Game Development Reference
In-Depth Information
Figure 11 - Rotation around the origin of a point in 2D space.
Our goal is to rotate the point
p
which is defined as p -> {x,y} to a new position p' defined
as p' -> {x',y'}. For this we will turn to trigonometry, which is the study of angles and the
angular relationships of figures in two or three dimensions.
Figure 12 - Trigonometric properties of a unit circle.
To best understand these relationships, we will consider the simplest case, a
unit circle
.
The angle
Ɵ
is measured starting on the x axis counterclockwise along the circumference
of the circle. The trigonometric function cos Ɵ represents the horizontal coordinate of our
point x | x ϵ p, and sin Ɵ is the vertical coordinate y | y ϵ p. The ratio of sin Ɵ / cos Ɵ is
defined as tan Ɵ.
