# Introduction to the Mathematics of Computer Graphics

Share this page
*Nathan Carter*

MAA Press: An Imprint of the American Mathematical Society

This text, by an award-winning author, was
designed to accompany his first-year seminar in the mathematics of
computer graphics. Readers learn the mathematics behind the
computational aspects of space, shape, transformation, color,
rendering, animation, and modeling. The software required is freely
available on the Internet for Mac, Windows, and Linux.

The text answers questions such as these: How do artists build up
realistic shapes from geometric primitives? What computations is my
computer doing when it generates a realistic image of my 3D scene?
What mathematical tools can I use to animate an object through space?
Why do movies always look more realistic than video games?

Containing the mathematics and computing needed for making their
own 3D computer-generated images and animations, the text, and the
course it supports, culminates in a project in which students create a
short animated movie using free software. Algebra and trigonometry
are prerequisites; calculus is not, though it helps. Programming is
not required. Includes optional advanced exercises for students with
strong backgrounds in math or computer science. Instructors
interested in exposing their liberal arts students to the beautiful
mathematics behind computer graphics will find a rich resource in this
text.

An instructor's manual for this title is available
electronically. Please send email to textbooks@ams.org for more
information.

# Table of Contents

## Introduction to the Mathematics of Computer Graphics

- Cover cov11
- Half title i3
- Copyright ii4
- Title iii5
- Series iv6
- Contents vii9
- Why should you read this book? xii14
- Origins xiii15
- Acknowledgments xiv16
- Overview xv17
- 1 Topics in computer graphics 121
- I Affine space 1232
- 2 Two-dimensional space 1333
- A Introductionto POV-Ray 2949
- 3 Affine transformations 4464
- 3.1 Why is this fun? 4464
- 3.2 Shapes 4464
- 3.3 A simple scene 4666
- 3.4 A toolbox of affine transformations 4767
- 3.5 Combining transformations 5474
- 3.6 Algebra of transformations of the same type 5878
- 3.7 Algebra of transformations of different types 5979
- 3.8 Inverting affine transformations 6383
- 3.9 Where are we now? 6484
- 3.10 Exercises 6484

- 4 Three dimensions 7494
- B Arranging a scene 96116
- 5 Matrices 108128

- II Ray tracing 131151
- III Animation 253273
- IV Modeling 356376
- Solutions to selected exercises 433453
- Index 454474
- Index of mathematical symbols 458478
- Index of POV-Ray reserved words 459479
- Bibliography 461481
- Back cover 463483