On the Complexity of Visibility Problems with Moving Viewpoints

We investigate visibility problems with moving viewpoints in n-dimensional space. We show that these problems are NP-hard if the underlying bodies are balls, H-polytopes, or V-polytopes. This is contrasted by polynomial time solvability results for fixed dimension. We relate the computational complexity to existing algebraic-geometric aspects of the visibility problems, to the theory of packing and covering, and to the view obstruction problem from diophantine approximation.