Here's a function which implements resolving a relative URL according to RFC 2396 section 5.2. No doubt there are more efficient implementations, but this one tries to remain close to the standard for clarity. It relies on a function called "unparse_url" to implement section 7, left as an exercise for the reader (or you can substitute the "glue_url" function posted earlier).
<?php
/**
 * Resolve a URL relative to a base path. This happens to work with POSIX
 * filenames as well. This is based on RFC 2396 section 5.2.
 */
function resolve_url($base, $url) {
 if (!strlen($base)) return $url;
 // Step 2
 if (!strlen($url)) return $base;
 // Step 3
 if (preg_match('!^[a-z]+:!i', $url)) return $url;
 $base = parse_url($base);
 if ($url{0} == "#") {
 // Step 2 (fragment)
 $base['fragment'] = substr($url, 1);
 return unparse_url($base);
 }
 unset($base['fragment']);
 unset($base['query']);
 if (substr($url, 0, 2) == "//") {
 // Step 4
 return unparse_url(array(
 'scheme'=>$base['scheme'],
 'path'=>$url,
 ));
 } else if ($url{0} == "/") {
 // Step 5
 $base['path'] = $url;
 } else {
 // Step 6
 $path = explode('/', $base['path']);
 $url_path = explode('/', $url);
 // Step 6a: drop file from base
 array_pop($path);
 // Step 6b, 6c, 6e: append url while removing "." and ".." from
 // the directory portion
 $end = array_pop($url_path);
 foreach ($url_path as $segment) {
 if ($segment == '.') {
 // skip
 } else if ($segment == '..' && $path && $path[sizeof($path)-1] != '..') {
 array_pop($path);
 } else {
 $path[] = $segment;
 }
 }
 // Step 6d, 6f: remove "." and ".." from file portion
 if ($end == '.') {
 $path[] = '';
 } else if ($end == '..' && $path && $path[sizeof($path)-1] != '..') {
 $path[sizeof($path)-1] = '';
 } else {
 $path[] = $end;
 }
 // Step 6h
 $base['path'] = join('/', $path);
 }
 // Step 7
 return unparse_url($base);
}
?>