Projectile Motion

<?php
function projectileMotion($x, $velocity1, $velocity2, $gravity){
    //$velocity1 is the initial upwards velocity (eg 10)
    //$velocity2 is the initial horizontal velocity (eg 50)
    //$gravity is the downwards acceleration (eg 9.8)
    //$y = $velocity1*$time + 0.5*$gravity*$time^2; //s = ut + 1/2*at^2
    //shit.... working out the X-pos isn't going to work.
    // x = v*t, y = ut + 0.5*at^2
    // t = x/v, therefore; y = u(x/v) + 0.5a(x/v)^2
    return $velocity1*($x/$velocity2) + 0.5*$gravity*pow(($x/$velocity2), 2);
}

$velocity1 = 50;
$velocity2 = 5;
$gravity = -9.8;
//THE FILE PRINTER STARTS HERE

//Your parameters
$domain = array("neg" => 0, "pos" => 75); //Please don't use decimal values. :\
$lineThickness = 2; //Decimals are cool here.
$accuracy = 0.1; //lower the number = higher the accuracy, longer the processing time, larger the image. Please only use values of 10^x

//---Begin main program
$maxheight = 0;
$minheight = 0;
for($n = -$domain["neg"]/$accuracy; $n <= $domain["pos"]/$accuracy; $n++){
  $j++;
  $i = projectileMotion(abs($n*$accuracy), $velocity1, $velocity2, $gravity); //This is where the values are loaded
  if($i > $maxheight || $j == 0){ //if the result is larger than all the  rest, the new result will become the largest result.
    $maxheight = $i;
  }
  if($i < $minheight || $j == 0){
    $minheight = $i;
  }
  echo $n*$accuracy." = $i\n";
  $x[$j] = $i; //$n is the position along the x-axis, $i is the position along the y-axis.
}
$x[0] = $x[1]; //<same as the line below me>
$x[$j+1] = $x[$j]; //This is because of line 72, where $dif is set. It will try to reference an array with no entry, so dif would otherwise become $x[$CurPx]
//var_dump($x);

//---begin writing file
unlink("image.ppm"); //file that we will be editing, we are are deleting the file so we have a clean file to work on
$fh = fopen("image.ppm", 'a+'); //creates the image file that we will be editting and opens the file for appending

$domain["dif"] = $domain["neg"]+$domain["pos"];
$width = floor($domain["dif"]/$accuracy); //width of the image is the largest number that was tested
$height = floor(abs($minheight - $maxheight)+1); //height is the largest amount of steps that it took to reach zero

$startWrite = "P3\n# image.ppm\n".$width." ".$height."\n255"; //fomatting the ppm file
fwrite($fh, $startWrite);

$j = 0;
for($k = -$domain["neg"]/$accuracy; $k < $width*$height; $k++){
  $CurPx = $j%$width; //basic modulus to decide when a new line must be made
  if($j%5 == 0){ //basic formatting decides when a new line must be placed
    $Nl = " \n";
  }else{
    $Nl = " ";
  }
  if($CurPx == 0){
    $CurPy++;
  }
  $dist = $x[$CurPx] - ($maxheight-$CurPy+1);
  $dif = abs($x[$CurPx]-$x[$CurPx+1])+$lineThickness;
  if($dist > -$dif && $dist < $dif){ //basic algebra, fuck I hate zero being counted as an integer
    $red = "255"; //if the if statement above reflects the array which was made on line 23, the pixel will be white
    $green = "255";
    $blue = "255";
  }elseif($CurPy >= $maxheight+1){ //if Y >= 0
    $clr = str_pad(abs(255-abs(floor(255*(($CurPy-$maxheight-2)/$minheight)))), 3, "0", STR_PAD_LEFT);
    if(0 == $CurPx%($width/$domain["dif"])){
      $red = "128";
      $green = "128";
      $blue = "128";
    }elseif($CurPx <= $domain["neg"]/$accuracy){
      $blue = $clr;
      $red = $clr;
      $green = "000";
    }else{
      $green = $clr;
      $blue = "000";
      $red = "000";
    }
  }elseif($CurPy < $maxheight+1){ //if Y < 0
    $clr = str_pad(abs(floor(255*($CurPy/$maxheight))), 3, "0", STR_PAD_LEFT);
    if(0 == $CurPx%($width/$domain["dif"])){
      $red = "128";
      $green = "128";
      $blue = "128";
    }elseif($CurPx <= $domain["neg"]/$accuracy){
      $blue = $clr;
      $red = "000";
      $green = "000";
    }else{
      $red = $clr;
      $blue = "000";
      $green = "000";
    }
  }
  $write = "$Nl$red $green $blue"; //the line that is to be outputted
    fwrite($fh, $write); //write the pixel to the file.
    $j++;
}
fclose($fh); //close the file, done!
?>