Boolean operations on 3D selective Nef complexes: data structure, algorithms, optimized implementation, experiments and applications

Nef polyhedra in d-dimensional space are the closure of half-spaces under boolean set operations. Consequently, they can represent non-manifold situations, open and closed sets, mixed-dimensional complexes, and they are closed under all boolean and topological operations, such as complement and boundary. The generality of Nef complexes is essential for some applications. In this thesis, we present a new data structure for the boundary representation of three-dimensional Nef polyhedra and efficient algorithms for boolean operations. We use exact arithmetic to avoid well known problems with floating-point arithmetic and handle all degeneracies. Furthermore, we present important optimizations for the algorithms, and evaluate this optimized implementation with extensive experiments. The experiments supplement the theoretical runtime analysis and illustrate the effectiveness of our optimizations. We compare our implementation with the ACIS CAD kernel. ACIS is mostly faster, by a factor up to six. There are examples on which ACIS fails. Nef polyhedra can be used in many a variety of applications. We present simple implementations of the visual hull, and of the Minkowski sum of two closed Nef polyhedra.