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.

翻译：我们研究旋转射线的沃罗诺伊图，这是一种沃罗诺伊结构，其中输入站点为射线，而点与站点（射线）之间的距离函数定义为逆时针方向的角度距离。这一新型沃罗诺伊图源于照明或覆盖问题：域需由均匀角度的泛光灯/扇形光覆盖，目标是找到覆盖该域所需的最小角度。我们研究了平面上的该图结构，给出了其结构性质、组合复杂度界限以及构造算法。当射线由凸多边形诱导时，我们展示了如何在线性时间内构造该多边形内的沃罗诺伊图。利用这一信息，我们可在最优线性时间内求得布罗卡角，即均匀角度的泛光灯照亮凸多边形所需的最小角度。