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我正在尝试实现 2D 单纯形噪声，并想知道为什么大多数实现使用置换表而不是像 Ken Perlin 用来生成渐变的位操作。我一直在关注 Stefan Gustavson https://weber.itn.liu.se/~stegu/aqsis/aqsis-newnoise/simplexnoise1234.cpp的 2D simplex implementation 。

我想像 Ken Perlin 首先建议的那样通过位操作来生成渐变，但是我找不到使用这种方法的资源。如果有人可以向我解释位操作算法是如何工作的，并且可能提供示例代码，我将不胜感激。提前谢谢你。

如果需要，这是我当前的代码：

public static class Noise {
  public static int floor(float n){ return n > 0 ? (int)n : (int)n - 1; }

  public static float simplex(float x, float y){
    const float f2 = 0.3660253882408142f; // 0.5*(sqrt(3.0)-1.0)
    const float g2 = 0.2113248705863953f; // (3.0-Math.sqrt(3.0))/6.0

    float s = (x + y) * f2;
    int i = floor(x + s);
    int j = floor(y + s);

    float t = (i + j) * g2;
    float x0 = x - (i - t);
    float y0 = y - (j - t);

    int x_step = 0;
    int y_step = 0;

    if (x0 > y0) { x_step = 1; } else { y_step = 1; }
    
    float x1 = x0 - x_step + g2;
    float y1 = y0 - y_step + g2;
    float x2 = x0 - 1f + 2f * g2;
    float y2 = y0 - 1f + 2f * g2;

    int ii = i & 0xff;
    int jj = j & 0xff;

    float t0 = 0.5f - x0 * x0 - y0 * y0;
    float t1 = 0.5f - x1 * x1 - y1 * y1;
    float t2 = 0.5f - x2 * x2 - y2 * y2;

    float n0 = t0 >= 0f ? t0 * t0 * t0 * t0 * gradient(permutation[ii + permutation[jj]], x0, y0) : 0f;
    float n1 = t1 >= 0f ? t1 * t1 * t1 * t1 * gradient(permutation[ii + x_step + permutation[jj + y_step]], x1, y1) : 0f;
    float n2 = t2 >= 0f ? t2 * t2 * t2 * t2 * gradient(permutation[ii + 1 + permutation[jj + 1]], x2, y2) : 0f;
    
    return 40f * (n0 + n1 + n2);
  }

  private static float gradient(int hash, float x, float y){
    int h = hash & 7;
    float u = h < 4 ? x : y;
    float v = h < 4 ? y : x;
    return ((h & 1) != 0 ? -u : u) + ((h & 2) != 0 ? -2.0f * v : 2.0f * v);
  }

  private static readonly byte[] permutation = {
    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
  };
}
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