The problem of generating \random" geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the speciic problem of generating a random x-monotone polygon on a given set of n vertices. Here, \random" is taken to mean that we select uniformly at random a polygon, from among all those x-monotone polygons having the given n vertices. We give an algo...

Let S be a collection of n non-intersecting line segments in the plane in general position. Two segments u and v are deened as visible if a line segment could be drawn from some point of u to some point of v that intersects no other segment in S. The full visibility graph associated with S is denoted as G(S), and deened to be the graph whose n vertices correspond to the line segments of S and w...

Imaging the vicinity of black hole is one of the ultimate goals of VLBI astronomy. The closest massive black hole, SgrA*, located at Galactic center is the leading candidate for such observations. Combined with recent VLBI recording technique and sub-mm radio engineering, we now have the sufficient sensitivity for the observations. We here show performance simulations of sub-mm VLBI arrays for ...

In this paper we consider the problem of drawing a graph in the plane so that the vertices of the graph are drawn as rectangles and the edges are horizontal or vertical line segments. We are in particular interested in drawings where each of the line segments can be thickened to have positive width, and none of these thickened segments (which we call bands of visibility) intersects the interior...

Obstacle representations of graphs have been investigated quite intensely over the last few years. We focus on graphs that can be represented by a single obstacle. Given a (topologically open) polygon C and a finite set P of points in general position in the complement of C, the visibility graph GC(P ) has a vertex for each point in P and an edge pq for any two points p and q in P that can see ...

The challenge of estimating the crystalline-fraction of dense randomly-oriented nano-particles, contained in a (less-dense) amorphous support, is increasingly important in fields as diverse as heterogeneous-catalyst design and electronic-data storage. Lattice-fringe visibility-analysis [1,2] is a potential tool in this context, but of course interfering contrast from the amorphous support (as w...

In a geometric context, two objects are “visible” to each other if there is a line segment connecting them that does not cross any obstacles. Over 500 papers have been published on aspects of visibility in computational geometry in the last 40 years. The research can be broadly classified as primarily focused on combinatorial issues, or primarily focused on algorithms. We partition the combinat...

OBJECTIVE The aim of this study was to determine and compare the reliability to accomplish of common mandibular landmarks and to determine the incidence of incisive canals, anterior looping, and lingual foramina in children from panoramic and CBCT images. DESIGN Panoramic and CBCT images from 100 children and adolescent patients were randomly selected. In order to grade the visibility of mand...

Viewshed and line-of-sight are spatial analysis functions used in applications ranging from urban design to archaeology to hydrology. Vegetation data, a difficult variable to effectively emulate in computer models, is typically omitted from visibility calculations or unrealistically simulated. In visibility analyzes performed on a small scale, where calculation distances are a few hundred meter...

The visibility graph of a finite set of points in the plane has the points as vertices and an edge between two vertices if the line segment between them contains no other points. This paper establishes bounds on the edgeand vertex-connectivity of