Geometric Modeling and Scientific Visualization are both established disciplines, each with their own series of workshops, conferences and journals. But clearly both disciplines overlap, which led to the idea of composing a book on Geometric Modeling for Scientific Visualization. The editors received 39 submissions of high-quality research and survey papers, from which the 27 strongest are published in this book. All papers underwent a strict refereeing process. Topics covered include: Surface Reconstruction and Interpolation; Surface Interrogation and Modeling; Wavelets and Compression on Surfaces; Topology, Distance Fields and Solid Modeling; and others.