Triangulations in the Plane and in Space

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Abstract Decompostitions of space play a major role in almost all areas of computing that have to do with geometric spaces. For example, finite element approximation methods are based on "meshes" that are cell complexes decomposing domains into smaller and simpler parts. Depending on the application different quality criteria govern the way the decompostition is created. This research will study decompositions with emphasis of triangulations (simplicial cell complexes) and the possibilities and impossibilities to meet quality criteria such as constrained numbers of simplices and lower and upper bounds on angles and other shape descriptors.