Bar k-visibility graphs are graphs admitting a representation in which the vertices correspond to horizontal line segments, called bars, and the edges correspond to vertical lines of sight which can traverse up to k bars. These graphs were introduced by Dean et al. [4] who conjectured that bar 1-visibility graphs have thickness at most 2. We construct a bar 1-visibility graph having thickness 3...

Worker posture, task time and performance are often affected when one-handed manual dexterous tasks performed in small overhead spaces under an obscured view. A common method used for supplementing visual feedback these cases is a hand-held telescopic mirror, but that involves working with both arms extended overhead, accompanied by awkward neck shoulder postures. video camera was considered as...

We investigate the problem of constructing a shortest path of a point{like robot between two conngurations in the euclidean plane cluttered with (intersecting) convex polygonal obstacles. One common approach is to construct the visibility graph and search within this graph in a total time of O(n 2). We show that in general it is not necessary to construct the entire visibility graph. In contras...

Westudy a new class of visibility problems based on the notion of α-visibility. Given an angle α and a collection of line segments S in the plane, a segment t is said to be α-visible from a point p, if there exists an empty triangle with one vertex at p and the side opposite to p on t such that the angle at p is α. In this model of visibility, we study the classical variants of point visibility...

We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and set partitions size n. Our main results are formulas expressing expected degree graph nodes in terms simple explicit functions a finite collection Stirling Bernoulli numbers.

In the Any-Angle Pathfinding problem, the goal is to find the shortest path between a pair of vertices on a uniform square grid, that is not constrained to any fixed number of possible directions over the grid. Visibility Graphs are a known optimal algorithm for solving the problem with the use of preprocessing. However, Visibility Graphs are known to perform poorly in terms of running time, es...