Given a simple polygon P in the plane, we present a parallel algorithm for computing the visibility polygon of an observer point q inside P. We use chain visibility concept and a bottom-up merge method for constructing the visibility polygon of point q. The algorithm is simple and mainly designed for GPU architectures, where it runs in O(log n) time using O(n) processors. This is the first work...

We extend results of [1, 2, 3] on the visibility problem for lattice points in Zd to the case of function fields over finite fields which are related to important questions regarding the corresponding q-Jacobsthal function. Résumé. Nous étendons résultats de [1, 2, 3] sur le probleme de la visibilité des points du réseau entier Zd au cas des corps de fonctions sur un corps fini, en rapport avec...

We present a dynamic placement technique for annotations of virtual landscapes that is based on efficient view management. Annotations represent textual or symbolic descriptions and provide explanatory or thematic information associated with spatial positions. The technique handles external annotations as 2.5 dimensional objects and adjusts their positions with respect to available space in the...

We show that the visibility graph of a set of disjoint congruent discs in IR is Hamiltonian, as long as the discs are not all supported by the same line. The proof is constructive, and leads to efficient algorithms for obtaining a Hamilton circuit.

We examine how the Fusion method handles the followings aspects which characterize a better documentation of the inter-object behavior, namely styles of specification, readability, formal basis, composition and refinement, completeness, temporal ordering of operations, structural constraints, global invariants, individual object specification, preand postconditions, and finally, use case descri...

We study versions of cop and robber pursuit-evasion games on the visibility graphs of polygons, and inside polygons with straight and curved sides. Each player has full information about the other player’s location, players take turns, and the robber is captured when the cop arrives at the same point as the robber. In visibility graphs we show the cop can always win because visibility graphs ar...

We consider the problem of finding a minimalistic configuration of sensors that enable a simple robot inside an initially unknown polygon P on n vertices to reconstruct the visibility graph of P . The robot can sense features of its environment through its sensors, and it is allowed to move from vertex to vertex. We aim at understanding which sensorial capabilities are sufficient for the recons...

Time series can be transformed into graphs called horizontal visibility graphs (HVGs) in order to gain useful insights. Here, the maximum eigenvalue of the adjacency matrix associated to the HVG derived from several time series is calculated. The maximum eigenvalue methodology is able to discriminate between chaos and randomness and is suitable for short time series, hence for experimental resu...

This paper presents a radio paths modeling framework for simulating RF coverage in complex indoor environments. We propose an algorithm which utilizes a geometric visibility graph of a building to traverse all possible bounded radio paths. These paths are needed for the computation of signal strength captured at a given receiver location. We have implemented the suggested algorithm and conducte...

We consider two problems where our goal is to find a point x such that the area of the region V (x) “controlled” by x is as large as possible. In the first problem, we are given a simple polygon P , and V (x) is the visibility polygon of x, that is, the region of points y inside P such that the segment xy does not intersect the boundary of P . In the second problem, we are given a set of points...