Computer Graphics and Geometric Modeling.

Front cover

By David Salomon. Published by Springer (1999). ISBN 0-387-98682-0. LCCN T385 S243 1999. xviii + 851 pages.

Written over a ten year period through May, 1998. Produced August, 1998 through March, 1999. In addition to a mathematical appendix and an index, the book includes 335 figures, many tables, and numerous exercises sprinkled throughout the text, offering the reader a chance to test their knowledge and understanding "on the fly." Answers are provided. The book is bound as a hardcover with a colorful cover depicting a chalice as a wire-frame surface.

A BibTeX style file and an Errata list are available.

The author would like to thank J. Robert Henderson, and Nelson H. F. Beebe for their help, comments, and encouragment.

Table of contents

Ch. 1 page

Preface page

Front matter
Table of contents [xv-xviii].
Preface [vii--xiv].
Chapter 1. First Principles [1--25].
The CRT, Bitmap scaling and rotation, Practical Drawing.
Ch. 3 page

Ch. 2 page

Chapter 2. Scan-Converting Methods [27--57].
Scan-converting methods (intuitive and DDA) for lines and circles. Antialiasing.
Chapter 3. Transformations and Projections [59--171].
Two and three-dimensional transformations: translation, rotation, scaling, and shearing. Parallel, perspective, and nonlinear projections. Perspective projections are treated in depth, including the general case where the observer may be located anywhere. Nonlinear projections include fisheye, panoramic, microscopic, telescopic, and sphere projections.
Ch. 5 page

Ch. 4 page

Chapter 4. Curves [173--413].
All the important types of parameteric curves used in pracice are discussed, with examples. These include Lagrange interpolation, Newton interpolation, Hermite interpolation, quadratic and cubic splines with different end conditions, Catmull-Rom and Kochanek-Bartels slines, B\'ezier curves, and B-splines. The concepts of curvature and torsion are also introduced.
Chapter 5. Surfaces [415--534].
Parametric surfaces are introduced, both as a Cartesian product and as a refinement of a mesh of points. Among the important surface methods covered are polygonal, bilinear, lofted, Coons, Catmull-Rom, B\'zier, Gordon, B-spline, surfaces of revolution, and sweep surfaces. The important concept of a surface normal is also discussed.
Ch. 7 page

Ch. 6 page

Chapter 6. Rendering [537--555].
A simple shading model is introduced, with reflection. Refraction is also discussed. The Gouraud and Phong shading methods for polygonal surfaces are explained. Ray tracing, texture and bump mapping are briefly mentioned.
Chapter 7. Color [557--573].
Color, color representations, and the CIE chromaticity diagrams are the main topics of this short chapter.
Ch. 9 page

Ch. 8 page

Chapter 8. Computer Animation [575--607].
This mathematically-oriented chapter discusses methods for interpolating positions and rotations. Vector-based methods as well as methods based on quaternions are introduced, with detailed examples. The interesting concepts of morphing and deformations are also mentioned.
Chapter 9. Image Compression [609--657].
The principles of image compression are discussed and several practical methods are explained in detail in this chapter. Among them are run-length encoding, fax cmpression, quadtrees, FELICS, and MLP.
Ap. A page

Ch. 10 page

Chapter 10. Short Topics [661--691].
Graphics standards, dithering, halftoning, fractals, and image processing are the short topics dealt with in this chapter.
Appendix A. Mathematical Topics [693--721].
Fourier transforms, Forward differences, Coordinate systems, Vector agebra, Matrices, Trigonometric identities, Complex numbers, Quaternions, and Groups are the mathematical topics discussed.


Back matter
References [723--731].
Answers to Exercises [733--831].
Index [833-851].

Auxiliary Material

1. (Feb 2002). Sections 4.16.9 and 4.16.10 have been rewritten and are available here (PDF, 4 pages, 292KB)

2. (January 2010). There has been much technological progress since the book was written. For one thing, the digital camera has become part of our daily lives. The file found here (PDF, 16 pages, 1MB) is a discussion of digital cameras, their principles, main parts, and operation.


That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to represent.

Benoît B. Mandelbrot

Last Updated 3 Jan, 2010.