Das Buch gibt einen Querschnitt durch das Spektrum der Anwendungen der Computergraphik in Mathematik und Naturwissenschaften. Dabei werden auch neue computergraphische Algorithmen, komplexe Anwenderpakete und sogar Hardwarelösungen diskutiert. Die Beiträge in diesem Band, die auf Vorträgen der ersten Bremer Computer-Graphik-Tage vom Juli 1988 basieren, sind entsprechend vielfältig: Sie reichen von der Berechnung und Visualisierung mathematischer Objekte und Fraktale über Probleme des Medical Imaging bei der Darstellung volumetrischer Daten, Untersuchungen von Oberflächentexturen für Bildsynthese bis hin zur Diskussion verschiedener Ansätze der Parallelisierung computergraphischer Algorithmen. Bei der Darstellung neuer Lösungswege für komplexe Probleme der Visualisierung wurde besonderer Wert auf die praktischen Details gelegt, so daß der interessierte Leser diese Lösungen auch in einer eigenen Implementierung nachvollziehen kann.

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with actual trends and topics of future research, are reported in the last section. The topics of the book are divides into four sections: Fundamentals, Computer Graphics and Optical Simulation, Simulation of Natural Phenomena, Image Processing and Image Analysis.

What is computer graphics and what are the conceptual tasks of research in this area? To the average person the term still conveys more or less the design of - gos and the manipulation of pictures with the help of image-editing programs. However, during the past four decades, computer graphics has evolved into an innovative multifaceted ?eld of research and computing that affects many other sciences. In many areas and for many problems we can best convey an und- standing through images that trigger our sense with the highest capability: our eye. And, what is more, aside from algorithms, formulas, and tables, the c- puter graphics scientist often is able to create beauty. Though it is a beauty of its own, it often fascinates the viewer, especially when complex aesthetic images emerge from simple mathematical concepts. Also, there are only a few other areas that advance as dynamically as inf- matics and especially computer graphics. While CPU capacity still increases and is almost doubled every 18 months, the rendering speed and ef?ciency of graphics boards has increased even more during recent years. Today, images can be rendered in real time that some years ago still required several hours of computing. Parallel to the rapid improvement of computer hardware, many newalgorithms weredevelopedthattoday form the basis for some fundamental changes and achievements in graphics.

In diesem Buch setzen sich renommierte Wissenschaftler wie Herbert W. Franke, Wolfgang Dahmen, Achim Bachem, Heinz-Otto Peitgen oder Frieder Nake aus der jeweils unterschiedlichen Sicht ihres Fachgebietes mit dem Thema auseinander. Erleben wir den Beginn eines visuellen Zeitalters? Technisch erzeugte Bilder prägen die alltäglichen Formen moderner Unterhaltung ebenso wie sie in Wissenschaft und Forschung zur Quelle neuer Erkenntnis werden.

Implicit surfaces offer special effects animators, graphic designers, CAD engineers, graphics students, and hobbyists a new range of capabilities for the modeling of complex geometric objects. In contrast to traditional parametric surfaces, implicit surfaces can easily describe smooth, intricate, and articulatable shapes. These powerful yet easily understood surfaces are finding use in a growing number of graphics applications. This comprehensive introduction develops the fundamental concepts and techniques of implicit surface modeling, rendering, and animating in terms accessible to anyone with a basic background in computer graphics. + provides a thorough overview of implicit surfaces with a focus on their applications in graphics + explains the best methods for designing, representing, and visualizing implicit surfaces + surveys the latest research With contributions from seven graphics authorities, this innovative guide establishes implicit surfaces as a powerful and practical tool for animation and rendering.

The fourteen chapters of this book cover the central ideas and concepts of chaos and fractals as well as many related topics including: the Mandelbrot set, Julia sets, cellular automata, L-systems, percolation and strange attractors. This new edition has been thoroughly revised throughout. The appendices of the original edition were taken out since more recent publications cover this material in more depth. Instead of the focussed computer programs in BASIC, the authors provide 10 interactive JAVA-applets for this second edition.

Few people outside of mathematics are aware of the varieties of mathemat ical experience - the degree to which different mathematical subjects have different and distinctive flavors, often attractive to some mathematicians and repellant to others. The particular flavor of the subject of minimal surfaces seems to lie in a combination of the concreteness of the objects being studied, their origin and relation to the physical world, and the way they lie at the intersection of so many different parts of mathematics. In the past fifteen years a new component has been added: the availability of computer graphics to provide illustrations that are both mathematically instructive and esthetically pleas ing. During the course of the twentieth century, two major thrusts have played a seminal role in the evolution of minimal surface theory. The first is the work on the Plateau Problem, whose initial phase culminated in the solution for which Jesse Douglas was awarded one of the first two Fields Medals in 1936. (The other Fields Medal that year went to Lars V. Ahlfors for his contributions to complex analysis, including his important new insights in Nevanlinna Theory.) The second was the innovative approach to partial differential equations by Serge Bernstein, which led to the celebrated Bernstein's Theorem, stating that the only solution to the minimal surface equation over the whole plane is the trivial solution: a linear function.