Incremental Update of the Visibility Map as Seen by a Moving Viewpoint in Two Dimensions

Abstract

Consider the following problem: A viewpoint moves amongst a set of line segments in the plane and it is desired to maintain the sequence of lines visible from the viewpoint at every increment in its position. The sequence of visible lines is identical for most increments in the position of the viewpoint. It is different only when the viewpoint crosses a visual discontinuity line. Our objective is to be able to quickly report whether the sequence of visible lines needs to be updated and perform the update quickly in that case. We propose an algorithm that satisfies both criteria while using space linear in the number of visual discontinuity lines. This last condition is important because constructing the arrangement of these lines would take space quadratic in their number.