Generated image with text always off-center

I have a simple PHP avatar generator that takes someone's username, and makes an image with their initials on it. This works well, but somehow the text is always off center and I cannot figure out have to always have the text properly centered.

This uses the Ubuntu font.

$im = imagecreatetruecolor(125, 125);

$str = 'dpoint';
if (str_word_count($str) > 1)
{
    $words = explode(' ', $str);
    $text = $words[0][0]. $words[1][0];
}
else
{
    $text = substr($str, 0, 2);
}

$font_size = '50';
$white = imagecolorallocate($im, 255, 255, 255);
$angle = 0;

// Get image dimensions
$width = imagesx($im);
$height = imagesy($im);
// Get center coordinates of image
$centerX = $width / 2;
$centerY = $height / 2;
// Get size of text
list($left, $bottom, $right, , , $top) = imageftbbox($font_size, $angle, './Ubuntu-L.ttf', $text);
// Determine offset of text
$left_offset = ($right - $left) / 2;
$top_offset = ($bottom - $top) / 2;
// Generate coordinates
$x = $centerX - $left_offset;
$y = $centerY + $top_offset;
// Add text to image
imagettftext($im, $font_size, $angle, $x, $y, $white, './Ubuntu-L.ttf', $text);

// Set the content type header
header('Content-Type: image/jpeg');

// Skip the file parameter using NULL, then set the quality
imagejpeg($im, NULL, 100);

// Free up memory
imagedestroy($im);

That for example ends up like this: You can see it's much lower down that it should be. What positioning am I doing wrong here?

Ideally I just want it so no matter the text size or lower-case or upper-case, it just centers it vertically and horizontally properly inside the box.

The y parameter of imagettftext() is the position of the baseline, not of the bottom of the character:

The y-ordinate. This sets the position of the font's baseline, not the very bottom of the character.

See the illustration from the Wikipedia page (red line).

Here is a way to fix this issue:

• Check if the string contains a known character with a descender

• If it does, compute the descender height by comparing the heights of a and p, and subtract it from $y

Example:

function hasDescender(string $text): bool
{
    // Only English letters are tested here
    return preg_match('/[gjpqyQ]/', $text);
}

function getDescenderHeight(float $font_size, string $font): int
{
    $box_a = imageftbbox($font_size, 0, $font, 'a');
    $box_p = imageftbbox($font_size, 0, $font, 'p');
    return $box_p[1] - $box_a[1];
}

$width = 125;
$height = 125;
$font_size = 50;
$font = './Ubuntu-L.ttf';
$text = 'dp';

$centerX = $width / 2;
$centerY = $height / 2;
list($left, $bottom, $right, , , $top) = imageftbbox($font_size, 0, $font, $text);
$left_offset = ($right - $left) / 2;
$top_offset = ($bottom - $top) / 2;
$x = $centerX - $left_offset;
$y = $centerY + $top_offset;
if(hasDescender($text))
    $y -= getDescenderHeight($font_size, $font);

$im = imagecreatetruecolor($width, $height);
$white = imagecolorallocate($im, 255, 255, 255);
imagettftext($im, $font_size, 0, (int)$x, (int)$y, $white, $font, $text);
header('Content-Type: image/png');
imagepng($im);
imagedestroy($im);

Output:

EDIT: it turns out there is a better solution, see Hakre's answer.