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A slightly modified implementation of Ken Perlin's improved noise that allows for tiling the noise arbitrarily.
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public class Perlin { | |
public int repeat; | |
public Perlin(int repeat = -1) { | |
this.repeat = repeat; | |
} | |
public double OctavePerlin(double x, double y, double z, int octaves, double persistence) { | |
double total = 0; | |
double frequency = 1; | |
double amplitude = 1; | |
double maxValue = 0; // Used for normalizing result to 0.0 - 1.0 | |
for(int i=0;i<octaves;i++) { | |
total += perlin(x * frequency, y * frequency, z * frequency) * amplitude; | |
maxValue += amplitude; | |
amplitude *= persistence; | |
frequency *= 2; | |
} | |
return total/maxValue; | |
} | |
private static readonly int[] permutation = { 151,160,137,91,90,15, // Hash lookup table as defined by Ken Perlin. This is a randomly | |
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, // arranged array of all numbers from 0-255 inclusive. | |
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 | |
}; | |
private static readonly int[] p; // Doubled permutation to avoid overflow | |
static Perlin() { | |
p = new int[512]; | |
for(int x=0;x<512;x++) { | |
p[x] = permutation[x%256]; | |
} | |
} | |
public double perlin(double x, double y, double z) { | |
if(repeat > 0) { // If we have any repeat on, change the coordinates to their "local" repetitions | |
x = x%repeat; | |
y = y%repeat; | |
z = z%repeat; | |
} | |
int xi = (int)x & 255; // Calculate the "unit cube" that the point asked will be located in | |
int yi = (int)y & 255; // The left bound is ( |_x_|,|_y_|,|_z_| ) and the right bound is that | |
int zi = (int)z & 255; // plus 1. Next we calculate the location (from 0.0 to 1.0) in that cube. | |
double xf = x-(int)x; // We also fade the location to smooth the result. | |
double yf = y-(int)y;i | |
double zf = z-(int)z; | |
double u = fade(xf); | |
double v = fade(yf); | |
double w = fade(zf); | |
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), // The gradient function calculates the dot product between a pseudorandom | |
grad (baa, xf-1, yf , zf), // gradient vector and the vector from the input coordinate to the 8 | |
u); // surrounding points in its unit cube. | |
x2 = lerp( grad (aba, xf , yf-1, zf), // This is all then lerped together as a sort of weighted average based on the faded (u,v,w) | |
grad (bba, xf-1, yf-1, zf), // values we made earlier. | |
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)+1)/2; // For convenience we bound it to 0 - 1 (theoretical min/max before is -1 - 1) | |
} | |
public int inc(int num) { | |
num++; | |
if (repeat > 0) num %= repeat; | |
return num; | |
} | |
public static double grad(int hash, double x, double y, double z) { | |
int h = hash & 15; // Take the hashed value and take the first 4 bits of it (15 == 0b1111) | |
double u = h < 8 /* 0b1000 */ ? x : y; // If the most significant bit (MSB) of the hash is 0 then set u = x. Otherwise y. | |
double v; // In Ken Perlin's original implementation this was another conditional operator (?:). I | |
// expanded it for readability. | |
if(h < 4 /* 0b0100 */) // If the first and second significant bits are 0 set v = y | |
v = y; | |
else if(h == 12 /* 0b1100 */ || h == 14 /* 0b1110*/)// If the first and second significant bits are 1 set v = x | |
v = x; | |
else // If the first and second significant bits are not equal (0/1, 1/0) set v = z | |
v = z; | |
return ((h&1) == 0 ? u : -u)+((h&2) == 0 ? v : -v); // Use the last 2 bits to decide if u and v are positive or negative. Then return their addition. | |
} | |
public static double fade(double t) { | |
// Fade function as defined by Ken Perlin. This eases coordinate values | |
// so that they will "ease" towards integral values. This ends up smoothing | |
// the final output. | |
return t * t * t * (t * (t * 6 - 15) + 10); // 6t^5 - 15t^4 + 10t^3 | |
} | |
public static double lerp(double a, double b, double x) { | |
return a + x * (b - a); | |
} | |
} |
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Fixed the bug in the code.
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