Westudy a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility...

the direction and speed of winds play an important role in the occurrence of pollutions and dust stormas well as location placement for the establishment of industries and the expansion of cities. yazd is a dry area of iran, and constantly exposed to the dust particles in the air; and this in terms of human life and health issues are of special importance. in this paper a day when due to the am...

We consider the problem of routing on a network in the presence of line segment constraints (i.e., obstacles that edges in our network are not allowed to cross). Let P be a set of n points in the plane and let S be a set of non-crossing line segments whose endpoints are in P . We present two deterministic 1-local O(1)-memory routing algorithms that are guaranteed to find a path of at most linea...

This paper examines differences of four approaches in finding the visibility graph of a polygonal region with obstacles defined by simple polygons. Each has been implemented and tuned. Experimental comparisons via time measurements have been carried out against a variety of testcases ranging in graph density from maximal, O(† n 2), to minimal, † W(n). In this manner, expected asymptotic time bo...

In this paper we consider the problem of computing the weak visibility polygon of any query line segment pq (or WVP(pq)) inside a given polygon P . Our first non-trivial algorithm runs in simple polygons and needs O(n log n) time and O(n) space in the preprocessing phase to report WVP(pq) of any query line segment pq in time O(log n + |WVP(pq)|). We also give an algorithm to compute the weak vi...

Given a collection of objects in the plane along with a viewpoint !, the visibility problem involves determining the portion of each object that is visible to an observer positioned at !. The visibility problem is central to various application areas including computer graphics , image processing, VLSI design, and robot navigation, among many others. The main contribution of this work is to pro...

Here we present Depthmap, a program designed to perform visibility graph analysis of spatial environments. The program allows a user to import a 2D layout in drawing exchange format (DXF), and to fill the open spaces of this layout with a grid of points. The user may then use the program to make a visibility graph representing the visible connections between those point locations. Once the grap...