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<?php

function get_vimeo_video_id( $vimeo_url ) {
    // ----- http://stackoverflow.com/a/10489007/1291469 ----- //
    $video_id = (int) substr(parse_url($vimeo_url, PHP_URL_PATH), 1);
    return $video_id;
}

function get_vimeo_thumbnail( $vimeo_url ) {
    // ----- http://stackoverflow.com/a/1361192/1291469 ----- //
    $id = get_vimeo_video_id( $vimeo_url );
    $hash = unserialize(file_get_contents("https://vimeo.com/api/v2/video/$id.php"));
    return $hash[0]['thumbnail_medium'];
}