunction3D,\n NoiseFunction4D,\n createNoise2DWithDerivatives,\n createNoise3DWithDerivatives,\n createNoise4DWithDerivatives,\n createNoise2D,\n createNoise3D,\n createNoise4D,\n} from './simplex-noise/simplex-noise';\n\nimport { aleaFactory } from './alea/alea';\n\nfunction lerp(a: number, b: number, t: number): number {\n return (b - a) * t + a;\n}\n\ntype VectorLikeObject = {\n x: number;\n y: number;\n z?: number;\n w?: number;\n};\n\ntype NoiseParameter = number | UberNoise;\n\ntype NoiseOptions = {\n /**\n * seed for the noise, if not provided, Math.random() will be used,\n *\n * @default Math.random()\n */\n seed?: string | number;\n\n /**\n * minimun value of noise\n *\n * @default -1\n */\n min?: number | UberNoise | NoiseOptions;\n\n /**\n * maximum value of noise\n *\n * @default 1\n */\n max?: number | UberNoise | NoiseOptions;\n\n /**\n * scale of the noise (\"zoom\" in or out)\n *\n * @default 1\n */\n scale?: number | UberNoise | NoiseOptions;\n\n /**\n * power of the noise (1 = linear, 2 = quadratic, etc)\n *\n * @default 1\n */\n power?: number | UberNoise | NoiseOptions;\n\n /**\n * move noise in 2D, 3D or 4D space\n *\n * @default [0, 0, 0, 0]\n */\n shift?: number[];\n\n /**\n * number of layers for fbm noise\n *\n * @default 0\n */\n octaves?: number;\n\n /**\n * how much to multiply amplitude per fbm layer\n *\n * @default 0.5\n */\n gain?: number | UberNoise | NoiseOptions;\n\n /**\n * how much to multiply scale per fbm layer\n *\n * @default 2\n */\n lacunarity?: number | UberNoise | NoiseOptions;\n\n /**\n * array of amplitudes for each fbm layer\n *\n * @default []\n */\n amps?: number[];\n\n /**\n * custom noise options for each fbm layer\n *\n * @default []\n */\n layers?: NoiseOptions[];\n\n /**\n * billowed or rigded noise (0 = normal, 1 = billowed, -1 = ridged)\n *\n * @default 0\n */\n sharpness?: number | UberNoise | NoiseOptions;\n\n /**\n * will turn noise into discrete steps (integer, number of steps)\n *\n * @default 0\n */\n steps?: number | UberNoise | NoiseOptions;\n\n /**\n * how much to warp the noise\n *\n * @default 0\n */\n warp?: number | UberNoise | NoiseOptions;\n\n /**\n * custom noise to warp the noise with\n *\n * @default undefined\n */\n warpNoise?: UberNoise;\n\n /**\n * second warp, can only be used if warp is used too\n *\n * @default 0\n */\n warp2?: number | UberNoise | NoiseOptions;\n /**\n * second warp noise\n *\n * @default undefined\n */\n warpNoise2?: UberNoise;\n\n /**\n * should the noise be inverted\n *\n * @default false\n */\n invert?: boolean;\n\n /**\n * should we take the absolute value of the noise\n *\n * @default false\n */\n abs?: boolean;\n\n /**\n * should we clamp the noise between min and max\n *\n * @default false\n */\n clamp?: boolean;\n\n /**\n * tile the noise in x direction\n *\n * @default false\n */\n tileX?: boolean;\n /**\n * tile the noise in y direction\n *\n * @default false\n */\n tileY?: boolean;\n /**\n * tile the noise in all directions (will override tileX and tileY)\n *\n * @default false\n */\n tile?: boolean;\n\n /**\n * generate noise with derivatives\n *\n * @default false\n */\n withDerivatives?: boolean;\n};\n\nclass UberNoise {\n private noise2D?: NoiseDerivFunction2D | NoiseFunction2D;\n private noise3D?: NoiseDerivFunction3D | NoiseFunction3D;\n private noise4D?: NoiseDerivFunction4D | NoiseFunction4D;\n private seed: string | number;\n\n private _min: NoiseParameter = -1;\n private _max: NoiseParameter = 1;\n\n private _scale: NoiseParameter = 1;\n private _power: NoiseParameter = 1;\n\n private shift: VectorLikeObject = {\n x: 0,\n y: 0,\n };\n\n private octaves = 0;\n private _gain: NoiseParameter = 0.5;\n private _lacunarity: NoiseParameter = 2;\n\n private amps: number[] = [];\n\n private _sharpness: NoiseParameter = 0;\n private _steps: NoiseParameter = 0;\n\n private _warp: NoiseParameter = 0;\n private _warpNoise?: UberNoise;\n private _warp2: NoiseParameter = 0;\n private _warpNoise2?: UberNoise;\n\n private tileX = false;\n private tileY = false;\n\n private position: VectorLikeObject = {\n x: 0,\n y: 0,\n };\n\n private pngr;\n\n private layers: UberNoise[] = [];\n\n constructor(options: NoiseOptions = {}) {\n this.seed = options.seed ?? Math.random();\n this.pngr = aleaFactory(this.seed).random;\n\n this.min = options.min ?? -1;\n this.max = options.max ?? 1;\n\n this.scale = options.scale ?? 1;\n this.power = options.power ?? 1;\n\n this.octaves = options.octaves ?? options.layers?.length ?? 0;\n this.gain = options.gain ?? 0.5;\n this.lacunarity = options.lacunarity ?? 2;\n\n this.sharpness = options.sharpness ?? 0;\n this.steps = options.steps ?? 0;\n\n this.warp = options.warp ?? 0;\n this.warpNoise = options.warpNoise;\n this.warp2 = options.warp2 ?? 0;\n this.warpNoise2 = options.warpNoise2;\n\n this.amps = options.amps ?? [];\n\n this.tileX = options.tileX ?? options.tile ?? false;\n this.tileY = options.tileY ?? options.tile ?? false;\n\n this.createLayers(options);\n }\n\n private createLayers(options: NoiseOptions) {\n // process layers\n for (let i = 0; i < this.octaves; i++) {\n const layerOptions = options.layers?.[i] ?? {};\n if (layerOptions instanceof UberNoise) {\n this.layers[i] = layerOptions;\n continue;\n }\n\n if (layerOptions.seed === undefined) layerOptions.seed = this.pngr();\n this.layers[i] = new UberNoise(layerOptions);\n }\n if (this.layers.length == 0) {\n if (options.withDerivatives) {\n this.noise2D = createNoise2DWithDerivatives(this.pngr);\n this.noise3D = createNoise3DWithDerivatives(this.pngr);\n this.noise4D = createNoise4DWithDerivatives(this.pngr);\n } else {\n this.noise2D = createNoise2D(this.pngr);\n this.noise3D = createNoise3D(this.pngr);\n this.noise4D = createNoise4D(this.pngr);\n }\n }\n }\n\n private warpPosition(warp: number, warpNoise: UberNoise | undefined) {\n if (warp == undefined || warp == 0) return;\n\n if (warpNoise != undefined) warpNoise.position = this.position;\n\n let x = this.position.x,\n y = this.position.y,\n z = this.position.z,\n w = this.position.w;\n\n const noise = warpNoise ?? this;\n const scl = this.scale;\n\n // move some amount so that we don't sample the same point as the original noise\n this.position.x = x + 54.47 * scl;\n this.position.y = y - 34.98 * scl;\n if (z != undefined) this.position.z = z + 21.63 * scl;\n if (w != undefined) this.position.w = w - 67.1 * scl;\n\n x += noise.getFBM() * warp;\n y += noise.getFBM() * warp;\n if (z != undefined) z += noise.getFBM() * warp;\n if (w != undefined) w += noise.getFBM() * warp;\n\n this.position.x = x;\n this.position.y = y;\n this.position.z = z;\n this.position.w = w;\n }\n\n private tilePosition() {\n if (!this.tileX && !this.tileY) return;\n const x = this.position.x;\n const y = this.position.y;\n let newX = 0,\n newY = 0,\n newZ = 0,\n newW = 0;\n if (this.tileX) {\n newX = Math.sin(x * Math.PI * 2);\n newY = Math.cos(x * Math.PI * 2);\n }\n if (this.tileY) {\n newZ = Math.sin(y * Math.PI * 2);\n newW = Math.cos(y * Math.PI * 2);\n }\n if (this.tileX && !this.tileY) {\n this.position.x = newX;\n this.position.y = newY + y;\n } else if (this.tileY && !this.tileX) {\n this.position.x = newZ + x;\n this.position.y = newW;\n } else if (this.tileX && this.tileY) {\n this.position.x = newX;\n this.position.y = newY;\n this.position.z = newZ;\n this.position.w = newW;\n }\n }\n\n private getNoiseValue(\n dimension: 2 | 3 | 4,\n x: number,\n y: number,\n z?: number,\n w?: number,\n ): number {\n if (dimension === 2 && this.noise2D != undefined) {\n const result = this.noise2D(x, y);\n return typeof result === 'number' ? result : result.value;\n } else if (dimension === 3 && this.noise3D != undefined) {\n const result = this.noise3D(x, y, z!);\n return typeof result === 'number' ? result : result.value;\n } else if (dimension === 4 && this.noise4D != undefined) {\n const result = this.noise4D(x, y, z!, w!);\n return typeof result === 'number' ? result : result.value;\n }\n return 0;\n }\n\n private getFBM(): number {\n const x = this.position.x,\n y = this.position.y,\n z = this.position.z,\n w = this.position.w;\n\n const scale = this.scale;\n\n if (this.layers.length == 0) {\n if (z != undefined && w != undefined && this.noise4D != undefined) {\n return this.getNoiseValue(\n 4,\n x * scale,\n y * scale,\n z * scale,\n w * scale,\n );\n }\n if (z != undefined && this.noise3D != undefined) {\n return this.getNoiseValue(3, x * scale, y * scale, z * scale);\n }\n if (this.noise2D != undefined) {\n return this.getNoiseValue(2, x * scale, y * scale);\n }\n return 0;\n }\n\n let maxAmp = 1;\n let amp = 1,\n freq = scale;\n\n const lacunarity = this.lacunarity;\n const gain = this.gain;\n\n let n = 0;\n\n for (let i = 0; i < this.octaves; i++) {\n const layer = this.layers[i];\n\n const layerAmp = this.amps[i] ?? 1;\n\n const value =\n layer.get(\n x * freq,\n y * freq,\n z != undefined ? z * freq : undefined,\n w != undefined ? w * freq : undefined,\n ) *\n amp *\n layerAmp;\n n += value;\n\n amp *= gain;\n freq *= lacunarity;\n maxAmp += amp * layerAmp;\n }\n return n / maxAmp;\n }\n\n private applyShift() {\n const shift = this.shift;\n if (shift !== undefined) {\n this.position.x += shift.x;\n this.position.y += shift.y;\n if (this.position.z) this.position.z += shift.z ?? 0;\n if (this.position.w) this.position.w += shift.w ?? 0;\n }\n }\n\n private applyPower(norm: number) {\n const power = this.power;\n if (power != 1) {\n // convert to [0 - 1], apply power and back to [-1, 1]\n norm = (Math.pow((norm + 1) * 0.5, power) - 0.5) * 2;\n }\n return norm;\n }\n\n private applySharpness(norm: number) {\n const sharpness = this.sharpness;\n if (sharpness != 0) {\n const billow = (Math.abs(norm) - 0.5) * 2;\n const ridged = (0.5 - Math.abs(norm)) * 2;\n\n norm = lerp(norm, billow, Math.max(0, sharpness));\n norm = lerp(norm, ridged, Math.max(0, -sharpness));\n }\n return norm;\n }\n\n private applySteps(norm: number) {\n const steps = this.steps;\n if (steps != 0) {\n // convert from -1 to 1 to 0 to 1\n norm = (norm + 1) * 0.5;\n // apply steps\n norm = Math.floor(norm * steps) / steps;\n // convert back to -1 to 1\n norm = norm * 2 - 1;\n }\n return norm;\n }\n\n private getNoise(\n x: number,\n y: number,\n z: number | undefined = undefined,\n w: number | undefined = undefined,\n ): number {\n // set position\n this.position.x = x;\n this.position.y = y;\n this.position.z = z;\n this.position.w = w;\n\n // apply shift\n this.applyShift();\n\n // apply tiling\n this.tilePosition();\n\n // apply warp\n this.warpPosition(this.warp, this.warpNoise);\n this.warpPosition(this.warp2, this.warpNoise2);\n\n let norm = this.getFBM();\n\n // apply power\n norm = this.applyPower(norm);\n\n // apply sharpness\n norm = this.applySharpness(norm);\n\n // apply steps\n norm = this.applySteps(norm);\n\n return norm;\n }\n\n /**\n * get noise value at position x, y, z, w\n *\n * all transformations will be applied to the noise (shift, warp, power, sharpness, steps, min, max, fmb, etc)\n *\n * either pass in\n * - x, y, z, w as separate arguments\n * - as first argument an object {x, y, z, w}\n * - as first argument an array [x, y, z, w]\n *\n * if y is not provided, it will be set to 0\n * if z is not provided, will use 2D noise\n * if w is not provided, will use 3D noise\n *\n * @param x {number | VectorLikeObject | Array}\n * @param y {number | undefined}\n * @param z {number | undefined}\n * @param w {number | undefined}\n * @returns {number}\n */\n get(\n x: number | VectorLikeObject | Array,\n y: number | undefined = undefined,\n z: number | undefined = undefined,\n w: number | undefined = undefined,\n ): number {\n const norm = this.normalized(x, y, z, w);\n return this.normalizedToMinMax(norm);\n }\n\n /**\n * get normalized noise value at position x, y, z, w\n *\n * all transformations will be applied to the noise (shift, warp, power, sharpness, steps, fmb, etc)\n * EXCEPT min and max, noise will be returned as a value between -1 and 1\n *\n * either pass in\n * - x, y, z, w as separate arguments\n * - as first argument an object {x, y, z, w}\n * - as first argument an array [x, y, z, w]\n *\n * if y is not provided, it will be set to 0\n * if z is not provided, will use 2D noise\n * if w is not provided, will use 3D noise\n *\n * @param x {number | VectorLikeObject | Array}\n * @param y {number | undefined}\n * @param z {number | undefined}\n * @param w {number | undefined}\n * @returns {number}\n */\n normalized(\n x: number | VectorLikeObject | Array,\n y: number | undefined = undefined,\n z: number | undefined = undefined,\n w: number | undefined = undefined,\n ): number {\n // if x is an array, treat it as a vector\n if (Array.isArray(x)) {\n w = x[3];\n z = x[2];\n y = x[1];\n x = x[0];\n } else if (typeof x === 'object') {\n w = x.w;\n z = x.z;\n y = x.y;\n x = x.x;\n }\n // if y is undefined, treat it as 2D noise with y = 0\n y = y ?? 0;\n\n return this.getNoise(x, y, z, w);\n }\n\n /**\n * convert value between min and max to normalized value between -1 and 1\n *\n * @param value {number}\n * @returns {number}\n */\n minMaxToNormalized(value: number): number {\n return ((value - this.min) / (this.max - this.min)) * 2 - 1;\n }\n\n /**\n * convert normlized value to value between min and max\n *\n * @param value {number}\n * @returns {number}\n */\n normalizedToMinMax(value: number): number {\n return (value + 1) * 0.5 * (this.max - this.min) + this.min;\n }\n\n /**\n *\n * shift the noise in 2D, 3D or 4D space, will be added to the position\n *\n * if called multiple times, the shifts will be added\n *\n * returns the UberNoise object for chaining\n *\n * @param x {number}\n * @param y {number}\n * @param z {number | undefined}\n * @param w {number | undefined}\n * @returns {UberNoise}\n */\n move(\n x: number,\n y: number,\n z: number | undefined = undefined,\n w: number | undefined = undefined,\n ) {\n if (!this.shift) {\n this.shift = { x, y, z, w };\n return;\n }\n\n this.shift.x += x;\n this.shift.y += y;\n if (z != undefined) {\n this.shift.z = (this.shift.z ?? 0) + z;\n }\n if (w != undefined) {\n this.shift.w = (this.shift.w ?? 0) + w;\n }\n\n return this;\n }\n\n private checkParameterInput(\n value: number | UberNoise | NoiseOptions,\n ): UberNoise | number {\n if (typeof value === 'object' && !(value instanceof UberNoise)) {\n if (value.seed === undefined) {\n value.seed = this.pngr();\n }\n value = new UberNoise(value);\n }\n return value;\n }\n\n private getParameter(value: NoiseParameter): number {\n if (typeof value === 'number') {\n return value;\n }\n return value.get(this.position);\n }\n\n // getter and setter for min and max\n get min(): number {\n return this.getParameter(this._min);\n }\n set min(value: number | UberNoise | NoiseOptions) {\n this._min = this.checkParameterInput(value);\n }\n get max(): number {\n return this.getParameter(this._max);\n }\n set max(value: number | UberNoise | NoiseOptions) {\n this._max = this.checkParameterInput(value);\n }\n\n // getter and setter for scale and power\n get scale(): number {\n return this.getParameter(this._scale);\n }\n set scale(value: number | UberNoise | NoiseOptions) {\n this._scale = this.checkParameterInput(value);\n }\n get power(): number {\n return this.getParameter(this._power);\n }\n set power(value: number | UberNoise | NoiseOptions) {\n this._power = this.checkParameterInput(value);\n }\n\n // getter and setter for gain and lacunarity\n get gain(): number {\n return this.getParameter(this._gain);\n }\n set gain(value: number | UberNoise | NoiseOptions) {\n this._gain = this.checkParameterInput(value);\n }\n get lacunarity(): number {\n return this.getParameter(this._lacunarity);\n }\n set lacunarity(value: number | UberNoise | NoiseOptions) {\n this._lacunarity = this.checkParameterInput(value);\n }\n\n get sharpness(): number {\n return this.getParameter(this._sharpness);\n }\n set sharpness(value: number | UberNoise | NoiseOptions) {\n this._sharpness = this.checkParameterInput(value);\n }\n get steps(): number {\n return Math.round(this.getParameter(this._steps));\n }\n set steps(value: number | UberNoise | NoiseOptions) {\n this._steps = this.checkParameterInput(value);\n }\n\n get warp(): number {\n return this.getParameter(this._warp);\n }\n set warp(value: number | UberNoise | NoiseOptions) {\n this._warp = this.checkParameterInput(value);\n }\n get warpNoise(): UberNoise | undefined {\n return this._warpNoise;\n }\n set warpNoise(value: UberNoise | NoiseOptions | undefined) {\n if (value == undefined) {\n this._warpNoise = undefined;\n return;\n }\n\n const processed = this.checkParameterInput(value);\n if (processed instanceof UberNoise) {\n this._warpNoise = processed;\n }\n }\n get warp2(): number {\n return this.getParameter(this._warp2);\n }\n set warp2(value: number | UberNoise | NoiseOptions) {\n this._warp2 = this.checkParameterInput(value);\n }\n get warpNoise2(): UberNoise | undefined {\n return this._warpNoise2;\n }\n set warpNoise2(value: UberNoise | NoiseOptions | undefined) {\n if (value == undefined) {\n this._warpNoise2 = undefined;\n return;\n }\n\n const processed = this.checkParameterInput(value);\n if (processed instanceof UberNoise) {\n this._warpNoise2 = processed;\n }\n }\n}\n\nif (!globalThis.UberNoise) {\n globalThis.UberNoise = UberNoise;\n globalThis.alea = aleaFactory;\n}\n\ndeclare global {\n var UberNoise: typeof import('./uber-noise').UberNoise;\n var alea: typeof import('./alea/alea').aleaFactory;\n}\n\nexport {\n UberNoise,\n type NoiseOptions,\n type NoiseParameter,\n type VectorLikeObject as VectorObject,\n UberNoise as noise,\n aleaFactory as 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