### Fourth Revision, July

2009

This is a tutorial on *vector*

algebra and *matrix* algebra from the viewpoint of computer graphics.

It covers most vector and matrix topics needed to read college-level computer

graphics text books. Most graphics texts cover these subjects in an appendix,

but it is often too short. This tutorial covers the same material at greater

length, and with many examples.

A mirror site that contains this material is:

Mirror Site

Computer graphics requires more math than is covered here.

The purpose of these

notes is to expand on the mathematical appendix included with most graphics

books, not to teach the mathematical material in the main text of those books.

Although primarily aimed

at university computer science students, this tutorial is useful to any programmer interested

in 3D computer graphics or 3D computer game programming. In spite of their appealing

blood-and-gore covers, mass trade books on game programming require the same

understanding of vectors and matrices as college text books (and usually defer

these topics to the same skimpy mathematical appendix).

This tutorial is useful

for more than computer graphics. Vectors and matrices are used in all scientific

and engineering fields, and any other field that uses computers (are there any

that don’t?) In many fields, the vocabulary used for vectors and matrices does

not match that used in computer graphics. But the ideas are the same, and reading

these notes will take only a slight mental adjustment.

These notes assume that

you have studied plane geometry and trigonometry sometime in the past. Notions

such as *point*, *line*, *plane*, and *angle* should

be familiar to you. Other notions such as *sine*, *cosine*, *determinant*,*
real number*, and the common trig identities should at least be a distant

memory.

These pages were designed

at 800 by 600 resolution. They have been (somewhat) tested with not-too-old

versions of Firefox and Internet Explorer. Many pages require Javascript,

and some pages require Java. If you lack these (or are behind a firewall that

blocks these) you will be able to read most pages, but the interactive features

will be lost.

Some sections are years

old and have been used in class many times (and hence are “classroom tested”

and likely to be technically correct and readable). Other sections

are more recent and might fall short of both goals.

## DownLoads

*Vector Math for 3D Computer Graphics* by Bradley Kjell is licensed under a

Creative Commons Attribution-NonCommercial 4.0 International License.