Entering the matrix

Now for the topic that strikes fear into the heart of all new game programmers: matrices. Matrices are a mathematical device (part of linear algebra) that makes it easier to work with large sets of related numbers.

In its simplest form, a matrix is a table of numbers. Let's say that I wanted to represent a coordinate in space. I could write its value down as follows:

Vectors

A single row or single column of a matrix is called a vector. Vectors are important because they can be used to both position things and move things.

The typical matrix used in games contains four values: x, y, z, and w. These x, y, and z components typically refer to a position in the 3D coordinate system, while the w is a switch:

• The value 1 means that this vector is a position

• The value 0 means that this vector is a velocity

Here's an example:

• The vector, (1, 5, 10, 1), represents a point at x = 1, y = 5, and z = 10 in a 3D coordinate system.

• The vector, (1, 5, 10, 0), is a point that moves 1 unit in the...