Visibility computations: From discrete algorithms to real algebraic geometry
Thorsten Theobald · DIMACS series in discrete mathematics and theoretical computer science · 2003
We investigate visibility computations with moving viewpoints.The initial problems are of discrete and algorithmic nature, but even for simple classes of objects (such as balls and polytopes), they lead to interesting and difficult problems from real algebraic geometry.Namely, it is necessary to characterize and compute the common tangent lines to a given set of convex bodies.In particular, we present a new sweep algorithm in dimension 2, as well as survey and extend recent algebraic-geometric results on the tangent problems in dimension 3.