java - 定点柏林噪声返回输入点的总和作为输出

Question

我采用了定点柏林噪声实现:http://mrl.nyu.edu/~perlin/noise/INoise.java并对其稍作修改，以便在 c# 下编译。在这个版本中 1.0 由 2^16 表示。

当我传入输入坐标 (int x, int y, int z) 时，输出只是 x 和 z 坐标的总和。我的类或输入点有什么问题？以下是返回输出的示例:

    for (int y = 0; y < 1; y++) {

        for (int x = 0; x < 16; x++) {

            for (int z = 0; z < 16; z++) {

                Debug.Log(PerlinNoiseFixedPoint.Noise3D(x, y, z));
            }
        }
    }

Output: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 
 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
 15, 16, 17, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 4, 5, 6, 7,
 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 5, 6, 7, 8, 9, 10, 11, 12, 13, 
 14, 15, 16, 17, 18, 19, 20, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,
 20, 21, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 8, 9, 10,
 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 9, 10, 11, 12, 13, 14, 15,
 16, 17, 18, 19, 20, 21, 22, 23, 24, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,
 21, 22, 23, 24, 25, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
 26, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 13, 14, 15,
 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 14, 15, 16, 17, 18, 19, 20,
 21, 22, 23, 24, 25, 26, 27, 28, 29, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,
 26, 27, 28, 29, 30

public class PerlinNoiseFixedPoint {

    public static int Noise3D(int x, int y, int z) {

        int X = x >> 16 & 255, Y = y >> 16 & 255, Z = z >> 16 & 255, N = 1 << 16;

        x &= N - 1; y &= N - 1; z &= N - 1;

        int u = Fade(x), v = Fade(y), w = Fade(z), 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-N , y   , z   )), 
                               Lerp(u, Grad(p[AB  ], x   , y-N , z   ),  
                                       Grad(p[BB  ], x-N , y-N , z   ))),
                       Lerp(v, Lerp(u, Grad(p[AA+1], x   , y   , z-N ),  
                                       Grad(p[BA+1], x-N , y   , z-N )), 
                               Lerp(u, Grad(p[AB+1], x   , y-N , z-N ),
                                       Grad(p[BB+1], x-N , y-N , z-N ))));
    }
    static int Lerp(int t, int a, int b) { 

        return a + (t * (b - a) >> 12);
    }

    static int Grad(int hash, int x, int y, int z) {

        int h = hash & 15, u = h < 8 ? x : y, v = h < 4 ? y : h == 12 || h == 14 ? x : z;
        return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
    }

    static int Fade(int t) {

        int t0 = f[t >> 8], t1 = f[Math.Min(255, (t >> 8) + 1)];
        return t0 + ( (t & 255) * (t1 - t0) >> 8 );
    }

    static int[] p = new int[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 int[] f = new int[256] {

        0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 4, 6, 7, 
        9, 10, 12, 14, 17, 19, 22, 25, 29, 32, 36, 40, 45, 49, 54, 60, 
        65, 71, 77, 84, 91, 98, 105, 113, 121, 130, 139, 148, 158, 167, 178, 188, 
        199, 211, 222, 234, 247, 259, 273, 286, 300, 314, 329, 344, 359, 374, 390, 407, 
        424, 441, 458, 476, 494, 512, 531, 550, 570, 589, 609, 630, 651, 672, 693, 715, 
        737, 759, 782, 805, 828, 851, 875, 899, 923, 948, 973, 998, 1023, 1049, 1074, 1100, 
        1127, 1153, 1180, 1207, 1234, 1261, 1289, 1316, 1344, 1372, 1400, 1429, 1457, 1486, 1515, 1543, 
        1572, 1602, 1631, 1660, 1690, 1719, 1749, 1778, 1808, 1838, 1868, 1898, 1928, 1958, 1988, 2018, 
        2048, 2077, 2107, 2137, 2167, 2197, 2227, 2257, 2287, 2317, 2346, 2376, 2405, 2435, 2464, 2493, 
        2523, 2552, 2580, 2609, 2638, 2666, 2695, 2723, 2751, 2779, 2806, 2834, 2861, 2888, 2915, 2942, 
        2968, 2995, 3021, 3046, 3072, 3097, 3122, 3147, 3172, 3196, 3220, 3244, 3267, 3290, 3313, 3336, 
        3358, 3380, 3402, 3423, 3444, 3465, 3486, 3506, 3525, 3545, 3564, 3583, 3601, 3619, 3637, 3654, 
        3672, 3688, 3705, 3721, 3736, 3751, 3766, 3781, 3795, 3809, 3822, 3836, 3848, 3861, 3873, 3884, 
        3896, 3907, 3917, 3928, 3937, 3947, 3956, 3965, 3974, 3982, 3990, 3997, 4004, 4011, 4018, 4024, 
        4030, 4035, 4041, 4046, 4050, 4055, 4059, 4063, 4066, 4070, 4073, 4076, 4078, 4081, 4083, 4085, 
        4086, 4088, 4089, 4091, 4092, 4092, 4093, 4094, 4094, 4095, 4095, 4095, 4095, 4095, 4095, 4095, 
    };
}

Answer 1

1.0 IS REPRESENTED BY 2^16

这不是很明显，但结果是有意的。
按功能包装:

public static float Noise3D(float x, float y, float z)
{
    //65536 = 2 ^ 16
    return Noise3D((int)(x * 65536), (int)(y * 65536), (int)(z * 65536)) / 65536f; 
}

导致以下噪音:

附言 Code ， 以防万一