Determining sector visibility of a polygon
Binay Kumar Bhattacharya, David G. Kirkpatrick, Godfried Toussaint · 1989
We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width σ. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are Θ(n) when σ ≤ π or σ = 2π, but require Ω(n log n) time (at least), when π < σ < 2π.