Cropping any image down to 4:3 ratio - php

Question

I'm trying to modify an upload script, at the moment I can crop an image into a square while resizing - great!
However I would like the user to be able to upload any size image, and for the script to create 200x150, 400x300, 800x600 thumbnail/images - a 4:3 ratio.
My code so far is:
list($width,$height) = getimagesize($uploadedfile);
if ($thumb == 1){
if ($width > $height) {
$y = 0;
$x = ($width - $height) / 2;
$smallestSide = $height;
} else {
$x = 0;
$y = ($height - $width) / 2;
$smallestSide = $width;
}
// copying the part into thumbnail
$thumbSize = 200;
$tmp = imagecreatetruecolor($thumbSize, $thumbSize);
imagecopyresampled($tmp, $src, 0, 0, $x, $y, $thumbSize, $thumbSize, $smallestSide, $smallestSide);
// write thumbnail to disk
$write_thumbimage = $folder .'/thumb-'. $image;
switch($ext){
case "gif":
imagegif($tmp,$write_thumbimage);
break;
case "jpg":
imagejpeg($tmp,$write_thumbimage,100);
break;
case "jpeg":
imagejpeg($tmp,$write_thumbimage,100);
break;
case "png":
imagepng($tmp,$write_thumbimage);
break;
}
Does anyone know the required formula or can point me in the right direction?

Answer 1

Worked out the logic using some of what was on the C# duplicate:
$thumb_width = 200;
$thumb_height = 150;
$original_aspect = $width / $height;
$thumb_aspect = $thumb_width / $thumb_height;
if ( $original_aspect >= $thumb_aspect ) {
$new_height = $thumb_height;
$new_width = $width / ($height / $thumb_height);
} else {
$new_width = $thumb_width;
$new_height = $height / ($width / $thumb_width);
}
$tmp = imagecreatetruecolor( $thumb_width, $thumb_height );
// Resize and crop
imagecopyresampled($tmp,
$src,
0 - ($new_width - $thumb_width) / 2, // Center the image horizontally
0 - ($new_height - $thumb_height) / 2, // Center the image vertically
0, 0,
$new_width, $new_height,
$width, $height);