Rewrote the manual example into this function for creating a thumbnail image:

function thumbnail_jpeg ($original, $thumbnail, $width, $height, $quality) {
  list($width_orig, $height_orig) = getimagesize($original);
  if ($width && ($width_orig < $height_orig)) {
    $width = ($height / $height_orig) * $width_orig;
  }
        else {
    $height = ($width / $width_orig) * $height_orig;
  }
  $image_p = imagecreatetruecolor($width, $height);
  $image = imagecreatefromjpeg($originial);
  imagecopyresampled($image_p, $image, 0, 0, 0, 0, $width, $height, $width_orig, $height_orig);
  imagejpeg($image_p, $thumbnail, $quality);
  return;
}