Game Development Reference

In-Depth Information

To travel from the treasure back to the ship, the pirates can follow the same

line but in the opposite direction. This is achieved by flipping the vector such

that all coordinate values are multiplied by
−
1. In this case, to get back to the

ship they follow the vector (
−
3,7).

It might also be useful for the pirates to know how far the treasure is from the

ship. The length of a vector,
v
, called its
magnitude
and written |
v
|, is found

using Pythagoras' theorem shown in
Equation (2.1)
.

.

.

v vx vy

=

2

+

2

(2.1)

For the pirates, it means that their journey
is a lengt
h of 7.62 (kilometers, if the

units being used are kilometers), that is,

+−
.

Sometimes it is necessary to scale a vector so that it has a length equal to 1.

The process of scaling the length is called
normalizing
, and the resultant

vector, which still points in the same direction, is called a
unit vector
. To find

the unit vector, each coordinate of the vector is divided by the vector's length.

In the case of the pirate's journey, this would equate to (3/7.62,
−
7/7.62) =

(0.39,
−
0.92). If the pirate takes 0.39 steps to the west and 0.92 steps to the

south, he will end up a distance of 1 from his starting position, right on the

original vector, as shown in
Figure 2.2
. As can be seen, the vectors (3,
−
7)

and (0.39,
−
0.92) are parallel and the magnitude of (0.39,
−
0.92) is 1. The unit

3

2

( 7)

2

Fig 2.2
A normalized vector has

a length of 1.

(
0.39,0)

(0,-0.93)

leng
th
= 1

(3,-7)