Planare Nef Polyeder und generische hoeherdimensionale Geometrie

Nef polyhedra. The mathematical definition of this
polyhedral framework was founded by the Swiss mathematician W.~Nef.
Our design uses plane maps for the topological description (finite
representation) of planar Nef polyhedra. To unify the treatment of the
finite and infinite character of the vertices we use extended points
as introduced in the second part of the talk. The strength of
this design is its clear separation of the special geometric demands
of Nef polyhedra from the topological structure used to represent
them. We can thereby show that standard affine plane map overlay as
presented in the algorithmic part can be used transparently for the
solution of the geometrically unbounded but symbolically bounded
overlay problem that is part of the binary operations of Nef
polyhedra.