Game Development Reference
Before leaping into the use of vectors in games for defining motion, a crash
course in essential vector mathematics for game environments is presented in
the next section.
2.2 Principles of Vectors
In Chapter One, a vector was introduced as a line with a length (magnitude)
and a direction (indicated by an arrow). Vectors can be used to represent
measurements such as displacement, velocity, and acceleration. In 2D, a
vector has x and y coordinates. In 3D, it has x , y , and z coordinates. In pure
mathematics, a vector is not a point in space, but a set of changing coordinate
instructions. It can be likened to the instructions on a fictional pirate's treasure
map, for example, take three steps to the west and seven steps to the south.
As shown in Figure 2.1 , the instructions three steps to the west could be
interpreted as the vector (3,0), meaning move 3 in the positive x direction and
nothing in the y direction. The instructions move seven steps to the south
become the vector (0, − 7), meaning move only 7 in a negative y direction.
To determine the final location, vector x and y values are added to the starting
point x and y values. For example, in Figure 2.1 , the pirate ship lands at (4,8)
and moving (3,0) will place them at (4 + 3, 8 + 0) = (7,8). Then moving (0, − 7)
will put them at (7 + 0,8 − 7) = (7,1). They can also take a shortcut by going
directly in a straight line to the treasure. In this case, the two instruction
vectors (3,0) and (0, − 7) are added together and become (3, − 7). By taking the
starting location and adding this new vector, they will end up in the same
location [i.e., (4 + 3,8 − 7) = (7,1)].
Fig 2.1 A pirate's treasure map
illustrating the use of vectors.
shiver me timbers!
Ta ke 3 steps to
the west, then
7 steps to the south,
and there thee
shall find the
start = (4, 8)
treasure = (7,1)