Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of three-dimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R3 with a total of n edges consists of Θ(n2) connected components in the worst case. In the generic case, each connected component is a ...

Infrared observations of seaborne thermal sources are subject to the effects of atmospheric refraction. For low elevation angles at long ranges, out to the limit of visibility, the inevitable atmospheric temperature gradients frequently produce mirages. I present an analysis of a 22-min sequence of images recorded on 18 February 1994 at the U.S. Naval Surface Warfare Center at Wallops Island, V...

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...

A nonzero temperature generalization of the Fermi-Bose mapping theorem is used to study the exact quantum statistical dynamics of a one-dimensional gas of impenetrable bosons on a ring. We investigate the interference produced when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Nonzero te...

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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