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Reviewer: John B. Slater

Computer graphics is currently of considerable interest. Hardware and software developments are making possible the high resolution color displays that can show real-time movements at acceptable refresh rates. The combination of cheap memory, high bandwidth networking, better algorithms, and parallel processing have allowed graphical methods to work in a growing number of application areas. Much has happened since the first edition of the book in 1976. Therefore, a significant portion of the book was completely rewritten to include new technology, new algorithms, and the basic theory necessary to underpin the algorithms. The new sections are up to date and fit in well with the revised earlier material that has been retained. Modern standards have been properly included as have modern examples and up-to-date nomenclature. Thus, the book is a coherent, consistent whole in spite of the mixed pedigree. Chapter 1, which gives an overview of the technology and is a mixture of physics, technology, and computer science, provides a useful overview of the terminology. The varieties of means for output (conventional displays, flat panel displays, plotters, and printers) and input (joysticks, mice, trackballs, light pens, and tablets) are described physically and logically in a concise and useful fashion with a discussion of state-of-the-art devices and their characteristics as well as the processing and memory requirements to back them up. This chapter is well illustrated with the help of a variety of manufacturers and suppliers. It also contains a short section on modern standards for graphics software. Chapters 2–6 contain the bulk of the mathematics. Inevitably, the level of mathematics required varies somewhat between the chapters and within them, and the added work often requires more understanding. Thus, chapter 2 moves quickly from elementary point representation and matrix transformation with elementary linear operations through homogeneous coordinates in two-dimensional space to points at infinity. All of this is elementary to many, but others may have difficulty with the shift. Chapter 3 moves to three-dimensional transformations and projections, presented in homogeneous coordinates with three-dimensional scaling rotation, reflection with affine transformations being defined in a technical rather than a natural fashion. Although this may be natural for engineers, it is unnatural for the mathematician, even though the examples and diagrams give an exceptionally clear practical feel for what is happening in various projections and transformations. Chapter 4 is a fairly classical treatment of parametric representation with conic sections taking the major role. These three chapters are the least updated, as the references clearly show. Chapters 5 and 6, however, are completely rewritten and have an excellent extended set of references for following up the details of the topics covered. The presentation of cubic splines, blending, Be´zier curves, and B-splines in chapter 5 achieves a flowing but logical presentation that will be hard to match. Chapter 6 nearly equals this in its coverage of surfaces, leading from traditional quadric work through Coons surfaces, Be´zier surfaces, and B-spline surfaces, though the specific presentation of quadratic forms in three variables is somewhat lengthy. Again, the chapters are well illustrated, and the layout is excellent. The appendices are worth nothing. A brief description of the principles of GKS, GKS-3D, PHIGS, and PHIGS+ gives a clear overview. The appendices include some simple suggestions for standard transfer of specific data such as a B-spline. In addition, they present a number of useful algorithms, problems, and projects. The last ones are deficient, however, because there are not enough of them. The book is excellently presented and very readable, but it is not clear whether it can be easily mapped onto a specific course. This book would be useful to students and for general reference purposes.