Amirali Khosravi

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An optimal bsp for a set S of disjoint line segments in the plane is a bsp for S that produces the minimum number of cuts. We study optimal bsps for three classes of bsps, which differ in the splitting lines that can be used when partitioning a set of fragments in the recursive partitioning process: free bsps can use any splitting line, restricted bsps can(More)
Let <i>P</i> be a rectilinear simple polygon. The stabbing number of a partition of P into rectangles is the maximum number of rectangles stabbed by any axis-parallel line segment inside P. We present a 3-approximation algorithm for the problem of finding a partition with minimum stabbing number. It is based on an algorithm that finds an optimal partition(More)
Let S be a set of n points in R d , and let r be a parameter with 1 r n. A rectilinear r-partition for S is a collection Ψ (S) := {(S1, b1),. .. , (St, bt)}, such that the sets Si form a partition of S, each bi is the bounding box of Si, and n/2r |Si| 2n/r for all 1 i t. The (rectilinear) stabbing number of Ψ (S) is the maximum number of bounding boxes in Ψ(More)
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(More)
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