Dynamic algorithms for visibility polygons

We devise dynamic algorithms for the following (weak) visibility polygon computation problems: • Maintaining visibility polygon of a fixed point located interior to simple polygon amid vertex insertions and deletions to simple polygon. • Answering visibility polygon query corresponding to any point located exterior to simple polygon amid vertex insertions and deletions to simple polygon. • Maintaining weak visibility polygon of a fixed line segment located interior to simple polygon amid vertex insertions to simple polygon. • Answering weak visibility polygon query corresponding to any line segment located interior to simple polygon amid both vertex insertions and deletions to simple polygon. • Maintaining visibility polygon of a fixed point located in the free space of the polygonal domain amid vertex insertions to simple polygons in that polygonal domain. The proposed algorithms are output-sensitive, and the time complexities of algorithms for (weak) visibility polygon maintenance are expressed in terms of change in output complexity.