Planar Nef polyhedra and generic higher-dimensional geometry

We present two generic software projects that are part of the software library CGAL. The first part describes the design of a geometry kernel for higher-dimensional Euclidean geometry and the interaction with application programs. We describe the software structure, the interface concepts, and their models that are based on coordinate representation, number types, and memory layout. In the higher-dimensional software kernel the interaction between linear algebra and the geometric objects and primitives is one important facet. In the actual design our users can replace number types, representation types, and the traits classes that inflate kernel functionality into our current application programs: higher-dimensional convex hulls and Delaunay tedrahedralisations. In the second part we present the realization of planar Nef polyhedra. The concept of Nef polyhedra subsumes all kinds of rectilinear polyhedral subdivisions and is therefore of general applicability within a geometric software library. The software is based on the theory of extended points and segments that allows us to reuse classical algorithmic solutions like plane sweep to realize binary operations of Nef polyhedra.