Finding the Θ-Guarded Region
نویسنده
چکیده
We are given a finite set of m points (guards) G in the plane R 2 and an angle 0 ≤ Θ ≤ 2π. A Θ-cone is a cone with apex angle Θ. We call a Θ-cone empty (with respect to G) if it does not contain any point of G. A point p ∈ R is called Θ-guarded if every Θ-cone with apex located at p is non-empty. Moreover, the set of all Θ-guarded points is called Θ-region. We first show how to construct a data structure of O(m log m) time and space such that in time O(log m) we can compute whether some point p ∈ R is Θ-guarded. As a main result of our work we describe the Θ-region with only O(m/Θ) circular arcs and show a way to compute it.
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Finding the Theta-guarded region
We are given a finite set of n points (guards) G in the plane R 2 and an angle 0 ≤ Θ ≤ 2π. A Θ-cone is a cone with apex angle Θ. We call a Θ-cone empty (with respect to G) if it does not contain any point of G. A point p ∈ R is called Θ-guarded if every Θ-cone with its apex located at p is non-empty. Furthermore, the set of all Θ-guarded points is called the Θ-guarded region, or the Θ-region fo...
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