Game Development Reference
In-Depth Information
Figure 12.12
As you rotate a standard triangle around a circle centered on the origin of the Cartesian plane, the
values that describe the perimeter of the circle change from positive to negative depending on the
quadrant.
Rotation and the Unit Circle
The unit circle is a convenient vehicle for working with rotation and other
trigonometric activities. A unit circle is a circle that you graph with its center on
the origin of a Cartesian plane and its radius set to 1. Figure 12.13 illustrates a
unit circle. Such a representation of a circle proves useful when you seek a
convenient way to relate measurements of angles to measurements of rotation.
When you set the diameter of a circle to 1, if an angle measures, for example,
2
(90
8
), then the radian measure of the angle also tells you the length of the arc
that the angle designates on the perimeter of the circle. At the same time, as
emphasized previously, even though you work with radians, you can always
convert back to degrees if you have a need to do so.
If you employ a unit circle to map the cardinal and a few other coordinates and
their related sine values, you see a pattern unfold. With each revolution, you
move a distance of 2
radians. Regardless of how large the angle of rotation, it is
