Fourth Revision, July
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:
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
These pages were designed
at 800 by 600 resolution. They have been (somewhat) tested with not-too-old
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.
Vector Math for 3D Computer Graphics by Bradley Kjell is licensed under a
Creative Commons Attribution-NonCommercial 4.0 International License.