Grab a thumbnail of a private (but embeddable) Vimeo video

grab_vimeo_thumbnail.php

<?php
/**
 * Grab the url of a publicly embeddable video hosted on vimeo
 * @param  str $video_url The "embed" url of a video
 * @return str            The url of the thumbnail, or false if there's an error
 */
function grab_vimeo_thumbnail($vimeo_url){
    if( !$vimeo_url ) return false;

    $data = json_decode( file_get_contents( 'http://vimeo.com/api/oembed.json?url=' . $vimeo_url ) );

    if( !$data ) return false;

    return $data->thumbnail_url;
}