Around and around [computer graphics]

Everybody loves making pictures with a spirograph. Spirograph produces planar curves that are known as roulettes. The simplest way to create a roulette is probably to use a circle for the wheel and a straight line for the frame. This results in a figure that has the special name cycloid. Spirograph only has a few curve types available. To make other types of curves, it might be useful to attach a rigid arm to the center of the disk. As the disk rotates, the arm spins with it. Determining whether the pen tip is inside the rolling shape, right on its edge, or outside of it, is a useful tool for distinguishing among different roulette types. The first distinction is whether the wheel is inside or outside of the frame. If it´s outside, we call it an epitrochoid; otherwise it´s a hypotrochoid. If the pen is right on the edge of the wheel, then it´s an epicycloid or hypocycloid. If the pen is not on the edge, then the curve is an epiroulette or hyporoulette. There are two forms of each of these. If the pen is inside the wheel, then we have a cutate epiroulette or hyporoulette, otherwise it´s a prolate epiroulette or hyporoulette. There are also some special cases of these curves that we have mentioned briefly.