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Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization.§Experts in both fields from all over the world have been invited to participate in the book. We received 39 submissions of high-quality research and survey papers, from which we could only allow the 27 strongest to be published in this book. All papers underwent a strict refereeing process.§The topics covered in this collection include§- Surface Reconstruction and Interpolation§- Surface Interrogation and Modeling§- Wavelets and Compression on Surfaces§- Topology, Distance Fields and Solid Modeling§- Multiresolution Data Representation§- Biomedical and Physical ApplicationsGeometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap; this observation led to the idea of composing a book on Geometric Modeling for Scientific Visualization.