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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