Before revision:  The link distance  between s, t with visibility q, and its path are provided in time O(\log n) and O(k+\log n)  for the above two cases, where k is the number of links.
After revision:  The link distance of a q-visible path between s, t with visibility q, and its path are provided in time O(\log n) and O(k+\log n) for the above two cases, where k is the number of links.