We study 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 visibilit...

In this paper, we are concerned with computing and maintaining the exact visibility polygon V (q) of a moving point observer q in planar scenes represented by a polygon with holes with complexity of n. We propose an algorithm that applies and computes each change to V (q) in constant time as q moves to a new neighboring position. In fact, in our method changes to V (q), as the observer q moves,...

We prove that a graph is 4-colorable if and only if it can be drawn with vertices in the integer lattice, using as edges only line segments not containing a third point of the lattice.

We consider visibility representations of graphs in which the vertices are represented by a collection O of non-overlapping convex regions on the plane. Two points x and y are visible if the straight-line segment xy is not obstructed by any object. Two objects A; B 2 O are called visible if there exist points x 2 A; y 2 B such that x is visible from y. We consider visibility only for a nite set...

We show that every segment endpoint visibility graph on disjoint line segments in the plane admits an alternating path of length , answering a question of Bose. This bound is optimal apart from a constant factor. We also give bounds on the constants hidden by the asymptotic notation.