Said Boufares

Vector Math for 3D Computer Graphics Said Boufares

This is a tutorial on vector algebra and matrix algebra from the viewpoint of computer graphics. It covers most vector and matrix topics needed for 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. Although primarily aimed at computer science students, this tutorial is useful to all programmers 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 more staid 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 with "web safe" colors. They have been (somewhat) tested with not-too-old versions of Netscape Navigator and Internet Explorer, using "Times Roman" font (the usual browser default font). Many pages require Javascript, and some pages require Java. If you lack these (or are behind a firewall that does not allow these inside) you will be able to read most pages, but the interactive features will be lost. Some sections are more than three years old and have been used in several lecture sections (and hence are "classroom tested" and likely to be technically correct and readable). Other sections have just been written and might fall short of both goals. This tutorial may be freely downloaded and used as long as copyright and authorship information is not removed. (They are contained in HTML comments on each page.) People who wish to reward this effort may do so by going to their local public library and checking out any long neglected, lonely book from the stacks.