Planar visibility: testing and counting

We devise an algorithm for maintaining the visibility polygon of any query point in a dynamic polygonal domain, i.e., as the polygonal domain is modified with vertex insertions and deletions to its obstacles, we update the data structures that ...${}_{{\mathcal{}}^{}}{{}^{}}^{\mathrm{}}$${{}^{}}^{\mathrm{}}{}_{{\mathcal{}}^{}}$${}_{{\mathcal{}}^{}}$${\mathcal{}}^{}$${}^{}$${\mathcal{}}^{}$${\mathcal{}}^{}$${}_{{\mathcal{}}^{}}$${\mathcal{}}^{}$${}_{{\mathcal{}}^{}}$${}_{{\mathcal{}}^{}}$${}_{{\mathcal{}}^{}}$${{}^{}}^{\mathrm{}}$${{}^{}}^{\mathrm{}}$${\mathcal{}}^{}$${}^{}$${\mathcal{}}^{}$${\mathcal{}}^{}$${\mathcal{}}^{}$

A simple polygon P is LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is visible from some point of the other boundary of P from t to s and vice versa. We show that P is not ...

We study the problem of computing the visibility graph defined by a set P of n points inside a polygon Q: two points p,q ε P are joined by an edge if the segment ‾_pq ⊂ Q. Efficient output-sensitive algorithms are known for the case in which P is the set ...