5.14. Determining Points Along a Circle
You want to calculate the coordinates of a point along a circle given the circle’s radius and the sweep angle.
Math.sin( ) and
) methods to calculate the coordinates using basic
Finding the coordinates of a point along a circle is easy with some trigonometry. So let’s look at the formulas you can use within your ActionScript code and the theory behind them.
Given any point on the Stage—a point we’ll
call p0, with coordinates (x0, y0)—plus a distance and the
angle from the horizontal, you can find the coordinates of another
point—which we’ll call p1, with coordinates
(x1, y1)—using some basic trigonometric ratios. The angle is
formed between a conceptual line from p0 to p1 and a line parallel to
the X axis, as shown in Figure 5-2. The
opposite side (O) is the side furthest away from
the angle. The
adjacent side (A) is the side
that forms the angle with the help of the hypotenuse (H).
Figure 5-2. The angle, adjacent side, opposite side, and hypotenuse of a right triangle
If you know the distance between two points and the angle to the horizontal, as shown in Figure 5-2, you can calculate the x and y coordinates of the destination point using trigonometric functions. The trigonometric sine of the angle is equal to the ratio of the opposite side over the hypotenuse:
sine(angle) = opposite/hypotenuse ...