The Voronoi Diagram of Rotating Rays With applications to Floodlight Illumination

We introduce the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays, and the distance function is the counterclockwise angular distance between a point and a ray-site. This novel Voronoi diagram is motivated by illumination and coverage problems, where a domain has to 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 ray 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. This last algorithm improves upon previous results, settling an interesting open problem

Workgroup D. Artificial Green Floating Islands

The project aims at reducing the gap between the Eastern and Western part of the Danube River, regarding economic disparities and environmental problems. This gap can be reduced by introducing Artificial Green Floating Islands in the Danube region, with the following objectives: improvement of water quality using specific plants that purify the water to be used in agriculture, attraction of tourists to the less developed countries to make a profit, opening of new jobs for young and inexperienced people, creation for the local people of public places where they can get together and socialize. The introduction of the Artificial Green Floating Islands would also change how people and countries of the area perceive the Danube River turning it from a natural border into a centre for social interaction between different coastal states