id     name     left     right

//
 *  -- create new space for subtree
 *  UPDATE tags SET lpos = lpos + :width WHERE lpos >= :newpos
 *  UPDATE tags SET rpos = rpos + :width WHERE rpos >= :newpos
 *
 *  -- move subtree into new space
 *  UPDATE tags SET lpos = lpos + :distance, rpos = rpos + :distance
 *           WHERE lpos >= :tmppos AND rpos < :tmppos + :width
 *
 *  -- remove old space vacated by subtree
 *  UPDATE tags SET lpos = lpos - :width WHERE lpos > :oldrpos
 *  UPDATE tags SET rpos = rpos - :width WHERE rpos > :oldrpos
 */

// calculate position adjustment variables
int width = node.getRpos() - node.getLpos() + 1;
int distance = newpos - node.getLpos();
int tmppos = node.getLpos();

// backwards movement must account for new space
if (distance < 0) {
    distance -= width;
    tmppos += width;
}

$step = 1+ $this->_categoriesTable->rgt
                - $this->_categoriesTable->lft;
$lft = $this->_categoriesTable->lft;
$rgt = $this->_categoriesTable->rgt;
$id = $this->_categoriesTable->id;
$distance = $lft - $parentLeft - 1;
                $query = '
                    UPDATE %s SET lft=-lft, rgt=-rgt
                        WHERE lft>=%d AND lft<=%d;
                    UPDATE %s SET lft=lft+%d WHERE lft>%d AND lft<%d;
                    UPDATE %s SET rgt=rgt+%d WHERE rgt>%d AND rgt<%d;
                    UPDATE %s SET lft=-lft-%d, rgt=-rgt-%d WHERE lft<=-%d
                        AND lft>=-%d;
                    UPDATE %s SET parent_id=%d, title=%s, description=%s,
                        metadescription=%s WHERE id=%s';

                $query = sprintf($query,
                    $this->_db->nameQuote('#__categories'),
                        $lft, $rgt,
                    $this->_db->nameQuote('#__categories'), $step,
                        $parentLeft, $lft,
                    $this->_db->nameQuote('#__categories'), $step,
                        $parentLeft, $lft,
                    $this->_db->nameQuote('#__categories'), $distance,
                        $distance, $lft, $rgt,
                    $this->_db->nameQuote('#__categories'),
                        $data['parent_id'],
                        $this->_db->Quote($this->_categoriesTable->title),
                        $this->_db->Quote($this->_categoriesTable->description),
                        $this->_db->Quote(
                            $this->_categoriesTable->metadescription),
                        $this->_db->Quote($id));

// and for the moving to the "right" case
$step = 1+ $this->_categoriesTable->rgt
                - $this->_categoriesTable->lft;
$distance = $parentLeft - $this->_categoriesTable->rgt;

// Memorize this because we bind and we need the old values
$lft = $this->_categoriesTable->lft;
$rgt = $this->_categoriesTable->rgt;
$id = $this->_categoriesTable->id;

$query = sprintf($query,
                    $this->_db->nameQuote('#__categories'),
                        $lft, $rgt,
                    $this->_db->nameQuote('#__categories'), $step,
                        $rgt, $parentLeft,
                    $this->_db->nameQuote('#__categories'), $step,
                        $rgt, $parentLeft,
                    $this->_db->nameQuote('#__categories'), $distance,
                        $distance, $lft, $rgt,
                    $this->_db->nameQuote('#__categories'),
                        $data['parent_id'],
                        $this->_db->Quote($this->_categoriesTable->title),
                        $this->_db->Quote($this->_categoriesTable->description),
                        $this->_db->Quote(
                            $this->_categoriesTable->metadescription),
                        $this->_db->Quote($id));

#Set IDs
SET @dirId := :dirId; #folder (subtree) you wanna move
SET @targetId := :folderId; #target

#get datas
SELECT rgt, lft, rgt-lft+1, level INTO @dir_rgt, @dir_lft, @dir_size, @dir_level FROM files WHERE id = @dirId;

#put the moving tree aside (lft and rgt columns must allow negative int)
UPDATE files SET lft = 0-lft, rgt = 0-rgt WHERE lft BETWEEN @dir_lft AND @dir_rgt;

#fill the empty space
UPDATE files SET rgt = rgt-@dir_size WHERE rgt > @dir_rgt;
UPDATE files SET lft = lft-@dir_size WHERE lft > @dir_rgt;

#get datas of the target-folder
SELECT lft, level INTO @target_lft, @target_level FROM files WHERE id = @targetId;

#create space in the target-folder
UPDATE files SET rgt = rgt+@dir_size WHERE rgt >= @target_lft;
UPDATE files SET lft = lft+@dir_size WHERE lft > @target_lft;

#edit all nodes in the moving-tree
UPDATE files SET
   lft     = 0 - lft - (@dir_lft - @target_lft - 1), #this formula fits for all moving directions
   rgt     = 0 - rgt - (@dir_lft - @target_lft - 1),
   level   = level - (@dir_level - @target_level) + 1

WHERE
   lft < 0; #that could be more precise...