Before revision:  Otherwise, our algorithm outputs the visibility polygon corresponding to the exterior visibility of p. * An  output-sensitive algorithm to compute the weak visibility polygon corresponding to any query line segment located interior to the simple polygon amid both the vertex insertions and deletions to the simple polygon.
After revision:  Otherwise, our algorithm outputs the visibility polygon corresponding to the exterior visibility of p. * An incremental algorithm to maintain the weak visibility polygon of a fixed-line segment located interior to the simple polygon amid vertex insertions to the simple polygon. The time complexity to update the weak visibility polygon of a line segment pq due to the insertion of vertex v to the current simple polygon is expressed in terms of the sum of the number of combinatorial updates needed to the geodesic shortest path trees rooted at p and q due to the insertion of v. * An output-sensitive algorithm to compute the weak visibility polygon corresponding to any query line segment located interior to the simple polygon amid both the vertex insertions and deletions to the simple polygon.