Given a simple polygon P with n vertices, the visibility polygon (VP) of a point q (VP(q)), or a segment pq (VP(pq)) inside P can be computed in linear time. We propose a linear time algorithm to extend VP of a viewer (point or segment), by converting some edges of P into mirrors, such that a given non-visible segment uw can also be seen from the viewer. Various definitions for the visibility o...

We show that the segment endpoint visibility graph of any finite set of 2n line segments contains a planar matching that does not use any segment edge, if the line segments in our set are convexly independent.

We consider visibility graphs involving bars and arcs in which lines of sight can pass through at most k objects. We prove a new edge bound for arc k-visibility graphs, provide maximal constructions for arc visibility graphs and semi-arc k-visibility graphs, and give a complete characterization of semi-arc visibility graphs. We further show that the family of arc i-visibility graphs is never co...

We show that the segment endpoint visibility graph of any finite set of disjoint line segments in the plane admits a simple Hamiltonian polygon, if not all segments are collinear. This proves a conjecture of Mirzaian.

We define a natural class of graphs by generalizing prior notions of visibility, allowing the representing regions and sightlines to be arbitrary. We consider mainly the case of compact connected representing regions, proving two results giving necessary properties of visibility graphs, and giving some examples of classes of graphs that can be so represented. Finally, we give some applications ...

A new technique is presented for determining the positions where a range sensor should be located to acquire the surfaces of a complex scene. The algorithm consists of two stages. The first stage applies a voting scheme that considers occlusion edges. Most of the surfaces of the scene are recovered through views computed in that way. Then, the second stage fills up remaining holes through a sch...

atmospheric visibility is a key factor in everyday life mainly in aviation, industry and surface traffic. it has been defined as the greatest distance at which an observer can just see a black object viewed against the horizon sky which is known as the visual range. furthermore, light extinction which is mostly due to absorption and scattering effects of aerosols in the atmosphere, can be calcu...

In this paper, we survey kinetic visibility problems. Unlike the research in traditional visibility problems, the researchers have also taken moving objects into consideration. These problems have been addressed from different practical aspects, such as computational graphics and robotic design. Over the years, some general combinatorial results of the visibility graph have been shown. Leveragi...