In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing,modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applicationsinclude CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany.Topics treated are: curve and surface modelling - non-manifold modelling in CAD - multiresolution analysis of complex geometric models - surface reconstruction - variational design - computational geometry of curves and surfaces - 3D meshing - geometric modelling for scientific visualization - geometric models for biomedical applications