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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)