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...

INTRODUCTION: The visualization of structures in MRI highly depends on many user defined scan parameters. The selection of them is always done heuristically and requires a vast experience from the operator. Furthermore, sometimes it is not simple to predict the effect on the visibility of the structures of interest when a parameter is modified. We propose a methodology based on an automatic opt...

We present in this paper a generic and parameter-free algorithm to efficiently build a wide variety of optical components, such as mirrors or lenses, that satisfy some light energy constraints. In all of our problems, one is given a collimated or point light source and a desired illumination after reflection or refraction and the goal is to design the geometry of a mirror or lens which transpor...

An optical Fourier transform processor converts visibility data at its input to a sky brightness function at its output. Scattered light and spurious terms resulting from the method of encoding the complex visibility function as a real -valued and nonnegative transmittance result in errors in the processor output. In this paper, we discuss the degree to which each of these undesired terms degra...

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...

Transfer functions play a key role in volume rendering of medical data, but transfer function manipulation is unintuitive and can be time-consuming; achieving an optimal visualization of patient anatomy or pathology is difficult. To overcome this problem, we present a system for automatic transfer function design based on visibility distribution and projective color mapping. Instead of assignin...