Alireza Zarei

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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)
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)
Determining whether two segments s and t in a planar polygonal 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 polygonal scenes, this problem is 3sum-hard and its time complexity is Ω(n) where n is the(More)
For a set of n points in the plane, this paper presents simple kinetic data structures (KDS’s) for solutions to some fundamental proximity problems, namely, the all nearest neighbors problem, the closest pair problem, and the Euclidean minimum spanning tree (EMST) problem. Also, the paper introduces KDS’s for maintenance of two well-studied sparse proximity(More)
In this paper, we consider the restricted version of the well-known 2D line simplification problem under area measures and for restricted version. We first propose a unified definition for both of sum-area and difference-area measures that can be used on a general path of n vertices. The optimal simplification runs in O(n) under both of these measures.(More)