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Foundations of Geometric Algebra Computing
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applic...
Learning Processing
The free, open-source Processing programming language environment was created at MIT for people who want to develop images, animation, and sound. Based on the ubiquitous Java, it provides an alternative to daunting languages and expensive proprietary software. This book gives graphic designers, artists and illustrators of all stripes a jump start to working with processing by providing detailed information on the basic principles of programming with the language, followed by careful, step-by-step explanations of select advanced techniques.The author teaches computer graphics at NYU's Tisch School of the Arts, and his book has been developed with a supportive learning experience at its core. ...
Geometric Algebra for Computer Science
Until recently, almost all of the interactions between objects in virtual 3D worlds have been based on calculations performed using linear algebra. Linear algebra relies heavily on coordinates, however, which can make many geometric programming tasks very specific and complex-often a lot of effort is required to bring about even modest performance enhancements. Although linear algebra is an efficient way to specify low-level computations, it is not a suitable high-level language for geometric programming. Geometric Algebra for Computer Science presents a compelling alternative to the limitations of linear algebra. Geometric algebra, or GA, is a compact, time-effective, and performance-enhanc...
Visualization in Medicine
Visualization in Medicine is the first book on visualization and its application to problems in medical diagnosis, education, and treatment. The book describes the algorithms, the applications and their validation (how reliable are the results?), and the clinical evaluation of the applications (are the techniques useful?). It discusses visualization techniques from research literature as well as the compromises required to solve practical clinical problems. The book covers image acquisition, image analysis, and interaction techniques designed to explore and analyze the data. The final chapter shows how visualization is used for planning liver surgery, one of the most demanding surgical disciplines. The book is based on several years of the authors' teaching and research experience. Both authors have initiated and lead a variety of interdisciplinary projects involving computer scientists and medical doctors, primarily radiologists and surgeons.* A core field of visualization and graphics missing a dedicated book until now* Written by pioneers in the field and illustrated in full color* Covers theory as well as practice
From Past to Future: Graßmann's Work in Context
On the occasion of the 200th anniversary of the birth of Hermann Graßmann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Graßmann's hometown Szczecin, Poland. The idea of the conference was to present a multi-faceted picture of Graßmann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the 20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Graßmann's work for philos...
Mathematical Optimization in Computer Graphics and Vision
Mathematical optimization is used in nearly all computer graphics applications, from computer vision to animation. This book teaches readers the core set of techniques that every computer graphics professional should understand in order to envision and expand the boundaries of what is possible in their work. Study of this authoritative reference will help readers develop a very powerful tool- the ability to create and decipher mathematical models that can better realize solutions to even the toughest problems confronting computer graphics community today. - Distills down a vast and complex world of information on optimization into one short, self-contained volume especially for computer graphics - Helps CG professionals identify the best technique for solving particular problems quickly, by categorizing the most effective algorithms by application - Keeps readers current by supplementing the focus on key, classic methods with special end-of-chapter sections on cutting-edge developments
Digital Modeling of Material Appearance
Computer graphics systems are capable of generating stunningly realistic images of objects that have never physically existed. In order for computers to create these accurately detailed images, digital models of appearance must include robust data to give viewers a credible visual impression of the depicted materials. In particular, digital models demonstrating the nuances of how materials interact with light are essential to this capability. Digital Modeling of Material Appearance is the first comprehensive work on the digital modeling of material appearance: it explains how models from physics and engineering are combined with keen observation skills for use in computer graphics rendering....
Game Physics Engine Development
Physics is really important to game programmers who need to know how to add physical realism to their games. They need to take into account the laws of physics when creating a simulation or game engine, particularly in 3D computer graphics, for the purpose of making the effects appear more real to the observer or player.The game engine ne
Divided Spheres
This well-illustrated book—in color throughout—presents a thorough introduction to the mathematics of Buckminster Fuller’s invention of the geodesic dome, which paved the way for a flood of practical applications as diverse as weather forecasting and fish farms. The author explains the principles of spherical design and the three main categories of subdivision based on geometric solids (polyhedra). He illustrates how basic and advanced CAD techniques apply to spherical subdivision and covers modern applications in product design, engineering, science, games, and sports balls.
Guide to Geometric Algebra in Practice
This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
