我看到Perlin Noise的许多实现，将排列表加倍，因为索引可能超出[0, 255]范围。
private static readonly int[] p;
static Perlin() {
p = new int[512];
for(int x=0;x<512;x++) {
p[x] = permutation[x%256];
}
}
private static readonly int[] 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
};
public double perlin(double x, double y, double z) {
if(repeat > 0) {
x = x%repeat;
y = y%repeat;
z = z%repeat;
}
// This means xi/yi/zi is in the range [0,255]
int xi = (int)x & 255;
int yi = (int)y & 255;
int zi = (int)z & 255;
double xf = x-(int)x;
double yf = y-(int)y;
double zf = z-(int)z;
double u = fade(xf);
double v = fade(yf);
double w = fade(zf);
// inc(xi) basically means xi + 1
// thus we may be selecting permutation[255 + 1], which is out of range
// hence we create a p[] array, that's double of permutation[] array.
int aaa, aba, aab, abb, baa, bba, bab, bbb;
aaa = p[p[p[ xi ]+ yi ]+ zi ];
aba = p[p[p[ xi ]+inc(yi)]+ zi ];
aab = p[p[p[ xi ]+ yi ]+inc(zi)];
abb = p[p[p[ xi ]+inc(yi)]+inc(zi)];
baa = p[p[p[inc(xi)]+ yi ]+ zi ];
bba = p[p[p[inc(xi)]+inc(yi)]+ zi ];
bab = p[p[p[inc(xi)]+ yi ]+inc(zi)];
bbb = p[p[p[inc(xi)]+inc(yi)]+inc(zi)];
double x1, x2, y1, y2;
x1 = lerp( grad (aaa, xf , yf , zf),
grad (baa, xf-1, yf , zf),
u);
x2 = lerp( grad (aba, xf , yf-1, zf),
grad (bba, xf-1, yf-1, zf),
u);
y1 = lerp(x1, x2, v);
x1 = lerp( grad (aab, xf , yf , zf-1),
grad (bab, xf-1, yf , zf-1),
u);
x2 = lerp( grad (abb, xf , yf-1, zf-1),
grad (bbb, xf-1, yf-1, zf-1),
u);
y2 = lerp (x1, x2, v);
return lerp (y1, y2, w);
}
但是，我看到one implementation只是在排列表中添加了另一个数字。所以它会跳过所有的工作。
public static float Noise(float x, float y, float z)
{
var X = Mathf.FloorToInt(x) & 0xff;
var Y = Mathf.FloorToInt(y) & 0xff;
var Z = Mathf.FloorToInt(z) & 0xff;
x -= Mathf.Floor(x);
y -= Mathf.Floor(y);
z -= Mathf.Floor(z);
var u = Fade(x);
var v = Fade(y);
var w = Fade(z);
// This implementation doesn't create p[] array
// It just repeated a number so that permutation has 257 items.
// And cap the result so that we never select index beyond 256.
var A = (perm[X ] + Y) & 0xff;
var B = (perm[X+1] + Y) & 0xff;
var AA = (perm[A ] + Z) & 0xff;
var BA = (perm[B ] + Z) & 0xff;
var AB = (perm[A+1] + Z) & 0xff;
var BB = (perm[B+1] + Z) & 0xff;
return Lerp(w, Lerp(v, Lerp(u, Grad(perm[AA ], x, y , z ), Grad(perm[BA ], x-1, y , z )),
Lerp(u, Grad(perm[AB ], x, y-1, z ), Grad(perm[BB ], x-1, y-1, z ))),
Lerp(v, Lerp(u, Grad(perm[AA+1], x, y , z-1), Grad(perm[BA+1], x-1, y , z-1)),
Lerp(u, Grad(perm[AB+1], x, y-1, z-1), Grad(perm[BB+1], x-1, y-1, z-1))));
}
//...
static int[] perm = {
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 // It just repeated a number at index 0
};
这是Perlin Noise的有效实现吗？