Review of visibility algorithms in the plane by Subir Kumar Ghosh (Cambridge University Press, 2007)

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{}}^{}$

Given a polygonal domain, we devise a fully dynamic algorithm for maintaining the visibility polygon of any query point, i.e., as the polygonal domain is modified with vertex insertions and deletions to its obstacles, we update the visibility ...