For Computer Graphics

Focussing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD).

Computer graphics is important in many areas including engineering design, architecture, education, and computer art and animation. This book examines a wide array of current methods used in creating real-looking objects in the computer, one of the main aims of computer graphics.

We have written this book principally for users and practitioners of computer graphics. In particular, system designers, independent software vendors, graphics system implementers, and application program developers need to understand the basic standards being put in place at the so-called Virtual Device Interface and how they relate to other industry standards, both formal and de facto. Secondarily, the book has been targetted at technical managers and advanced students who need some understanding of the graphics standards and how they fit together, along with a good overview of the Computer Graphics Interface (CGI) proposal and Computer Graphics Metafile (CGM) standard in particular. Part I, Chapters 1,2, and 3; Part II, Chapters 10 and 11; Part III, Chapters 15, 16, and 17; and some of the Appendices will be of special interest. Finally, these same sections will interest users in government and industry who are responsible for selecting, buying and installing commercial implementations of the standards. The CGM is already a US Federal Information Processing Standard (FIPS 126), and we expect the same status for the CGI when its development is completed and it receives formal approval by the standards-making bodies.

Students studying different branches of computer graphics have to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces and as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems.

Students studying different branches of computer graphics need to be familiar with geometry, matrices, vectors, rotation transforms, quaternions, curves and surfaces. And as computer graphics software becomes increasingly sophisticated, calculus is also being used to resolve its associated problems.

Since its invention, geometric algebra has been applied to various branches of physics such as cosmology and electrodynamics, and is now being embraced by the computer graphics community where it is providing new ways of solving geometric problems. It took over two thousand years to discover this algebra, which uses a simple and consistent notation to describe vectors and their products.

Information theory (IT) tools, widely used in scientific fields such as engineering, physics, genetics, neuroscience, and many others, are also emerging as useful transversal tools in computer graphics. In this book, we present the basic concepts of IT and how they have been applied to the graphics areas of radiosity, adaptive ray-tracing, shape descriptors, viewpoint selection and saliency, scientific visualization, and geometry simplification. Some of the approaches presented, such as the viewpoint techniques, are now the state of the art in visualization. Almost all of the techniques presented in this book have been previously published in peer-reviewed conference proceedings or international journals.

Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis.

Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis.