atmospheric visibility has been defined as the greatest distance at which an observer can see a black object viewed against the horizon sky, which in quantitative terminology is known as visual range. visibility, in the absence of special meteorological events (e.g. rain and fog), is an excellent indicator of air quality. visibility impairment results from light scattering and absorption by atm...

Given a collection of polygonal obstacles with n vertices on the place, and any t > 1, we present an O(n logn) time algorithm that constructs a bounded-degree t-spanner of the visibility graph, without rst having to construct the visibility graph.

hyperactivity disorder (ADHD) Ainara Mira-Iglesias; J. Alberto Conejero; Esperanza Navarro-Pardo Fundación para el Fomento de la Investigación Sanitaria y Biomédica de la Comunidad Valenciana (FISABIO), Valencia, Spain Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Spain Departamento de Psicoloǵıa Evolutiva y de la Educación, Universitat de València,...

A visibility representation of a graph G is an assignment of the vertices of G to geometric objects such that vertices are adjacent if and only if their corresponding objects are “visible” each other, that is, there is an uninterrupted channel, usually axis-aligned, between them. Depending on the objects and definition of visibility used, not all graphs are visibility graphs. In such situations...

Given an arbitrary polygon P with holes, we construct a polytopal complex analogous to the associahedron based on convex diagonalizations of P . This polytopal complex is shown to be contractible, and a geometric realization is provided based on the theory of secondary polytopes. We then reformulate a combinatorial deformation theory and present an open problem based on visibility which is a cl...

We exhibit a family of graphs which can be realized as pseudo-visibility graphs of pseudo-polygons, but not of straight-line polygons. The example is based on the characterization of vertex-edge pseudo-visibility graphs of O’Rourke and Streinu [Proc. ACM Symp. Comput. Geometry, Nice, France, 1997, pp. 119–128] and extends a recent result of the author [Proc. ACM Symp. Comput. Geometry, Miami Be...

We consider direct visibility in simple orthogonal polygons and derive tight lower and upper bounds on the number of strictly internal and external visibility edges. We also show a lower bound of ⌈n2 ⌉ − 1 on the number of diffuse reflections required for completely illuminating an orthogonal polygon from an arbitrary point inside it. Further, we derive lower bounds on the combinatorial complex...

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We study polar visibility graphs, graphs whose vertices can be represented by arcs of concentric circles with adjacency determined by radial visibility including visibility through the origin. These graphs are more general than the well-studied bar-visibility graphs and are characterized here, when arcs are proper subsets of circles, as the graphs that embed on the plane with all but at most on...

Let P be a finite set of points in the plane and S a set of non-crossing line segments with endpoints in P . The visibility graph of P with respect to S, denoted Vis(P, S), has vertex set P and an edge for each pair of vertices u, v in P for which no line segment of S properly intersects uv. We show that the constrained half-θ6-graph (which is identical to the constrained Delaunay graph whose e...