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 Applications.