Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new...
Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs pre...
Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression and digital transmission of 3D geometric objects. This book is based on thirteen tutorials presented during the European Summer School "Principles of Multiresolution in Geometric Modelling," held at the Munich University of Technology, Germany, during August 22-30, 2001. The book covers: subdivision; wavelets; scattered data modelling; and...
Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several lev...
Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B- spline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts...
Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B- sp...
Visualization technology has become a crucial component of medical and b- medical data processing and analysis. This technology complements tra- tional image processing methods as it allows scientists and practicing medical doctors to visually interact with large, high-resolution three-dimensional - age data. Further, an ever increasing number of new data acquisition me- ods is being used in medicine and the life sciences, in particular in genomics and proteomics. The book contains papers discussing some of the latest data processing and visualization techniques and systems for e?ective...
Visualization technology has become a crucial component of medical and b- medical data processing and analysis. This technology complements tra- tiona...
Enabling insight into large and complex datasets is a prevalent theme in visualization research for which different approaches are pursued.
Topology-based methods are built on the idea of abstracting characteristic structures such as the topological skeleton from the data and to construct the visualizations accordingly. There are currently new demands for and renewed interest in topology-based visualization solutions. This book presents 13 peer-reviewed papers as written results from the 2005 workshop "Topology-Based Methods in Visualization" that was initiated to enable additional...
Enabling insight into large and complex datasets is a prevalent theme in visualization research for which different approaches are pursued.
Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative...
Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses ev...
The book contains twenty-two original scienti?c research articles that address the state-of-the-art in using partial di?erential equations for image and signal processing. The articles arose from presentations given at the inter- tional conference on PDE-Based Image Processing and Related Inverse Pr- lems, held at the Centre of Mathematics for Applications, University of Oslo, Norway, August 8-12, 2005. The purpose of the conference was to bring together international - searchers to present various aspects of new developments in using numerical techniques for partial di?erential equations to...
The book contains twenty-two original scienti?c research articles that address the state-of-the-art in using partial di?erential equations for image a...
This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations. Throughout the book we relate the theory to selected applications, in part- ular surface construction, meshing and visualization. The ?eld of triangulation is part of the huge area of computational ge- etry, and over many...
This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate t...
One of the greatest scientific challenges of the 21st century is how to master, organize and extract useful knowledge from the overwhelming flow of information made available by today's data acquisition systems and computing resources. Visualization is the premium means of taking up this challenge. This book is based on selected lectures given by leading experts in scientific visualization during a workshop held at Schloss Dagstuhl, Germany. Topics include user issues in visualization, large data visualization, unstructured mesh processing for visualization, volumetric...
One of the greatest scientific challenges of the 21st century is how to master, organize and extract useful knowledge from the overwhelm...
Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutions tobasicgeometricproblemsincludingconstructionsofdatastructures, convex hulls, triangulations, Voronoi diagrams and geometric arrangements as well as geometric optimisation. However, in the mid-nineties, it was recognized that the computational geometry techniques were far from satisfactory in practice and a vigorous e?ort has been undertaken to make computational geometry more practical. This e?ort led to major advances in robustness,...
Computational geometry emerged as a discipline in the seventies and has had considerable success in improving the asymptotic complexity of the solutio...
