Math Primer: Trigonometry 101 - Flash 3D: Animation, Interactivity, and Games - page 126

Let's generalize the preceding passage just a little bit more. Suppose the center of the
circle is at some arbitrary point (xo,yo) as shown in Figure 5.16 and we want to know
the coordinates of a point for any particular angle.

-Y

(0,0)

-X +X

(xo, yo) x

angle

y

r

(x, y)

+Y

Figure 5.16 Calculating a point on an offset circle

The equations above need to be modified as follows:

a = angle * Math.PI / 180
x = xo + r * Math.cos(a)
y = yo + r * Math.sin(a)

Figure 5.17 Formulas for calculating a point on any circle

Exercise 5.1: Circular Motion of One Object

Now that we know how to calculate the coordinates of a point on a circle when we are
given its angle, let's see what we can learn from solving the simple problem of having
a single object move along a circular path. Suppose we have a top view of a roulette
“training” wheel. It's not a real wheel but a simplified one so that, like so many of us,
the roulette ball can practice going around in circles. Figure 5.18 illustrates a typical
screen from our exercise.