Abstract
This paper provides a gradient search algorithm for finding the maximal visible area polygon (VAP) viewed by an interior point in a simple polygon P. The algorithm is based on a natural partition of P into convex sets, such that each element of the partition is associated with a unique analytical form of the area function. We call this partition a back diagonal partition of P. Our maximal VAP algorithm converges in a finite number of steps, and is polynomial with a complexity of , for a simple polygon P with n vertices, and r reflex vertices. We use the maximal VAP algorithm as a basis for a greedy heuristic for the well known guardhouse problem with a computation complexity of .
Highlights
A visual polygon is a polygon in which any pair of points is mutually visible
A visible polygon from a point x in a simple polygon P with n vertices can be found with a computational complexity of O (n) by the algorithm of El Gindy and Avis [1]
The algorithm we suggest for this problem is based on a gradient search which converges with a finite number of steps
Summary
A visual polygon is a polygon in which any pair of points is mutually visible. A visible polygon from a point x in a simple polygon P with n vertices can be found with a computational complexity of O (n) by the algorithm of El Gindy and Avis [1]. (2015) A Gradient Search Algorithm for the Maximal Visible Area Polygon Problem. We denote this problem as the maximal visible area polygon (VAP) problem. We offer a greedy algorithm, which repeatedly uses the gradient search method for finding the maximal VAP, and for solving the guardhouse problem.
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