| /* |
| Copyright (C) 2013 Andrew Magill |
| |
| This software is provided 'as-is', without any express or implied |
| warranty. In no event will the authors be held liable for any damages |
| arising from the use of this software. |
| |
| Permission is granted to anyone to use this software for any purpose, |
| including commercial applications, and to alter it and redistribute it |
| freely, subject to the following restrictions: |
| |
| 1. The origin of this software must not be misrepresented; you must not |
| claim that you wrote the original software. If you use this software |
| in a product, an acknowledgment in the product documentation would be |
| appreciated but is not required. |
| 2. Altered source versions must be plainly marked as such, and must not be |
| misrepresented as being the original software. |
| 3. This notice may not be removed or altered from any source distribution. |
| |
| */ |
| |
| part of vector_math; |
| |
| /* |
| * This is based on the implementation of Simplex Noise by Stefan Gustavson |
| * found at: http://webstaff.itn.liu.se/~stegu/simplexnoise/SimplexNoise.java |
| */ |
| |
| @Deprecated('This API will be removed ' |
| '(see https:github.com/google/vector_math.dart/issues/270)') |
| class SimplexNoise { |
| static final List<List<double>> _grad3 = <List<double>>[ |
| <double>[1.0, 1.0, 0.0], |
| <double>[-1.0, 1.0, 0.0], |
| <double>[1.0, -1.0, 0.0], |
| <double>[-1.0, -1.0, 0.0], |
| <double>[1.0, 0.0, 1.0], |
| <double>[-1.0, 0.0, 1.0], |
| <double>[1.0, 0.0, -1.0], |
| <double>[-1.0, 0.0, -1.0], |
| <double>[0.0, 1.0, 1.0], |
| <double>[0.0, -1.0, 1.0], |
| <double>[0.0, 1.0, -1.0], |
| <double>[0.0, -1.0, -1.0] |
| ]; |
| |
| static final List<List<double>> _grad4 = <List<double>>[ |
| <double>[0.0, 1.0, 1.0, 1.0], |
| <double>[0.0, 1.0, 1.0, -1.0], |
| <double>[0.0, 1.0, -1.0, 1.0], |
| <double>[0.0, 1.0, -1.0, -1.0], |
| <double>[0.0, -1.0, 1.0, 1.0], |
| <double>[0.0, -1.0, 1.0, -1.0], |
| <double>[0.0, -1.0, -1.0, 1.0], |
| <double>[0.0, -1.0, -1.0, -1.0], |
| <double>[1.0, 0.0, 1.0, 1.0], |
| <double>[1.0, 0.0, 1.0, -1.0], |
| <double>[1.0, 0.0, -1.0, 1.0], |
| <double>[1.0, 0.0, -1.0, -1.0], |
| <double>[-1.0, 0.0, 1.0, 1.0], |
| <double>[-1.0, 0.0, 1.0, -1.0], |
| <double>[-1.0, 0.0, -1.0, 1.0], |
| <double>[-1.0, 0.0, -1.0, -1.0], |
| <double>[1.0, 1.0, 0.0, 1.0], |
| <double>[1.0, 1.0, 0.0, -1.0], |
| <double>[1.0, -1.0, 0.0, 1.0], |
| <double>[1.0, -1.0, 0.0, -1.0], |
| <double>[-1.0, 1.0, 0.0, 1.0], |
| <double>[-1.0, 1.0, 0.0, -1.0], |
| <double>[-1.0, -1.0, 0.0, 1.0], |
| <double>[-1.0, -1.0, 0.0, -1.0], |
| <double>[1.0, 1.0, 1.0, 0.0], |
| <double>[1.0, 1.0, -1.0, 0.0], |
| <double>[1.0, -1.0, 1.0, 0.0], |
| <double>[1.0, -1.0, -1.0, 0.0], |
| <double>[-1.0, 1.0, 1.0, 0.0], |
| <double>[-1.0, 1.0, -1.0, 0.0], |
| <double>[-1.0, -1.0, 1.0, 0.0], |
| <double>[-1.0, -1.0, -1.0, 0.0] |
| ]; |
| |
| // To remove the need for index wrapping, double the permutation table length |
| late final List<int> _perm; |
| late final List<int> _permMod12; |
| |
| // Skewing and unskewing factors for 2, 3, and 4 dimensions |
| static final _F2 = 0.5 * (math.sqrt(3.0) - 1.0); |
| static final _G2 = (3.0 - math.sqrt(3.0)) / 6.0; |
| static const double _f3 = 1.0 / 3.0; |
| static const double _g3 = 1.0 / 6.0; |
| static final _F4 = (math.sqrt(5.0) - 1.0) / 4.0; |
| static final _G4 = (5.0 - math.sqrt(5.0)) / 20.0; |
| |
| double _dot2(List<double> g, double x, double y) => g[0] * x + g[1] * y; |
| |
| double _dot3(List<double> g, double x, double y, double z) => |
| g[0] * x + g[1] * y + g[2] * z; |
| |
| double _dot4(List<double> g, double x, double y, double z, double w) => |
| g[0] * x + g[1] * y + g[2] * z + g[3] * w; |
| |
| SimplexNoise([math.Random? r]) { |
| r ??= math.Random(); |
| final p = List<int>.generate(256, (_) => r!.nextInt(256), growable: false); |
| _perm = List<int>.generate(p.length * 2, (int i) => p[i % p.length], |
| growable: false); |
| _permMod12 = List<int>.generate(_perm.length, (int i) => _perm[i] % 12, |
| growable: false); |
| } |
| |
| double noise2D(double xin, double yin) { |
| double n0, n1, n2; // Noise contributions from the three corners |
| // Skew the input space to determine which simplex cell we're in |
| final s = (xin + yin) * _F2; // Hairy factor for 2D |
| final i = (xin + s).floor(); |
| final j = (yin + s).floor(); |
| final t = (i + j) * _G2; |
| final X0 = i - t; // Unskew the cell origin back to (x,y) space |
| final Y0 = j - t; |
| final x0 = xin - X0; // The x,y distances from the cell origin |
| final y0 = yin - Y0; |
| // For the 2D case, the simplex shape is an equilateral triangle. |
| // Determine which simplex we are in. |
| int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords |
| if (x0 > y0) { |
| i1 = 1; |
| j1 = 0; |
| } // lower triangle, XY order: (0,0)->(1,0)->(1,1) |
| else { |
| i1 = 0; |
| j1 = 1; |
| } // upper triangle, YX order: (0,0)->(0,1)->(1,1) |
| // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and |
| // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where |
| // c = (3-sqrt(3))/6 |
| final x1 = |
| x0 - i1 + _G2; // Offsets for middle corner in (x,y) unskewed coords |
| final y1 = y0 - j1 + _G2; |
| final x2 = x0 - |
| 1.0 + |
| 2.0 * _G2; // Offsets for last corner in (x,y) unskewed coords |
| final y2 = y0 - 1.0 + 2.0 * _G2; |
| // Work out the hashed gradient indices of the three simplex corners |
| final ii = i & 255; |
| final jj = j & 255; |
| final gi0 = _permMod12[ii + _perm[jj]]; |
| final gi1 = _permMod12[ii + i1 + _perm[jj + j1]]; |
| final gi2 = _permMod12[ii + 1 + _perm[jj + 1]]; |
| // Calculate the contribution from the three corners |
| var t0 = 0.5 - x0 * x0 - y0 * y0; |
| if (t0 < 0) { |
| n0 = 0.0; |
| } else { |
| t0 *= t0; |
| n0 = t0 * |
| t0 * |
| _dot2(_grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient |
| } |
| var t1 = 0.5 - x1 * x1 - y1 * y1; |
| if (t1 < 0) { |
| n1 = 0.0; |
| } else { |
| t1 *= t1; |
| n1 = t1 * t1 * _dot2(_grad3[gi1], x1, y1); |
| } |
| var t2 = 0.5 - x2 * x2 - y2 * y2; |
| if (t2 < 0) { |
| n2 = 0.0; |
| } else { |
| t2 *= t2; |
| n2 = t2 * t2 * _dot2(_grad3[gi2], x2, y2); |
| } |
| // Add contributions from each corner to get the final noise value. |
| // The result is scaled to return values in the interval [-1,1]. |
| return 70.0 * (n0 + n1 + n2); |
| } |
| |
| // 3D simplex noise |
| double noise3D(double xin, double yin, double zin) { |
| double n0, n1, n2, n3; // Noise contributions from the four corners |
| // Skew the input space to determine which simplex cell we're in |
| final s = |
| (xin + yin + zin) * _f3; // Very nice and simple skew factor for 3D |
| final i = (xin + s).floor(); |
| final j = (yin + s).floor(); |
| final k = (zin + s).floor(); |
| final t = (i + j + k) * _g3; |
| final X0 = i - t; // Unskew the cell origin back to (x,y,z) space |
| final Y0 = j - t; |
| final Z0 = k - t; |
| final x0 = xin - X0; // The x,y,z distances from the cell origin |
| final y0 = yin - Y0; |
| final z0 = zin - Z0; |
| // For the 3D case, the simplex shape is a slightly irregular tetrahedron. |
| // Determine which simplex we are in. |
| int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords |
| int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords |
| if (x0 >= y0) { |
| if (y0 >= z0) { |
| i1 = 1; |
| j1 = 0; |
| k1 = 0; |
| i2 = 1; |
| j2 = 1; |
| k2 = 0; |
| } // X Y Z order |
| else if (x0 >= z0) { |
| i1 = 1; |
| j1 = 0; |
| k1 = 0; |
| i2 = 1; |
| j2 = 0; |
| k2 = 1; |
| } // X Z Y order |
| else { |
| i1 = 0; |
| j1 = 0; |
| k1 = 1; |
| i2 = 1; |
| j2 = 0; |
| k2 = 1; |
| } // Z X Y order |
| } else { |
| // x0<y0 |
| if (y0 < z0) { |
| i1 = 0; |
| j1 = 0; |
| k1 = 1; |
| i2 = 0; |
| j2 = 1; |
| k2 = 1; |
| } // Z Y X order |
| else if (x0 < z0) { |
| i1 = 0; |
| j1 = 1; |
| k1 = 0; |
| i2 = 0; |
| j2 = 1; |
| k2 = 1; |
| } // Y Z X order |
| else { |
| i1 = 0; |
| j1 = 1; |
| k1 = 0; |
| i2 = 1; |
| j2 = 1; |
| k2 = 0; |
| } // Y X Z order |
| } |
| // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), |
| // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and |
| // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where |
| // c = 1/6. |
| final x1 = x0 - i1 + _g3; // Offsets for second corner in (x,y,z) coords |
| final y1 = y0 - j1 + _g3; |
| final z1 = z0 - k1 + _g3; |
| final x2 = |
| x0 - i2 + 2.0 * _g3; // Offsets for third corner in (x,y,z) coords |
| final y2 = y0 - j2 + 2.0 * _g3; |
| final z2 = z0 - k2 + 2.0 * _g3; |
| final x3 = |
| x0 - 1.0 + 3.0 * _g3; // Offsets for last corner in (x,y,z) coords |
| final y3 = y0 - 1.0 + 3.0 * _g3; |
| final z3 = z0 - 1.0 + 3.0 * _g3; |
| // Work out the hashed gradient indices of the four simplex corners |
| final ii = i & 255; |
| final jj = j & 255; |
| final kk = k & 255; |
| final gi0 = _permMod12[ii + _perm[jj + _perm[kk]]]; |
| final gi1 = _permMod12[ii + i1 + _perm[jj + j1 + _perm[kk + k1]]]; |
| final gi2 = _permMod12[ii + i2 + _perm[jj + j2 + _perm[kk + k2]]]; |
| final gi3 = _permMod12[ii + 1 + _perm[jj + 1 + _perm[kk + 1]]]; |
| // Calculate the contribution from the four corners |
| var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0; |
| if (t0 < 0) { |
| n0 = 0.0; |
| } else { |
| t0 *= t0; |
| n0 = t0 * t0 * _dot3(_grad3[gi0], x0, y0, z0); |
| } |
| var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1; |
| if (t1 < 0) { |
| n1 = 0.0; |
| } else { |
| t1 *= t1; |
| n1 = t1 * t1 * _dot3(_grad3[gi1], x1, y1, z1); |
| } |
| var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2; |
| if (t2 < 0) { |
| n2 = 0.0; |
| } else { |
| t2 *= t2; |
| n2 = t2 * t2 * _dot3(_grad3[gi2], x2, y2, z2); |
| } |
| var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3; |
| if (t3 < 0) { |
| n3 = 0.0; |
| } else { |
| t3 *= t3; |
| n3 = t3 * t3 * _dot3(_grad3[gi3], x3, y3, z3); |
| } |
| // Add contributions from each corner to get the final noise value. |
| // The result is scaled to stay just inside [-1,1] |
| return 32.0 * (n0 + n1 + n2 + n3); |
| } |
| |
| // 4D simplex noise, better simplex rank ordering method 2012-03-09 |
| double noise4D(double x, double y, double z, double w) { |
| double n0, n1, n2, n3, n4; // Noise contributions from the five corners |
| // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in |
| final s = (x + y + z + w) * _F4; // Factor for 4D skewing |
| final i = (x + s).floor(); |
| final j = (y + s).floor(); |
| final k = (z + s).floor(); |
| final l = (w + s).floor(); |
| final t = (i + j + k + l) * _G4; // Factor for 4D unskewing |
| final X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space |
| final Y0 = j - t; |
| final Z0 = k - t; |
| final W0 = l - t; |
| final x0 = x - X0; // The x,y,z,w distances from the cell origin |
| final y0 = y - Y0; |
| final z0 = z - Z0; |
| final w0 = w - W0; |
| // For the 4D case, the simplex is a 4D shape I won't even try to describe. |
| // To find out which of the 24 possible simplices we're in, we need to |
| // determine the magnitude ordering of x0, y0, z0 and w0. |
| // Six pair-wise comparisons are performed between each possible pair |
| // of the four coordinates, and the results are used to rank the numbers. |
| var rankx = 0; |
| var ranky = 0; |
| var rankz = 0; |
| var rankw = 0; |
| if (x0 > y0) { |
| rankx++; |
| } else { |
| ranky++; |
| } |
| if (x0 > z0) { |
| rankx++; |
| } else { |
| rankz++; |
| } |
| if (x0 > w0) { |
| rankx++; |
| } else { |
| rankw++; |
| } |
| if (y0 > z0) { |
| ranky++; |
| } else { |
| rankz++; |
| } |
| if (y0 > w0) { |
| ranky++; |
| } else { |
| rankw++; |
| } |
| if (z0 > w0) { |
| rankz++; |
| } else { |
| rankw++; |
| } |
| int i1, j1, k1, l1; // The integer offsets for the second simplex corner |
| int i2, j2, k2, l2; // The integer offsets for the third simplex corner |
| int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner |
| // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. |
| // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w |
| // impossible. Only the 24 indices which have non-zero entries make any sense. |
| // We use a thresholding to set the coordinates in turn from the largest magnitude. |
| // Rank 3 denotes the largest coordinate. |
| i1 = rankx >= 3 ? 1 : 0; |
| j1 = ranky >= 3 ? 1 : 0; |
| k1 = rankz >= 3 ? 1 : 0; |
| l1 = rankw >= 3 ? 1 : 0; |
| // Rank 2 denotes the second largest coordinate. |
| i2 = rankx >= 2 ? 1 : 0; |
| j2 = ranky >= 2 ? 1 : 0; |
| k2 = rankz >= 2 ? 1 : 0; |
| l2 = rankw >= 2 ? 1 : 0; |
| // Rank 1 denotes the second smallest coordinate. |
| i3 = rankx >= 1 ? 1 : 0; |
| j3 = ranky >= 1 ? 1 : 0; |
| k3 = rankz >= 1 ? 1 : 0; |
| l3 = rankw >= 1 ? 1 : 0; |
| // The fifth corner has all coordinate offsets = 1, so no need to compute that. |
| final x1 = x0 - i1 + _G4; // Offsets for second corner in (x,y,z,w) coords |
| final y1 = y0 - j1 + _G4; |
| final z1 = z0 - k1 + _G4; |
| final w1 = w0 - l1 + _G4; |
| final x2 = |
| x0 - i2 + 2.0 * _G4; // Offsets for third corner in (x,y,z,w) coords |
| final y2 = y0 - j2 + 2.0 * _G4; |
| final z2 = z0 - k2 + 2.0 * _G4; |
| final w2 = w0 - l2 + 2.0 * _G4; |
| final x3 = |
| x0 - i3 + 3.0 * _G4; // Offsets for fourth corner in (x,y,z,w) coords |
| final y3 = y0 - j3 + 3.0 * _G4; |
| final z3 = z0 - k3 + 3.0 * _G4; |
| final w3 = w0 - l3 + 3.0 * _G4; |
| final x4 = |
| x0 - 1.0 + 4.0 * _G4; // Offsets for last corner in (x,y,z,w) coords |
| final y4 = y0 - 1.0 + 4.0 * _G4; |
| final z4 = z0 - 1.0 + 4.0 * _G4; |
| final w4 = w0 - 1.0 + 4.0 * _G4; |
| // Work out the hashed gradient indices of the five simplex corners |
| final ii = i & 255; |
| final jj = j & 255; |
| final kk = k & 255; |
| final ll = l & 255; |
| final gi0 = _perm[ii + _perm[jj + _perm[kk + _perm[ll]]]] % 32; |
| final gi1 = |
| _perm[ii + i1 + _perm[jj + j1 + _perm[kk + k1 + _perm[ll + l1]]]] % 32; |
| final gi2 = |
| _perm[ii + i2 + _perm[jj + j2 + _perm[kk + k2 + _perm[ll + l2]]]] % 32; |
| final gi3 = |
| _perm[ii + i3 + _perm[jj + j3 + _perm[kk + k3 + _perm[ll + l3]]]] % 32; |
| final gi4 = |
| _perm[ii + 1 + _perm[jj + 1 + _perm[kk + 1 + _perm[ll + 1]]]] % 32; |
| // Calculate the contribution from the five corners |
| var t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0; |
| if (t0 < 0) { |
| n0 = 0.0; |
| } else { |
| t0 *= t0; |
| n0 = t0 * t0 * _dot4(_grad4[gi0], x0, y0, z0, w0); |
| } |
| var t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1; |
| if (t1 < 0) { |
| n1 = 0.0; |
| } else { |
| t1 *= t1; |
| n1 = t1 * t1 * _dot4(_grad4[gi1], x1, y1, z1, w1); |
| } |
| var t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2; |
| if (t2 < 0) { |
| n2 = 0.0; |
| } else { |
| t2 *= t2; |
| n2 = t2 * t2 * _dot4(_grad4[gi2], x2, y2, z2, w2); |
| } |
| var t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3; |
| if (t3 < 0) { |
| n3 = 0.0; |
| } else { |
| t3 *= t3; |
| n3 = t3 * t3 * _dot4(_grad4[gi3], x3, y3, z3, w3); |
| } |
| var t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4; |
| if (t4 < 0) { |
| n4 = 0.0; |
| } else { |
| t4 *= t4; |
| n4 = t4 * t4 * _dot4(_grad4[gi4], x4, y4, z4, w4); |
| } |
| // Sum up and scale the result to cover the range [-1,1] |
| return 27.0 * (n0 + n1 + n2 + n3 + n4); |
| } |
| } |