context: using System;
  
  namespace SunflowSharp.Maths
  {
      /**
       * Noise function from Ken Perlin. Additional routines are provided to emulate
       * standard Renderman calls. This code was adapted mainly from the mrclasses
       * package by Gonzalo Garramuno (http://sourceforge.net/projects/mrclasses/).
       * 
       * @link http://mrl.nyu.edu/~perlin/noise/
       */
      public class PerlinScalar
      {
          private static float[] G1 = { -1, 1 };
          private static float[,] G2 = { { 1, 0 }, { -1, 0 }, { 0, 1 },
              { 0, -1 } };
          private static float[,] G3 = { { 1, 1, 0 }, { -1, 1, 0 },
              { 1, -1, 0 }, { -1, -1, 0 }, { 1, 0, 1 }, { -1, 0, 1 },
              { 1, 0, -1 }, { -1, 0, -1 }, { 0, 1, 1 }, { 0, -1, 1 },
              { 0, 1, -1 }, { 0, -1, -1 }, { 1, 1, 0 }, { -1, 1, 0 },
              { 0, -1, 1 }, { 0, -1, -1 } };
          private static float[,] G4 = { { -1, -1, -1, 0 }, { -1, -1, 1, 0 },
              { -1, 1, -1, 0 }, { -1, 1, 1, 0 }, { 1, -1, -1, 0 },
              { 1, -1, 1, 0 }, { 1, 1, -1, 0 }, { 1, 1, 1, 0 },
              { -1, -1, 0, -1 }, { -1, 1, 0, -1 }, { 1, -1, 0, -1 },
              { 1, 1, 0, -1 }, { -1, -1, 0, 1 }, { -1, 1, 0, 1 },
              { 1, -1, 0, 1 }, { 1, 1, 0, 1 }, { -1, 0, -1, -1 },
              { 1, 0, -1, -1 }, { -1, 0, -1, 1 }, { 1, 0, -1, 1 },
              { -1, 0, 1, -1 }, { 1, 0, 1, -1 }, { -1, 0, 1, 1 }, { 1, 0, 1, 1 },
              { 0, -1, -1, -1 }, { 0, -1, -1, 1 }, { 0, -1, 1, -1 },
              { 0, -1, 1, 1 }, { 0, 1, -1, -1 }, { 0, 1, -1, 1 },
              { 0, 1, 1, -1 }, { 0, 1, 1, 1 } };
          private static int[] p = { 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 };
  
          public static float snoise(float x)
          {
              int xf = (int)Math.Floor(x);
              int X = xf & 255;
              x -= xf;
              float u = fade(x);
              int A = p[X], B = p[X + 1];
              return lerp(u, grad(p[A], x), grad(p[B], x - 1));
          }
  
          public static float snoise(float x, float y)
          {
              int xf = (int)Math.Floor(x);
              int yf = (int)Math.Floor(y);
              int X = xf & 255;
              int Y = yf & 255;
              x -= xf;
              y -= yf;
              float u = fade(x);
              float v = fade(y);
              int A = p[X] + Y, B = p[X + 1] + Y;
              return lerp(v, lerp(u, grad(p[A], x, y), grad(p[B], x - 1, y)), lerp(u, grad(p[A + 1], x, y - 1), grad(p[B + 1], x - 1, y - 1)));
          }
  
          public static float snoise(float x, float y, float z)
          {
              int xf = (int)Math.Floor(x);
              int yf = (int)Math.Floor(y);
              int zf = (int)Math.Floor(z);
              int X = xf & 255;
              int Y = yf & 255;
              int Z = zf & 255;
              x -= xf;
              y -= yf;
              z -= zf;
              float u = fade(x);
              float v = fade(y);
              float w = fade(z);
              int A = p[X] + Y, AA = p[A] + Z, AB = p[A + 1] + Z, B = p[X + 1] + Y, BA = p[B] + Z, BB = p[B + 1] + Z;
              return lerp(w, lerp(v, lerp(u, grad(p[AA], x, y, z), grad(p[BA], x - 1, y, z)), lerp(u, grad(p[AB], x, y - 1, z), grad(p[BB], x - 1, y - 1, z))), lerp(v, lerp(u, grad(p[AA + 1], x, y, z - 1), grad(p[BA + 1], x - 1, y, z - 1)), lerp(u, grad(p[AB + 1], x, y - 1, z - 1), grad(p[BB + 1], x - 1, y - 1, z - 1))));
          }
  
          public static float snoise(float x, float y, float z, float w)
          {
              int xf = (int)Math.Floor(x);
              int yf = (int)Math.Floor(y);
              int zf = (int)Math.Floor(z);
              int wf = (int)Math.Floor(w);
              int X = xf & 255;
              int Y = yf & 255;
              int Z = zf & 255;
              int W = wf & 255;
              x -= xf;
              y -= yf;
              z -= zf;
              w -= wf;
              float u = fade(x);
              float v = fade(y);
              float t = fade(z);
              float s = fade(w);
              int A = p[X] + Y, AA = p[A] + Z, AB = p[A + 1] + Z, B = p[X + 1] + Y, BA = p[B] + Z, BB = p[B + 1] + Z, AAA = p[AA] + W, AAB = p[AA + 1] + W, ABA = p[AB] + W, ABB = p[AB + 1] + W, BAA = p[BA] + W, BAB = p[BA + 1] + W, BBA = p[BB] + W, BBB = p[BB + 1] + W;
              return lerp(s, lerp(t, lerp(v, lerp(u, grad(p[AAA], x, y, z, w), grad(p[BAA], x - 1, y, z, w)), lerp(u, grad(p[ABA], x, y - 1, z, w), grad(p[BBA], x - 1, y - 1, z, w))), lerp(v, lerp(u, grad(p[AAB], x, y, z - 1, w), grad(p[BAB], x - 1, y, z - 1, w)), lerp(u, grad(p[ABB], x, y - 1, z - 1, w), grad(p[BBB], x - 1, y - 1, z - 1, w)))), lerp(t, lerp(v, lerp(u, grad(p[AAA + 1], x, y, z, w - 1), grad(p[BAA + 1], x - 1, y, z, w - 1)), lerp(u, grad(p[ABA + 1], x, y - 1, z, w - 1), grad(p[BBA + 1], x - 1, y - 1, z, w - 1))), lerp(v, lerp(u, grad(p[AAB + 1], x, y, z - 1, w - 1), grad(p[BAB + 1], x - 1, y, z - 1, w - 1)), lerp(u, grad(p[ABB + 1], x, y - 1, z - 1, w - 1), grad(p[BBB + 1], x - 1, y - 1, z - 1, w - 1)))));
          }
  
          public static float snoise(Point2 p)
          {
              return snoise(p.x, p.y);
          }
  
          public static float snoise(Point3 p)
          {
              return snoise(p.x, p.y, p.z);
          }
  
          public static float snoise(Point3 p, float t)
          {
              return snoise(p.x, p.y, p.z, t);
          }
  
          public static float noise(float x)
          {
              return 0.5f + 0.5f * snoise(x);
          }
  
          public static float noise(float x, float y)
          {
              return 0.5f + 0.5f * snoise(x, y);
          }
  
          public static float noise(float x, float y, float z)
          {
              return 0.5f + 0.5f * snoise(x, y, z);
          }
  
          public static float noise(float x, float y, float z, float t)
          {
              return 0.5f + 0.5f * snoise(x, y, z, t);
          }
  
          public static float noise(Point2 p)
          {
              return 0.5f + 0.5f * snoise(p.x, p.y);
          }
  
          public static float noise(Point3 p)
          {
              return 0.5f + 0.5f * snoise(p.x, p.y, p.z);
          }
  
          public static float noise(Point3 p, float t)
          {
              return 0.5f + 0.5f * snoise(p.x, p.y, p.z, t);
          }
  
          public static float pnoise(float xi, float period)
          {
              float x = (xi % period) + ((xi < 0) ? period : 0);
              return ((period - x) * noise(x) + x * noise(x - period)) / period;
          }
  
          public static float pnoise(float xi, float yi, float w, float h)
          {
              float x = (xi % w) + ((xi < 0) ? w : 0);
              float y = (yi % h) + ((yi < 0) ? h : 0);
              float w_x = w - x;
              float h_y = h - y;
              float x_w = x - w;
              float y_h = y - h;
              return (noise(x, y) * (w_x) * (h_y) + noise(x_w, y) * (x) * (h_y) + noise(x_w, y_h) * (x) * (y) + noise(x, y_h) * (w_x) * (y)) / (w * h);
          }
  
          public static float pnoise(float xi, float yi, float zi, float w, float h, float d)
          {
              float x = (xi % w) + ((xi < 0) ? w : 0);
              float y = (yi % h) + ((yi < 0) ? h : 0);
              float z = (zi % d) + ((zi < 0) ? d : 0);
              float w_x = w - x;
              float h_y = h - y;
              float d_z = d - z;
              float x_w = x - w;
              float y_h = y - h;
              float z_d = z - d;
              float xy = x * y;
              float h_yXd_z = h_y * d_z;
              float h_yXz = h_y * z;
              float w_xXy = w_x * y;
              return (noise(x, y, z) * (w_x) * h_yXd_z + noise(x, y_h, z) * w_xXy * (d_z) + noise(x_w, y, z) * (x) * h_yXd_z + noise(x_w, y_h, z) * (xy) * (d_z) + noise(x_w, y_h, z_d) * (xy) * (z) + noise(x, y, z_d) * (w_x) * h_yXz + noise(x, y_h, z_d) * w_xXy * (z) + noise(x_w, y, z_d) * (x) * h_yXz) / (w * h * d);
          }
  
          public static float pnoise(float xi, float yi, float zi, float ti, float w, float h, float d, float p)
          {
              float x = (xi % w) + ((xi < 0) ? w : 0);
              float y = (yi % h) + ((yi < 0) ? h : 0);
              float z = (zi % d) + ((zi < 0) ? d : 0);
              float t = (ti % p) + ((ti < 0) ? p : 0);
              float w_x = w - x;
              float h_y = h - y;
              float d_z = d - z;
              float p_t = p - t;
              float x_w = x - w;
              float y_h = y - h;
              float z_d = z - d;
              float t_p = t - p;
              float xy = x * y;
              float d_zXp_t = (d_z) * (p_t);
              float zXp_t = z * (p_t);
              float zXt = z * t;
              float d_zXt = d_z * t;
              float w_xXy = w_x * y;
              float w_xXh_y = w_x * h_y;
              float xXh_y = x * h_y;
              return (noise(x, y, z, t) * (w_xXh_y) * d_zXp_t + noise(x_w, y, z, t) * (xXh_y) * d_zXp_t + noise(x_w, y_h, z, t) * (xy) * d_zXp_t + noise(x, y_h, z, t) * (w_xXy) * d_zXp_t + noise(x_w, y_h, z_d, t) * (xy) * (zXp_t) + noise(x, y, z_d, t) * (w_xXh_y) * (zXp_t) + noise(x, y_h, z_d, t) * (w_xXy) * (zXp_t) + noise(x_w, y, z_d, t) * (xXh_y) * (zXp_t) + noise(x, y, z, t_p) * (w_xXh_y) * (d_zXt) + noise(x_w, y, z, t_p) * (xXh_y) * (d_zXt) + noise(x_w, y_h, z, t_p) * (xy) * (d_zXt) + noise(x, y_h, z, t_p) * (w_xXy) * (d_zXt) + noise(x_w, y_h, z_d, t_p) * (xy) * (zXt) + noise(x, y, z_d, t_p) * (w_xXh_y) * (zXt) + noise(x, y_h, z_d, t_p) * (w_xXy) * (zXt) + noise(x_w, y, z_d, t_p) * (xXh_y) * (zXt)) / (w * h * d * t);
          }
  
          public static float pnoise(Point2 p, float periodx, float periody)
          {
              return pnoise(p.x, p.y, periodx, periody);
          }
  
          public static float pnoise(Point3 p, Vector3 period)
          {
              return pnoise(p.x, p.y, p.z, period.x, period.y, period.z);
          }
  
          public static float pnoise(Point3 p, float t, Vector3 pperiod, float tperiod)
          {
              return pnoise(p.x, p.y, p.z, t, pperiod.x, pperiod.y, pperiod.z, tperiod);
          }
  
          public static float spnoise(float xi, float period)
          {
              float x = (xi % period) + ((xi < 0) ? period : 0);
              return (((period - x) * snoise(x) + x * snoise(x - period)) / period);
          }
  
          public static float spnoise(float xi, float yi, float w, float h)
          {
              float x = (xi % w) + ((xi < 0) ? w : 0);
              float y = (yi % h) + ((yi < 0) ? h : 0);
              float w_x = w - x;
              float h_y = h - y;
              float x_w = x - w;
              float y_h = y - h;
              return ((snoise(x, y) * (w_x) * (h_y) + snoise(x_w, y) * (x) * (h_y) + snoise(x_w, y_h) * (x) * (y) + snoise(x, y_h) * (w_x) * (y)) / (w * h));
          }
  
          public static float spnoise(float xi, float yi, float zi, float w, float h, float d)
          {
              float x = (xi % w) + ((xi < 0) ? w : 0);
              float y = (yi % h) + ((yi < 0) ? h : 0);
              float z = (zi % d) + ((zi < 0) ? d : 0);
              float w_x = w - x;
              float h_y = h - y;
              float d_z = d - z;
              float x_w = x - w;
              float y_h = y - h;
              float z_d = z - d;
              float xy = x * y;
              float h_yXd_z = h_y * d_z;
              float h_yXz = h_y * z;
              float w_xXy = w_x * y;
              return ((snoise(x, y, z) * (w_x) * h_yXd_z + snoise(x, y_h, z) * w_xXy * (d_z) + snoise(x_w, y, z) * (x) * h_yXd_z + snoise(x_w, y_h, z) * (xy) * (d_z) + snoise(x_w, y_h, z_d) * (xy) * (z) + snoise(x, y, z_d) * (w_x) * h_yXz + snoise(x, y_h, z_d) * w_xXy * (z) + snoise(x_w, y, z_d) * (x) * h_yXz) / (w * h * d));
          }
  
          public static float spnoise(float xi, float yi, float zi, float ti, float w, float h, float d, float p)
          {
              float x = (xi % w) + ((xi < 0) ? w : 0);
              float y = (yi % h) + ((yi < 0) ? h : 0);
              float z = (zi % d) + ((zi < 0) ? d : 0);
              float t = (ti % p) + ((ti < 0) ? p : 0);
              float w_x = w - x;
              float h_y = h - y;
              float d_z = d - z;
              float p_t = p - t;
              float x_w = x - w;
              float y_h = y - h;
              float z_d = z - d;
              float t_p = t - p;
              float xy = x * y;
              float d_zXp_t = (d_z) * (p_t);
              float zXp_t = z * (p_t);
  
gt:             float zXt = z * t;