AquilaX's development blog » Math

Perlin noise generator in PHP

AquilaX — Sun, 02 Mar 2008 10:56:17 +0000

Generating Perlin noise requires heavy calculation and PHP (in my opinion) is not the best language for this task but still it can be useful.
The algorithm is an adaptation form this pseudo code.
The class seems to work but I'm not if it works 100% correctly. The tricky part was to deal with the types because PHP tends to convert large integers to float, and the algorithm uses bitwise operators on some stages.

This class is just for testing purposes it consumes a lot of CPU cycles and I hardly recommend to avoid using it in live environment. Try to keep the cycles low as well as the octaves number close to 1.

Sample SVG result: noise.svg.
Example usage (generate SVG map of terrain):

 
  require("class.perlin.php");
  $per = new Perlin;
 
  $xl = 100;
  $yl = 40;
 
  header("Content-type: image/svg+xml");
  echo '';
  echo '';
  echo ';
  $size = 3;
  for ($x = 0; $x < $xl; $x++){
    for ($y = 0; $y < $yl; $y++){
      $n = $per->perlinNoise2d($x, $y)*255;
      $c = '#986121';
      if ($n < 50){
        $c = '#0000ff';
      }
      if ($n > 200){
        $c = '#FFFFFF';
      }
      echo "\"".($x*$size)."\" y=\"".($y*$size)."\"
            width=\"$size\" height=\"$size\" fill=\"$c\"/>\n";
    }
  }
  echo '';

Download: classperlinphp.zip

Point in triangle

AquilaX — Sat, 10 Nov 2007 19:55:03 +0000

A function in PHP to check if a point is in triangle.

 
 
  function fAB($t, $x, $y) {
    return ($y - $t['y1'])*($t['x2'] - $t['x1'])
      -($x - $t['x1'])*($t['y2'] - $t['y1']);
  }
 
  function fBC($t, $x, $y) {
    return ($y-$t['y2'])*($t['x3']-$t['x2'])
      -($x-$t['x2'])*($t['y3']-$t['y2']);
  }
 
  function fCA($t, $x, $y) {
    return ($y-$t['y3'])*($t['x1']-$t['x3'])
      -($x-$t['x3'])*($t['y1']-$t['y3']);
  }
 
  function CheckPointInside($t, $x, $y) {
    if (fAB($t, $x, $y)*fBC($t, $x, $y)>0
      && fBC($t, $x, $y)*fCA($t, $x, $y)>0) {
      return true;
    } else {
      return false;
    }
  }

Function CheckPointInside expects three parameters: $t an associative array of triangle's coordinates written as x1,y1, x2, y2, x3, y3 and $x, $y, the point's coordinates.

Pythagorean triple in PHP

AquilaX — Wed, 07 Nov 2007 05:13:45 +0000

Pythagorean triple is every integer a, b and c for which a² + b² = c² or in other words the a, b, and c are the sides of a right triangle. To generate triples in PHP, you can use the following function:

 
  function CalcTriple($n){
    $res = array();
    $res['a'] = (2*$n)+1;
    $res['b'] = (2*$n)*($n+1);
    $res['c'] = (2*$n)*($n+1)+1;
    return $res;
  }

$n is an Integer and the returned array contains the triple.
Unfortunately this function WON'T generate ALL triples. It just generates valid triples.
Seen on Wikipedia.

Prime numbers in PHP

AquilaX — Sat, 03 Nov 2007 23:18:47 +0000

This is quite fast (but unfortunately memory consuming) algorithm for generating all prime numbers up no n:

 
 
  $n = 100; //this is the upper limit
 
  for ($i = 2; $i <=$n; $i++){
    $primes[] = $i;
  }
 
  foreach ($primes as $num){
    if ($num != 1){
      $step = $num;
      for ($i = 2*$num-2; $i <= count($primes); $i= $i + $step){
        if ($primes[$i] != 1) {
          $primes[$i] = 1;
        }
      }
    }
  }
 
  $primes = array_unique($primes);
  $primes = array_values($primes);
  sort($primes);
  unset($primes[0]);

I found this on Wikipedia here. It needs optimization (for example count($primes) doesn't need to be called on every iteration) but helped me a lot for solving some Project Euler problems.