Boolean operations on 3D selective Nef complexes : optimized implementation and experiments

Nef polyhedra in d-dimensional space are the closure of half-spaces under boolean set operations. In consequence, they can represent non-manifold situations, open and closed sets, mixed-dimensional complexes and they are closed under all boolean and topological operations. We implemented a boundary representation of three-dimensional Nef polyhedra with efficient algorithms for boolean operations. These algorithms were designed for correctness and can handle all cases, in particular all degeneracies. The implementation is released as Open Source in the Cgal release 3.1. In this paper, we present experiments in order to (i) evaluate the practical runtime complexity, (ii) illustrate the effectiveness of several important optimizations, and (iii) compare our implementation with the Acis CAD kernel