A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Computing the link center of a simple polygon
Discrete & Computational Geometry - ACM Symposium on Computational Geometry, Waterloo
Computing the visibility polygon from a convex set and related problems
Journal of Algorithms
An O(n log n) algorithm for computing the link center of a simple polygon
Discrete & Computational Geometry
Handbook of discrete and computational geometry
Visibility with multiple diffuse reflections
Computational Geometry: Theory and Applications
Minimum link paths in polygons and related problems
Minimum link paths in polygons and related problems
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Algorithms for Computing Diffuse Reflection Paths in Polygons
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
The complexity of diffuse reflections in a simple polygon
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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In this paper we study the diffuse reflection diameter and diffuse reflection radius problems for convex-quadrilateralizable polygons. In the usual model of diffuse reflection, a light ray incident at a point on the reflecting surface is reflected from that point in all possible inward directions. A ray reflected from a polygonal edge may graze that reflecting edge but an incident ray cannot graze the reflecting edge. The diffuse reflection diameter of a simple polygon P is the minimum number of diffuse reflections that may be needed in the worst case to illuminate any target point t from any point light source s inside P. We show that the diameter is upper bounded by 3n-104 in our usual model of diffuse reflection for convex-quadrilateralizable polygons. To the best of our knowledge, this is the first upper bound on diffuse reflection diameter within a fraction of n for such a class of polygons. We also show that the diffuse reflection radius of a convex-quadrilateralizable simple polygon with n vertices is at most 3n-108 under the usual model of diffuse reflection. In other words, there exists a point inside such a polygon from which 3n-108usual diffuse reflections are always sufficient to illuminate the entire polygon. In order to establish these bounds for the usual model, we first show that the diameter and radius are n-42 and @?n-44@? respectively, for the same class of polygons for a relaxed model of diffuse reflections; in the relaxed model an incident ray is permitted to graze a reflecting edge before turning and reflecting off the same edge at any interior point on that edge. We also show that the worst-case diameter and radius lower bounds of n-42 and @?n-44@? respectively, are sometimes attained in the usual model, as well as in the relaxed model of diffuse reflection.