Let s denote a compact convex object in IR. The f-width of s is the perpendicular distance between two distinct parallel lines of support of s with direction f . A set of disjoint convex compact objects in IR is of equal f -width if there exists a direction f such that every pair of objects have equal f -width. A visibility matching, for a set of equal f -width objects is a matching using non-c...

It was shown recently that in the segment endpoint visibility graph Vis(S) of any set S of n disjoint line segments in the plane, there is an alternating path of length (log n), and this bound best possible apart from a constant factor. This talk focuses on the variant of the problem where S is a set of n disjoint axis-parallel line segments, and shows that the length of a longest alternating p...

In this paper we present a very simple proof of the following result due to Abello et al [5], concerning the visibility graphs of simple polygons. The result says that the visibility graph of any simple nondegenerate polygon is isomorphic to the visibility graph of some simple staircase polygon. As a result of the above proof we also give an O(n log n) time algorithm for the following problem: ...

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...