Visibility Computations: From Discrete Algorithms to Real Algebraic Geometry

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.

• Type: Conference
• Year: 2001
• Where: DIMACS
• Authors: Thorsten Theobald
• Keywords: Common Tangent Lines, DIMACS 2001, Initial Problems, Real Algebraic Geometry, Theoretical Computer Science