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# Flafla2/Perlin_Tiled.cs

Last active July 23, 2024 07:09
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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 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); } }

### eAi commented Apr 1, 2016

Line 61 has a typo - the extra 'i' at the end.

Good catch @eAi

### LiekeVanmulken commented Oct 5, 2017 • edited Loading

I liked this a lot, so i made a js implementation of it, which can be found here .

### DerDu commented Dec 28, 2020 • edited Loading

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);
}
}

``````

### maybebool commented Jul 23, 2022

Great explanation. Thanks for the work.

### Leslieghf commented Sep 24, 2022 • edited Loading

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

### eyeofparadox commented Mar 1, 2023

Anyone know of a Lua version?

### DavidAntliff commented Apr 2, 2023

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.

### Intilyc commented Sep 8, 2023

Anyone know of a Lua version?

Here ya go. Just so you know, Lua supports bitwise operators now, so depending on which version you're using you may have to go in and switch out bit32.band()

https://gist.github.com/kymckay/25758d37f8e3872e1636d90ad41fe2ed

### MisterE123 commented Feb 19, 2024

What is the license of this code?

### dmurph commented Jun 10, 2024 • edited Loading

This does some weird stuff when y is negative.... the output goes way outside 0 and 1.

Should `double xf = x-(int)x;` be.... `double xf = Math.abs(x-(int)x)`? Or somehow reverse into another unit square?

Fix - the xi and xf variables need to be using 'floor' instead of int casting, which will take -2.4 to -2 instead of -3 (there may be a faster way, please let me know if you find it 😄 )

``````    let xi = Math.floor(x) & 255;
let yi = Math.floor(y) & 255;
let zi = Math.floor(z) & 255;
let xf = x - Math.floor(x);
let yf = y - Math.floor(y);
let zf = z - Math.floor(z);
``````

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