PHP で画像をトリミングするときに画像のアスペクト比を維持するにはどうすればよいですか?

$image = imagecreatefromjpeg($_GET['src']);
$filename = 'images/cropped_whatever.jpg';

$thumb_width = 200;
$thumb_height = 150;

$width = imagesx($image);
$height = imagesy($image);

$original_aspect = $width / $height;
$thumb_aspect = $thumb_width / $thumb_height;

if ( $original_aspect >= $thumb_aspect )
{
    // 图像更宽（纵横比意义上）
    $new_height = $thumb_height;
    $new_width = $width / ($height / $thumb_height);
}
else
{
    // 缩略图更宽
    $new_width = $thumb_width;
    $new_height = $height / ($width / $thumb_width);
}

$thumb = imagecreatetruecolor( $thumb_width, $thumb_height );

// 调整大小并裁剪
imagecopyresampled($thumb,
    $image,
    0 - ($new_width - $thumb_width) / 2, // 水平居中图像
    0 - ($new_height - $thumb_height) / 2, // 垂直居中图像
    0, 0,
    $new_width, $new_height,
    $width, $height);
imagejpeg($thumb, $filename, 80);