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