On Visibility

On k-visibility graphs

We examine several types of visibility graphs in which sightlines can pass through k objects. For k ≥ 1 we bound the maximum thickness of semi-bar k-visibility graphs between d 2 3 (k + 1)e and 2k. In addition we show that the maximum number of edges in arc and circle k-visibility graphs on n vertices is at most (k+1)(3n− k− 2) for n > 4k+4 and ( n 2 ) for n ≤ 4k + 4, while the maximum chromati...

On Rectangle Visibility Graphs

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...

BSP Visibility on S

Despite over four decades of published algorithms for the computation of visibility, a large gap between theory and practice remains. A significant objective is to design and implement a robust and efficient algorithm that makes it possible to generate the set of polygons visible from an observer in a piecewise linear scene. We describe here and in the accompanying manuscript an algorithm that ...

On Visibility and Blockers

This expository paper discusses some conjectures related to visibility and blockers for sets of points in the plane.

On Rectangle Visibility Graphs. III. External Visibility and Complexity