When I wrote circle, I was able to re-use polygon because a many-sided polygon is a good approximation of a circle. But arc is not as cooperative; we can’t use polygon or circle to draw an arc.
One alternative is to start with a copy of polygon and transform it into arc. The result might look like this:
def arc(t, r, angle): arc_length = 2 * math.pi * r * angle / 360 n = int(arc_length / 3) + 1 step_length = arc_length / n step_angle = float(angle) / n for i in range(n): fd(t, step_length) lt(t, step_angle)
The second half of this function looks like polygon, but we can’t re-use polygon without changing the interface. We could generalize polygon to take an angle as a third argument, but then polygon would no longer be an appropriate name! Instead, let’s call the more general function polyline:
def polyline(t, n, length, angle): for i in range(n): fd(t, length) lt(t, angle)
Now we can rewrite polygon and arc to use polyline:
def polygon(t, n, length): angle = 360.0 / n polyline(t, n, length, angle) def arc(t, r, angle): arc_length = 2 * math.pi * r * angle / 360 n = int(arc_length / 3) + 1 step_length = arc_length / n step_angle = float(angle) / n polyline(t, n, step_length, step_angle)
Finally, we can rewrite circle to use arc:
def circle(t, r): arc(t, r, 360)
This process—rearranging a program to improve function interfaces and facilitate code re-use—is called refactoring. In this case, we noticed that there was similar code in arc and polygon, so we “factored it out” into polyline.
If we had planned ahead, we might have written polyline ﬁrst and avoided refactoring, but often you don’t know enough at the beginning of a project to design all the interfaces. Once you start coding, you understand the problem better. Sometimes refactoring is a sign that you have learned something.