Ngoc-Minh Lê

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We investigate the bisector systems of convex distance functions in 3-space and show that there is a substantial difference to the Euclidean metric which cannot be observed in 2-space. This disproves the general belief that Voronoi diagrams in convex distance functions are, in any dimension, analogous to Euclidean Voronoi diagrams. The fact is that more(More)
We investigate the structure of the bisector of point sites under arbitrary convex distance functions in three dimensions. Our results show that it is advantageous for analyzing bisectors to consider their central projection on the unit sphere, thereby reducing by one the dimension of the problem. From the concept of “silhouettes” and their intersections we(More)
We investigate a class of differential games, which we call pursuit games. Pursuit games have application to robotics: the pursuer models a moving obstacle and the evader models a robot that tries to reach a goal region without colliding with the moving obstacle, at each moment the robot does not know the future trajectory of the obstacle. The motion of the(More)