A moving object and observers in ℝ2 with a piecewise smooth shading set

Abstract

We consider the motion of an object t in the space ℝ², where a bodily bounded set G with piecewise smooth boundary hinders the motion and visibility. In a neighborhood of convex parts of the boundary, there are observers, which can hide from t in a shading set s(t) ⊂ ℝ²G in the case of danger from t. We find characteristic properties of a trajectory T of the object that maximizes the value min{ρ(t, s(t)): t ∈ T}.