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Efficient Visibility Maintenance of a Moving Segment Observer inside a Simple Polygon

In this paper we consider maintaining the visibility of a segment observer moving inside a simple polygon. A practical instance of this problem is to identify the regions of a planar scene illuminated by a fluorescent lamp while the lamp moves around. We consider both strong and weak visibility in this paper. Our method is based on the shortest path tree which builds a linear-sized data structure in O(n) time, where n is the number of the vertices of the underlying simple polygon P. We first compute VP(st), the initial view of the segment observer st. Then, as st moves, each change of VP(st) can be computed in O(log(|V P (st)|)) time when the observer is allowed to change its direction, and in O(log(|V P (st)|)) time when the observer moves along a given line.