Operators and representation schemes for geometric data -- Polyhedral chains -- A dual approach to detect polyhedral intersections in arbitrary dimensions -- The cell tree: An index for geometric databases -- The arc tree: An approximation scheme to represent arbitrary curved shapes -- Conclusions.

The efficient management of geometric data, such as points, curves, or polyhedra in arbitrary dimensions, is of great importance in many complex database applications like CAD/CAM, robotics, or computer vision. To provide optimal support for geometric operations, it is crucial to choose efficient data representation schemes. The first part of this book contains a taxonomy and critical survey of common operations and representation schemes for geometric data. Then several new schemes for the efficient support of set operations (union, intersection) and search operations (point location, range search) are presented.