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We study the following variant of the well-known line-simpli-ficationproblem: we are getting a possibly infinite sequence of points p<sub>0</sub>,p<sub>1</sub>,p<sub>2</sub>,... in the plane defining a polygonal path, and as wereceive the points we wish to maintain a simplification of the pathseen so far. We study this problem in a streaming setting, where… (More)

In this paper, we consider the problem of computing the visibility of a query point inside polygons with holes. The goal is to perform this computation efficiently per query with more cost in the preprocessing phase. Our algorithm is based on solutions in [13] and [2] proposed for simple polygons. In our solution, the preprocessing is done in time… (More)

For a set of n disjoint line segments S in R 2 , the visibility testing problem (VTP) is to test whether the query point p sees a query segment s ∈ S. For this configuration, the visibility counting problem (VCP) is to preprocess S such that the number of visible segments in S from any query point p can be computed quickly. In this paper, we solve VTP in… (More)

In this paper, we consider the problem of computing the visibility of a query point inside polygons with holes. The goal is to perform this computation efficiently per query considering the cost of the preprocessing phase. Our algorithm is based on solutions in [A. proposed for simple polygons. In our solution, the preprocessing is done in time O(n 3 log n)… (More)

Determining whether two segments s and t in a planar polyg-onal scene weakly see each other is a classical problem in computational geometry. In this problem we seek for a segment connecting two points of s and t without intersecting edges of the scene. In planar polygo-nal scenes, this problem is 3sum-hard and its time complexity is Ω(n 2) where n is the… (More)

Computing the visible region from a moving point in planar environments has many applications in computer graphics and computational geometry. This problem has been considered thoroughly before and several algorithms have been proposed for it. Almost all these solutions use a preprocess-ing step to build data structures which reflect the visibility… (More)