Visualization is now recognized as a powerful approach to get insight in large datasets produced by scientific experimentations and simulations. The contributions to this book cover technical aspects as well as concrete applications of visualization in various domains such as finance, physics, astronomy and medicine, providing researchers and engineers with valuable information for setting up new powerful environments.

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The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.

In Douglas Adams' book 'Hitchhiker's Guide to the Galaxy', hyper-intelligent beings reached a point in their existence where they wanted to understand the purpose of their own existence and the universe. They built a supercomputer, called Deep Thought, and upon completion, they asked it for the answer to the ultimate question of life, the universe and everything else. The computer worked for several millennia on the answers to all these questions. When the day arrived for hyper-intelligent beings the to receive the answer, they were stunned, shocked and disappointed to hear that the answer was simply 42. The still open questions to scientists and engineers are typically much sim pler and consequently the answers are more reasonable. Furthermore, because human beings are too impatient and not ready to wait for such a long pe riod, high-performance computing techniques have been developed, leading to much faster answers. Based on these developments in the last two decades, scientific and engineering computing has evolved to a key technology which plays an important role in determining, or at least shaping, future research and development activities in many branches of industry. Development work has been going on all over the world resulting in numerical methods that are now available for simulations that were not foreseeable some years ago. However, these days the availability of supercomputers with Teraflop perfor mance supports extensive computations with technical relevance. A new age of engineering has started.

Mathematical Visualization is a young new discipline. It offers efficient visualization tools to the classical subjects of mathematics, and applies mathematical techniques to problems in computer graphics and scientific visualization. Originally, it started in the interdisciplinary area of differential geometry, numerical mathematics, and computer graphics. In recent years, the methods developed have found important applications. The current volume is the quintessence of an international workshop in September 1997 in Berlin, focusing on recent developments in this emerging area. Experts present selected research work on new algorithms for visualization problems, describe the application and experiments in geometry, and develop new numerical or computer graphical techniques.

The application of modern methods in numerical mathematics on problems in chemical engineering is essential for designing, analyzing and running chemical processes and even entire plants. Scientific Computing in Chemical Engineering II gives the state of the art from the point of view of numerical mathematicians as well as that of engineers. The present volume as part of a two-volume edition covers topics such as computer-aided process design, combustion and flame, image processing, optimization, control, and neural networks. The volume is aimed at scientists, practitioners and graduate students in chemical engineering, industrial engineering and numerical mathematics.

Min Chen, Arie E. Kaufman and Roni Yage/ Volume graphics is concerned with graphics scenes defined in volume data types, where a model is specified by a mass of points instead of a collection of surfaces. The underlying mathematical definition of such a model is a set of scalar fields, which define the geometrical and physical properties of every point in three dimensional space. As true 3D representations, volume data types possess more descriptive power than surface data types, and are morphologically closer to many high-level modelling schemes in traditional surface graphics such as parametric surfaces, implicit surfaces and volume sweeping. The past decade has witnessed significant advances in volume visualisation, driven mainly by applications such as medical imaging and scientific computation. The work in this field has produced a number of volume rendering methods that enable 3D information in a volumetric dataset to be selectively rendered into 2D images. With modern computer hardware, such a process can easily be performed on an ordinary workstation. More importantly, volume-based rendering offers a consistent solution to the primary deficiencies of the traditional surface-based rendering, which include its inability to encapsulate the internal description of a model, and the difficulties in rendering amorphous phenomena. The emergence of volume-based techniques has not only broadened the extent of graphics applications, but also brought computer graphics closer to other scientific and engineering disciplines, including image processing, computer vision, finite element analysis and rapid prototyping.