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); | |
| } | |
| } |
Line 61 has a typo - the extra 'i' at the end.
Good catch @eAi
I liked this a lot, so i made a js implementation of it, which can be found here .
PHP Version
<?php
declare(strict_types=1);
namespace App\Noise;
/**
* Class Generator
*
* @package App\Noise
*/
class Generator
{
/**
* @var int
*/
private int $repeat;
/**
* @var int[]
*/
// @formatter:off
private array $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];
// @formatter:on
/**
* @var int[]
*/
private array $p = [];
public function __construct(int $repeat= -1)
{
$this->repeat= $repeat;
for ($x = 0; $x < 512; $x++) {
$this->p[$x] = $this->permutation[$x % 256];
}
}
public function noise(float $x, float $y, float $z, int $octaves, float $persistence): float
{
$total = 0.0;
$frequency = 1.0;
$amplitude = 1.0;
$maxValue = 0.0;
for ($i = 0; $i < $octaves; $i++) {
$total += $this->perlin($x * $frequency, $y * $frequency, $z * $frequency) * $amplitude;
$maxValue += $amplitude;
$amplitude *= $persistence;
$frequency *= 2;
}
return $total / $maxValue;
}
private function perlin(float $x, float $y, float $z): float
{
if ($this->seed > 0) {
$x = $x % $this->repeat;
$y = $y % $this->repeat;
$z = $z % $this->repeat;
}
$xi = (int)$x & 255;
$yi = (int)$y & 255;
$zi = (int)$z & 255;
$xf = $x - (int)$x;
$yf = $y - (int)$y;
$zf = $z - (int)$z;
$u = $this->fade($xf);
$v = $this->fade($yf);
$w = $this->fade($zf);
$aaa = $this->p[$this->p[$this->p[$xi] + $yi] + $zi];
$aba = $this->p[$this->p[$this->p[$xi] + $this->inc($yi)] + $zi];
$aab = $this->p[$this->p[$this->p[$xi] + $yi] + $this->inc($zi)];
$abb = $this->p[$this->p[$this->p[$xi] + $this->inc($yi)] + $this->inc($zi)];
$baa = $this->p[$this->p[$this->p[$this->inc($xi)] + $yi] + $zi];
$bba = $this->p[$this->p[$this->p[$this->inc($xi)] + $this->inc($yi)] + $zi];
$bab = $this->p[$this->p[$this->p[$this->inc($xi)] + $yi] + $this->inc($zi)];
$bbb = $this->p[$this->p[$this->p[$this->inc($xi)] + $this->inc($yi)] + $this->inc($zi)];
$x1 = $this->lerp($this->grad($aaa, $xf, $yf, $zf), $this->grad($baa, $xf - 1, $yf, $zf), $u);
$x2 = $this->lerp($this->grad($aba, $xf, $yf - 1, $zf), $this->grad($bba, $xf - 1, $yf - 1, $zf), $u);
$y1 = $this->lerp($x1, $x2, $v);
$x1 = $this->lerp($this->grad($aab, $xf, $yf, $zf - 1), $this->grad($bab, $xf - 1, $yf, $zf - 1), $u);
$x2 = $this->lerp($this->grad($abb, $xf, $yf - 1, $zf - 1), $this->grad($bbb, $xf - 1, $yf - 1, $zf - 1), $u);
$y2 = $this->lerp($x1, $x2, $v);
return ($this->lerp($y1, $y2, $w) + 1) / 2;
}
private function fade(float $t): float
{
return $t * $t * $t * ($t * ($t * 6 - 15) + 10);// 6t^5 - 15t^4 + 10t^3
}
private function inc(int $num): int
{
$num++;
if ($this->repeat > 0) {
$num %= $this->repeat;
}
return $num;
}
private function lerp(float $a, float $b, float $x): float
{
return $a + $x * ($b - $a);
}
private function grad(int $hash, float $x, float $y, float $z): float
{
$h = $hash & 15;
$u = ($h < 8 ? $x : $y);
if ($h < 4) {
$v = $y;
} elseif ($h == 12 || $h == 14) {
$v = $x;
} else {
$v = $z;
}
return (($h & 1) == 0 ? $u : -$u) + (($h & 2) == 0 ? $v : -$v);
}
}
Great explanation. Thanks for the work.
HLSL / Unity Compute Shader Version: https://gist.github.com/Leslieghf/334b8cd6ed75fb35ae334416627995ee
Disclaimer: I slightly modified this, namingly removing tileability and adding octave offsets (which have to be given by the CPU, as I couldn't manage to create a Seeded Ranged PRNG on the GPU).
If you have questions regarding How to use this or How to modify this, feel free to contact me :D
Anyone know of a Lua version?
Thanks for this, and the associated article, Adrian.
Could someone explain the meaning of the repeat value please? I don't understand what it's actually doing. The only sensible result I've managed to get is 4x4 "tiles" over 512x512 pixels when repeat is 4, and x and y are from 0.0 to 1.0 over their ranges. But if I try to apply this to other values of repeat (e.g. 1, 3, or 64, or 7) I just get weird diagonal striping, or vertical lines, or generally unpleasant output.
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http://flafla2.github.io/2014/08/09/perlinnoise.html