In this paper we consider the k-link visibility polygon of an object inside a polygonal environment with a reflective edge called a mirror. The k-link visibility polygon of an object inside a polygon P is the set of all points in P , which are visible to some points of that object with at most k − 1 intermediate points, under the property that consecutive intermediate points are mutually visibl...

A tower is a polygon consisting of two reflex chains sharing one common endpoint, together with one edge joining the other endpoints of the chains. A linear time algorithm is given to recognize the [vertex] visibility graphs of towers, and these graphs are characterized as bipartite permutation graphs with an added Hamiltonian cycle. Similar results have been obtained independently by Choi, Shi...

Then, two points p, q of an orthogonal polygon P are s-visible from one another if there exists a stair ase path from p to q that lies in P (Figure 1(a) shows two su h points p and q). The set of points that are s-visible from a point p form the s-visibility polygon of p. The s-kernel of P is the (possibly empty) set of points of P whose s-visibility polygon is equal to P , i.e., the set of poi...

The paper considers representations of bipartite graphs as rectangle-visibility graphs, Le., graphs whose vertices are rectangles in the plane, with adjacency detenmned by horizontal and vertical visibility.1t is shown that, for p ~ q, Kp,q has a representation with no rectangles having collinear sides if and only if p ~ 2 or p = 3 and q ~ 4. More generally, it is shown that Kp;q is a rectangle...

We characterize two types of bar-visibility graphs on the Mobius band (abbreviated "BVGMs"), in which vertices correspond to intervals that are parallel or orthogonal to the axis of the band, depen­ ding on type, and in which adjacency corresponds to orthogonal visibility of intervals. BVGMs with intervals orthogonal to the axis are shown to be equivalent to the "polar visibility graphs" studie...

In general, visibility reconstruction problems involve determining a set of objects in the plane that exhibit a speci ed set of visibility constraints. In this paper, an algorithm for reconstructing a set of parallel line segments is presented, from speci ed visibility information contained in an extended endpoint visibility graph. The algorithm runs in polynomial time and relies on simple vect...