The Floodlight Problem
Prosenjit K. Bose, Leonidas Guibas, Anna Lubiw, Mark H. Overmars, Diane L. Souvaine, Jorge Urrutia · International Journal of Computational Geometry & Applications · 1997
Given three angles summing to 2π, given n points in the plane and a tripartition k1 + k2 + k3 = n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge contains ki of the points. This new result on dissecting point sets is used to prove that lights of specified angles not exceeding π can be placed at n fixed points in the plane to illuminate the entire plane if and only if the angles sum to at least 2π. We give O(n log n) algorithms for both these problems.