Computer Graphics and Geometric Modeling.
By David Salomon.
Published by
Springer
(1999). ISBN 0387986820. 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 wireframe 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.


Front matter


Table of contents [xvxviii].


Preface [viixiv].


Chapter 1. First Principles [125].

The CRT, Bitmap scaling and rotation, Practical Drawing.


Chapter 2. ScanConverting Methods [2757].

Scanconverting methods (intuitive and DDA) for lines and circles. Antialiasing.


Chapter 3. Transformations and Projections [59171].

Two and threedimensional 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.


Chapter 4. Curves [173413].

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, CatmullRom and KochanekBartels slines, B\'ezier curves,
and Bsplines. The concepts of curvature and torsion are also introduced.


Chapter 5. Surfaces [415534].

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,
CatmullRom, B\'zier, Gordon, Bspline, surfaces of revolution, and sweep surfaces. The important
concept of a surface normal is also discussed.


Chapter 6. Rendering [537555].

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 [557573].

Color, color representations, and the CIE chromaticity diagrams are the main topics of this short
chapter.


Chapter 8. Computer Animation [575607].

This mathematicallyoriented chapter discusses methods for interpolating positions and rotations.
Vectorbased 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 [609657].

The principles of image compression are discussed and several practical methods are explained in
detail in this chapter. Among them are runlength encoding, fax cmpression, quadtrees, FELICS,
and MLP.


Chapter 10. Short Topics [661691].

Graphics standards, dithering, halftoning, fractals, and image processing are the short topics
dealt with in this chapter.


Appendix


Appendix A. Mathematical Topics [693721].

Fourier transforms, Forward differences, Coordinate systems, Vector agebra, Matrices,
Trigonometric identities, Complex numbers, Quaternions, and Groups are the mathematical topics
discussed.


Back matter


References [723731].


Answers to Exercises [733831].


Index [833851].


Colophon.

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.
Quotation
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.