We consider a variation of the Cops and Robber game where the cops can only see the robber when the distance between them is at most a fixed parameter `. We consider the basic consequences of this definition for some simple graph families, and show that this model is not monotonic, unlike common models where the robber is invisible. We see that cops’ strategy consists of a phase in which they n...

The visibility graph V(X) of a discrete point set X ⊂ R2 has vertex set X and an edge xy for every two points x, y ∈ X whenever there is no other point in X on the line segment between x and y. We show that for every graph G, there is a point set X ∈ R2, such that the subgraph of V(X∪Z2) induced by X is isomorphic to G. As a consequence, we show that there are visibility graphs of arbitrary hig...

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.

Here we present Depthmap, a program designed to perform visibility graph analysis of spatial environments. The program allows a user to import a 2D layout in drawing exchange format (DXF), and to fill the open spaces of this layout with a grid of points. The user may then use the program to make a visibility graph representing the visible connections between those point locations. Once the grap...

A bar visibility representation of a graph G is a collection of horizontal bars in the plane corresponding to the vertices of G such that two vertices are adjacent if and only if the corresponding bars can be joined by an unobstructed vertical line segment. In a bar k-visibility graph, two vertices are adjacent if and only if the corresponding bars can be joined by a vertical line segment that ...

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...

A visibility drawing of a plane graph G is a drawing of G where each vertex is drawn as a horizontal line segment and each edge is drawn as a vertical line segment such that the line segments use only grid points as their endpoints. The area of a visibility drawing is the area of the smallest rectangle on the grid which encloses the drawing. A minimum-area visibility drawing of a plane graph G ...

We describe a set of necessary conditions for a given graph to be the visibility graph of a simple polygon. For every graph satisfying these conditions we show that a uniform rank 3 oriented matroid can be constructed in polynomial time, which if affinely coordinatizable yields a simple polygon whose visibility graph is isomorphic to the given graph.

The visibility graph is a fundamental structure studied in the field of computational geometry, and pose some special challenges [12, 26]. Apart from theoretical interests, visibility graphs has important applications also. Some of the early applications include computing Euclidean shortest paths in the presence of obstacles [36] and decomposing two-dimensional shapes into clusters [40]. For mo...