Scenic Routes over Points in 2D Space

Consider a 2D coordinate space with a set of red and a set of blue points. We define a scenic point as a point that is equidistant to a red point and a blue point. The set of contiguous scenic points form a scenic path. The perpendicular bisectors to the line joining a red point and a blue point forms a scenic path between the red point and the blue point. A scenic route is a traversal made from scenic paths. In this paper, we address this novel problem by (i) designing algorithms for scenic route generation, (ii) studying the algorithms different properties and (iii) analyzing the routes generated by these algorithms. Scenic routes have applications in geo-spatial visualizations and visual analytics.