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 | ART GALLERY THEOREMS AND ALGORITHMS - Clark Science Center
The first chapter covers the original art gallery theorem (|/*/3j guards are necessary and sufficient), and basic polygon partitioning algorithms. I have found this material to form a suitable introduction to computational geometry.
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 | The Art Gallery Theorem
Finding the minimal number of cameras is NP-hard. Exercise 1: Consider a simple (no holes) polygon P with n vertices, where all edges are either vertical or horizontal. The simplest example is a rectangle and 1 camera sufices. Draw examples to justify that ⌊n/4⌋ cameras sufice.
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 | Lesson 9. The Art Gallery Problem - I628E Information ...
Art Gallery Problem (decision version): Input: An orthogonal polygon P and an integer k. Output: YES if P can be guarded by at most k guards placed on its boundary. NO otherwise. What if our art gallery is not a 2D polygon but a 3D polyhedron? Do the previous results generalize to 3D shapes?
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 | The Art Gallery Problem - IIT
The original art gallery problem (V. Klee, 1973) asked for the minimum number of guards sufficient to see every point of the interior of an n-vertex simple polygon. A simple polygon is a simply-connected closed region whose boundary consists of a finite set of line segments.
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 | Gazette 31 Vol 3 - Cornell University
A little more precisely, let us consider our art gallery to be the closed set of points bounded by a polygon. We will also need to make the somewhat unrealistic assumption that our guards are points and we will allow them to stand anywhere in the polygon, even along an edge or at a vertex.
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 | Polygon triangulation and the art gallery problem
Guarding an art gallery • A point guard (or camera) placed inside the gallery sees every point in the gallery to which it can be connected with an open line segment that lies completely in the interior of the gallery (interior of a polygon or interior of a polyhedron)
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