We study the presence of obstacles in computing BCP(s, t) (Best Coverage Path between two points s and t) in a 2D field under surveillance by sensors. Consider a set of m line segment obstacles and n point sensors on the plane. For any path between s to t, p is the least protected point along the path such that the Euclidean distance between p and its closest sensor is maximum. This distance (the path's cover value) is minimum for a BCP(s, t). We present two algorithmic results. For opaque obstacles, i.e., which obstruct paths and block sensing capabilities of sensors, computation of BCP(s, t) takes O((m 2n2 + n4)log(mn + n2)) time and O(m2n2 + n4) space. For transparent obstacles, i.e., which only obstruct paths, but allows sensing, computation of BCP(s, t) takes O(nm2 + n3) time and O(m2 + n 2) space. We believe, this is one of the first efforts to study the presence of obstacles in coverage problems in sensor networks.