/*--------------------------------------------------------------------

 Simplex Noise C++ implementation

 Based on a public domain code by Stefan Gustavson.

 (The original header is below)

--------------------------------------------------------------------*/

/*-- start of the original header --*/

/*

* A speed-improved simplex noise algorithm for 2D, 3D and 4D in Java.

*

* Based on example code by Stefan Gustavson (stegu@itn.liu.se).

* Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).

* Better rank ordering method by Stefan Gustavson in 2012.

*

* This could be speeded up even further, but it's useful as it is.

*

* Version 2012-03-09

*

* This code was placed in the public domain by its original author,

* Stefan Gustavson. You may use it as you see fit, but

* attribution is appreciated.

*

*/

/*-- end of the original header --*/

#include "iwa_simplexnoise.h"

#include <math.h>  //sqrt</math.h>

#include <iostream></iostream>

namespace {

static Grad grad3[] = {Grad(1, 1, 0),   Grad(-1, 1, 0),  Grad(1, -1, 0),

                       Grad(-1, -1, 0), Grad(1, 0, 1),   Grad(-1, 0, 1),

                       Grad(1, 0, -1),  Grad(-1, 0, -1), Grad(0, 1, 1),

                       Grad(0, -1, 1),  Grad(0, 1, -1),  Grad(0, -1, -1)};

static Grad grad4[] = {

    Grad(0, 1, 1, 1),    Grad(0, 1, 1, -1),   Grad(0, 1, -1, 1),

    Grad(0, 1, -1, -1),  Grad(0, -1, 1, 1),   Grad(0, -1, 1, -1),

    Grad(0, -1, -1, 1),  Grad(0, -1, -1, -1), Grad(1, 0, 1, 1),

    Grad(1, 0, 1, -1),   Grad(1, 0, -1, 1),   Grad(1, 0, -1, -1),

    Grad(-1, 0, 1, 1),   Grad(-1, 0, 1, -1),  Grad(-1, 0, -1, 1),

    Grad(-1, 0, -1, -1), Grad(1, 1, 0, 1),    Grad(1, 1, 0, -1),

    Grad(1, -1, 0, 1),   Grad(1, -1, 0, -1),  Grad(-1, 1, 0, 1),

    Grad(-1, 1, 0, -1),  Grad(-1, -1, 0, 1),  Grad(-1, -1, 0, -1),

    Grad(1, 1, 1, 0),    Grad(1, 1, -1, 0),   Grad(1, -1, 1, 0),

    Grad(1, -1, -1, 0),  Grad(-1, 1, 1, 0),   Grad(-1, 1, -1, 0),

    Grad(-1, -1, 1, 0),  Grad(-1, -1, -1, 0)};

// To remove the need for index wrapping, double the permutation table length

static short perm[512] = {

    151, 160, 137, 91,  90,  15,  131, 13,  201, 95,  96,  53,  194, 233, 7,

    225, 140, 36,  103, 30,  69,  142, 8,   99,  37,  240, 21,  10,  23,  190,

    6,   148, 247, 120, 234, 75,  0,   26,  197, 62,  94,  252, 219, 203, 117,

    35,  11,  32,  57,  177, 33,  88,  237, 149, 56,  87,  174, 20,  125, 136,

    171, 168, 68,  175, 74,  165, 71,  134, 139, 48,  27,  166, 77,  146, 158,

    231, 83,  111, 229, 122, 60,  211, 133, 230, 220, 105, 92,  41,  55,  46,

    245, 40,  244, 102, 143, 54,  65,  25,  63,  161, 1,   216, 80,  73,  209,

    76,  132, 187, 208, 89,  18,  169, 200, 196, 135, 130, 116, 188, 159, 86,

    164, 100, 109, 198, 173, 186, 3,   64,  52,  217, 226, 250, 124, 123, 5,

    202, 38,  147, 118, 126, 255, 82,  85,  212, 207, 206, 59,  227, 47,  16,

    58,  17,  182, 189, 28,  42,  223, 183, 170, 213, 119, 248, 152, 2,   44,

    154, 163, 70,  221, 153, 101, 155, 167, 43,  172, 9,   129, 22,  39,  253,

    19,  98,  108, 110, 79,  113, 224, 232, 178, 185, 112, 104, 218, 246, 97,

    228, 251, 34,  242, 193, 238, 210, 144, 12,  191, 179, 162, 241, 81,  51,

    145, 235, 249, 14,  239, 107, 49,  192, 214, 31,  181, 199, 106, 157, 184,

    84,  204, 176, 115, 121, 50,  45,  127, 4,   150, 254, 138, 236, 205, 93,

    222, 114, 67,  29,  24,  72,  243, 141, 128, 195, 78,  66,  215, 61,  156,

    180,

    151, 160, 137, 91,  90,  15,  131, 13,  201, 95,  96,  53,  194, 233, 7,

    225, 140, 36,  103, 30,  69,  142, 8,   99,  37,  240, 21,  10,  23,  190,

    6,   148, 247, 120, 234, 75,  0,   26,  197, 62,  94,  252, 219, 203, 117,

    35,  11,  32,  57,  177, 33,  88,  237, 149, 56,  87,  174, 20,  125, 136,

    171, 168, 68,  175, 74,  165, 71,  134, 139, 48,  27,  166, 77,  146, 158,

    231, 83,  111, 229, 122, 60,  211, 133, 230, 220, 105, 92,  41,  55,  46,

    245, 40,  244, 102, 143, 54,  65,  25,  63,  161, 1,   216, 80,  73,  209,

    76,  132, 187, 208, 89,  18,  169, 200, 196, 135, 130, 116, 188, 159, 86,

    164, 100, 109, 198, 173, 186, 3,   64,  52,  217, 226, 250, 124, 123, 5,

    202, 38,  147, 118, 126, 255, 82,  85,  212, 207, 206, 59,  227, 47,  16,

    58,  17,  182, 189, 28,  42,  223, 183, 170, 213, 119, 248, 152, 2,   44,

    154, 163, 70,  221, 153, 101, 155, 167, 43,  172, 9,   129, 22,  39,  253,

    19,  98,  108, 110, 79,  113, 224, 232, 178, 185, 112, 104, 218, 246, 97,

    228, 251, 34,  242, 193, 238, 210, 144, 12,  191, 179, 162, 241, 81,  51,

    145, 235, 249, 14,  239, 107, 49,  192, 214, 31,  181, 199, 106, 157, 184,

    84,  204, 176, 115, 121, 50,  45,  127, 4,   150, 254, 138, 236, 205, 93,

    222, 114, 67,  29,  24,  72,  243, 141, 128, 195, 78,  66,  215, 61,  156,

    180};

static short permMod12[512] = {

    7,  4,  5,  7, 6, 3,  11, 1,  9,  11, 0,  5, 2, 5,  7,  9,  8,  0,  7,

    6,  9,  10, 8, 3, 1,  0,  9,  10, 11, 10, 6, 4, 7,  0,  6,  3,  0,  2,

    5,  2,  10, 0, 3, 11, 9,  11, 11, 8,  9,  9, 9, 4,  9,  5,  8,  3,  6,

    8,  5,  4,  3, 0, 8,  7,  2,  9,  11, 2,  7, 0, 3,  10, 5,  2,  2,  3,

    11, 3,  1,  2, 0, 7,  1,  2,  4,  9,  8,  5, 7, 10, 5,  4,  4,  6,  11,

    6,  5,  1,  3, 5, 1,  0,  8,  1,  5,  4,  0, 7, 4,  5,  6,  1,  8,  4,

    3,  10, 8,  8, 3, 2,  8,  4,  1,  6,  5,  6, 3, 4,  4,  1,  10, 10, 4,

    3,  5,  10, 2, 3, 10, 6,  3,  10, 1,  8,  3, 2, 11, 11, 11, 4,  10, 5,

    2,  9,  4,  6, 7, 3,  2,  9,  11, 8,  8,  2, 8, 10, 7,  10, 5,  9,  5,

    11, 11, 7,  4, 9, 9,  10, 3,  1,  7,  2,  0, 2, 7,  5,  8,  4,  10, 5,

    4,  8,  2,  6, 1, 0,  11, 10, 2,  1,  10, 6, 0, 0,  11, 11, 6,  1,  9,

    3,  1,  7,  9, 2, 11, 11, 1,  0,  10, 7,  1, 7, 10, 1,  4,  0,  0,  8,

    7,  1,  2,  9, 7, 4,  6,  2,  6,  8,  1,  9, 6, 6,  7,  5,  0,  0,  3,

    9,  8,  3,  6, 6, 11, 1,  0,  0,

    7,  4,  5,  7, 6, 3,  11, 1,  9,  11, 0,  5, 2, 5,  7,  9,  8,  0,  7,

    6,  9,  10, 8, 3, 1,  0,  9,  10, 11, 10, 6, 4, 7,  0,  6,  3,  0,  2,

    5,  2,  10, 0, 3, 11, 9,  11, 11, 8,  9,  9, 9, 4,  9,  5,  8,  3,  6,

    8,  5,  4,  3, 0, 8,  7,  2,  9,  11, 2,  7, 0, 3,  10, 5,  2,  2,  3,

    11, 3,  1,  2, 0, 7,  1,  2,  4,  9,  8,  5, 7, 10, 5,  4,  4,  6,  11,

    6,  5,  1,  3, 5, 1,  0,  8,  1,  5,  4,  0, 7, 4,  5,  6,  1,  8,  4,

    3,  10, 8,  8, 3, 2,  8,  4,  1,  6,  5,  6, 3, 4,  4,  1,  10, 10, 4,

    3,  5,  10, 2, 3, 10, 6,  3,  10, 1,  8,  3, 2, 11, 11, 11, 4,  10, 5,

    2,  9,  4,  6, 7, 3,  2,  9,  11, 8,  8,  2, 8, 10, 7,  10, 5,  9,  5,

    11, 11, 7,  4, 9, 9,  10, 3,  1,  7,  2,  0, 2, 7,  5,  8,  4,  10, 5,

    4,  8,  2,  6, 1, 0,  11, 10, 2,  1,  10, 6, 0, 0,  11, 11, 6,  1,  9,

    3,  1,  7,  9, 2, 11, 11, 1,  0,  10, 7,  1, 7, 10, 1,  4,  0,  0,  8,

    7,  1,  2,  9, 7, 4,  6,  2,  6,  8,  1,  9, 6, 6,  7,  5,  0,  0,  3,

    9,  8,  3,  6, 6, 11, 1,  0,  0};

};

//----------------------------------------

// 2D simplex noise

//----------------------------------------

double SimplexNoise::noise(double xin, double yin) {

  // Skewing and unskewing factors for 2 dimensions

  static const double F2 = 0.5 * (sqrt(3.0) - 1.0);

  static const double G2 = (3.0 - sqrt(3.0)) / 6.0;

  double n0, n1, n2;  // Noise contributions from the three corners

  // Skew the input space to determine which simplex cell we're in

  double s  = (xin + yin) * F2;  // Hairy factor for 2D

  int i     = fastfloor(xin + s);

  int j     = fastfloor(yin + s);

  double t  = (i + j) * G2;

  double X0 = i - t;  // Unskew the cell origin back to (x,y) space

  double Y0 = j - t;

  double x0 = xin - X0;  // The x,y distances from the cell origin

  double 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

  double x1 =

      x0 - i1 + G2;  // Offsets for middle corner in (x,y) unskewed coords

  double y1 = y0 - j1 + G2;

  double x2 =

      x0 - 1.0 + 2.0 * G2;  // Offsets for last corner in (x,y) unskewed coords

  double y2 = y0 - 1.0 + 2.0 * G2;

  // Work out the hashed gradient indices of the three simplex corners

  int ii  = i & 255;

  int jj  = j & 255;

  int gi0 = permMod12[ii + perm[jj]];

  int gi1 = permMod12[ii + i1 + perm[jj + j1]];

  int gi2 = permMod12[ii + 1 + perm[jj + 1]];

  // Calculate the contribution from the three corners

  double t0 = 0.5 - x0 * x0 - y0 * y0;

  if (t0 < 0)

    n0 = 0.0;

  else {

    t0 *= t0;

    n0 = t0 * t0 *

         dot(grad3[gi0], x0, y0);  // (x,y) of grad3 used for 2D gradient

  }

  double t1 = 0.5 - x1 * x1 - y1 * y1;

  if (t1 < 0)

    n1 = 0.0;

  else {

    t1 *= t1;

    n1 = t1 * t1 * dot(grad3[gi1], x1, y1);

  }

  double t2 = 0.5 - x2 * x2 - y2 * y2;

  if (t2 < 0)

    n2 = 0.0;

  else {

    t2 *= t2;

    n2 = t2 * t2 * dot(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 SimplexNoise::noise(double xin, double yin, double zin) {

  // Skewing and unskewing factors for 3 dimensions

  static const double F3 = 1.0 / 3.0;

  static const double G3 = 1.0 / 6.0;

  double n0, n1, n2, n3;  // Noise contributions from the four corners

  // Skew the input space to determine which simplex cell we're in

  double s = (xin + yin + zin) * F3;  // Very nice and simple skew factor for 3D

  int i    = fastfloor(xin + s);

  int j    = fastfloor(yin + s);

  int k    = fastfloor(zin + s);

  double t = (i + j + k) * G3;

  double X0 = i - t;  // Unskew the cell origin back to (x,y,z) space

  double Y0 = j - t;

  double Z0 = k - t;

  double x0 = xin - X0;  // The x,y,z distances from the cell origin

  double y0 = yin - Y0;

  double 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

    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.

  double x1 = x0 - i1 + G3;  // Offsets for second corner in (x,y,z) coords

  double y1 = y0 - j1 + G3;

  double z1 = z0 - k1 + G3;

  double x2 = x0 - i2 + 2.0 * G3;  // Offsets for third corner in (x,y,z) coords

  double y2 = y0 - j2 + 2.0 * G3;

  double z2 = z0 - k2 + 2.0 * G3;

  double x3 = x0 - 1.0 + 3.0 * G3;  // Offsets for last corner in (x,y,z) coords

  double y3 = y0 - 1.0 + 3.0 * G3;

  double z3 = z0 - 1.0 + 3.0 * G3;

  // Work out the hashed gradient indices of the four simplex corners

  int ii  = i & 255;

  int jj  = j & 255;

  int kk  = k & 255;

  int gi0 = permMod12[ii + perm[jj + perm[kk]]];

  int gi1 = permMod12[ii + i1 + perm[jj + j1 + perm[kk + k1]]];

  int gi2 = permMod12[ii + i2 + perm[jj + j2 + perm[kk + k2]]];

  int gi3 = permMod12[ii + 1 + perm[jj + 1 + perm[kk + 1]]];

  // Calculate the contribution from the four corners

  double range = 0.6;

  double t0    = range - x0 * x0 - y0 * y0 - z0 * z0;

  if (t0 < 0)

    n0 = 0.0;

  else {

    t0 *= t0;

    n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);

  }

  double t1 = range - x1 * x1 - y1 * y1 - z1 * z1;

  if (t1 < 0)

    n1 = 0.0;

  else {

    t1 *= t1;

    n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);

  }

  double t2 = range - x2 * x2 - y2 * y2 - z2 * z2;

  if (t2 < 0)

    n2 = 0.0;

  else {

    t2 *= t2;

    n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);

  }

  double t3 = range - x3 * x3 - y3 * y3 - z3 * z3;

  if (t3 < 0)

    n3 = 0.0;

  else {

    t3 *= t3;

    n3 = t3 * t3 * dot(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]

  /*- 変更： [-0.5,0.5]　の範囲にする -*/

  return 16.0 * (n0 + n1 + n2 + n3);

  // return 32.0*(n0 + n1 + n2 + n3);

}

//----------------------------------------

// 4D simplex noise

//----------------------------------------

double SimplexNoise::noise(double x, double y, double z, double w) {

  // Skewing and unskewing factors for 4 dimensions

  static const double F4 = (sqrt(5.0) - 1.0) / 4.0;

  static const double G4 = (5.0 - sqrt(5.0)) / 20.0;

  // The skewing and unskewing factors are hairy again for the 4D case

  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

  double s  = (x + y + z + w) * F4;  // Factor for 4D skewing

  int i     = fastfloor(x + s);

  int j     = fastfloor(y + s);

  int k     = fastfloor(z + s);

  int l     = fastfloor(w + s);

  double t  = (i + j + k + l) * G4;  // Factor for 4D unskewing

  double X0 = i - t;  // Unskew the cell origin back to (x,y,z,w) space

  double Y0 = j - t;

  double Z0 = k - t;

  double W0 = l - t;

  double x0 = x - X0;  // The x,y,z,w distances from the cell origin

  double y0 = y - Y0;

  double z0 = z - Z0;

  double 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.

  int rankx = 0;

  int ranky = 0;

  int rankz = 0;

  int 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

  // x

  // 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 look that

  // up.

  double x1 = x0 - i1 + G4;  // Offsets for second corner in (x,y,z,w) coords

  double y1 = y0 - j1 + G4;

  double z1 = z0 - k1 + G4;

  double w1 = w0 - l1 + G4;

  double x2 =

      x0 - i2 + 2.0 * G4;  // Offsets for third corner in (x,y,z,w) coords

  double y2 = y0 - j2 + 2.0 * G4;

  double z2 = z0 - k2 + 2.0 * G4;

  double w2 = w0 - l2 + 2.0 * G4;

  double x3 =

      x0 - i3 + 3.0 * G4;  // Offsets for fourth corner in (x,y,z,w) coords

  double y3 = y0 - j3 + 3.0 * G4;

  double z3 = z0 - k3 + 3.0 * G4;

  double w3 = w0 - l3 + 3.0 * G4;

  double x4 =

      x0 - 1.0 + 4.0 * G4;  // Offsets for last corner in (x,y,z,w) coords

  double y4 = y0 - 1.0 + 4.0 * G4;

  double z4 = z0 - 1.0 + 4.0 * G4;

  double w4 = w0 - 1.0 + 4.0 * G4;

  // Work out the hashed gradient indices of the five simplex corners

  int ii  = i & 255;

  int jj  = j & 255;

  int kk  = k & 255;

  int ll  = l & 255;

  int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;

  int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;

  int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;

  int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;

  int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;

  /*- パラメータ調整 -*/

  double range = 0.66;

  // double range = 0.6;

  // Calculate the contribution from the five corners

  double t0 = range - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;

  if (t0 < 0)

    n0 = 0.0;

  else {

    t0 *= t0;

    n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);

  }

  double t1 = range - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;

  if (t1 < 0)

    n1 = 0.0;

  else {

    t1 *= t1;

    n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);

  }

  double t2 = range - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;

  if (t2 < 0)

    n2 = 0.0;

  else {

    t2 *= t2;

    n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);

  }

  double t3 = range - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;

  if (t3 < 0)

    n3 = 0.0;

  else {

    t3 *= t3;

    n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);

  }

  double t4 = range - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;

  if (t4 < 0)

    n4 = 0.0;

  else {

    t4 *= t4;

    n4 = t4 * t4 * dot(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);

}

/*----------------------------------------

 セルまたぎを防ぐために、現在の所属セルを得る

----------------------------------------*/

CellIds SimplexNoise::getCellIds(double xin, double yin, double zin) {

  // Skew the input space to determine which simplex cell we're in

  const double F3 = 1.0 / 3.0;

  double s = (xin + yin + zin) * F3;  // Very nice and simple skew factor for 3D

  int i    = fastfloor(xin + s);

  int j    = fastfloor(yin + s);

  int k    = fastfloor(zin + s);

  const double G3 = 1.0 / 6.0;  // Very nice and simple unskew factor, too

  double t        = (i + j + k) * G3;

  double X0       = i - t;  // Unskew the cell origin back to (x,y,z) space

  double Y0       = j - t;

  double Z0       = k - t;

  double x0       = xin - X0;  // The x,y,z distances from the cell origin

  double y0       = yin - Y0;

  double 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

    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

  }

  return CellIds(i, j, k, i1, j1, k1, i2, j2, k2);

}