  We study the Voronoi Diagram of Rotating Rays, a Voronoi structure where the
input sites are rays and the distance function between a point and a site/ray,
is the counterclockwise angular distance. This novel Voronoi diagram is
motivated by illumination or coverage problems, where a domain must be covered
by floodlights/wedges of uniform angle, and the goal is to find the minimum
angle necessary to cover the domain. We study the diagram in the plane, and we
present structural properties, combinatorial complexity bounds, and a
construction algorithm. If the rays are induced by a convex polygon, we show
how to construct the Voronoi diagram within this polygon in linear time. Using
this information, we can find in optimal linear time the Brocard angle, the
minimum angle required to illuminate a convex polygon with floodlights of
uniform angle.
