Planar Nef polyhedra and generic higher-dimensional geometry [Elektronische Ressource] / von Michael Seel

Planar Nef PolyhedraandGeneric Higher-dimensional GeometryDissertationzur Erlangung des Gradesdes Doktors der Ingenieurswissenschaften (Dr.-Ing.)der Naturwissenschaftlich-Technischen Fakultat¨ Ider Universitat¨ des SaarlandesvonMichael SeelSaarbruck¨ en8. August 2001AbstractWe present two generic software projects that are part of the software library CGAL. The first partdescribes the design of a geometry kernel for higher-dimensional Euclidean geometry and the inter-action with application programs. We describe the software structure, the interface concepts, andtheir models that are based on coordinate representation, number types, and memory layout. In thehigher-dimensional software kernel the interaction between linear algebra and the geometric objectsand primitives is one important facet. In the actual design our users can replace number types, re-presentation types, and the traits classes that inflate kernel functionality into our current applicationprograms: higher-dimensional convex hulls and Delaunay tedrahedralisations.In the second part we present the realization of planar Nef polyhedra. The concept of Nef polyhe-dra subsumes all kinds of rectilinear polyhedral subdivisions and is therefore of general applicabilitywithin a geometric software library.