Introducing vectors

What is a vector? A vector is an n-tuple of numbers. It represents a displacement measured as a magnitude and a direction. Each element of a vector is usually expressed as a subscript, such as (V0, V1, V2, … VN). In the context of games, vectors usually have two, three, or four components.

For example, a three-dimensional vector measures displacement on three unique axes: x, y, and z. Elements of vectors are often subscripted with the axis they represent, rather than an index. (VX, VY, VZ) and (V0, V1, V2) are used interchangeably.

When visualizing vectors, they are often drawn as arrows. The position of the base of an arrow does not matter because vectors measure displacement, not a position. The end of the arrow follows the displacement of the arrow on each axis.

For example, all of the arrows in the following figure represent the same vector:

Figure 2.1: Vector (2, 5) drawn in multiple locations

Each arrow has the same length and points in the same direction, regardless of where it is positioned. In the next section, you will start to implement the vector structure that will be used throughout the rest of this book.