Ribbon Twist Screensaver

A twisting-ribbons screensaver, called Ribbons, shipped with Windows Vista, where it needed Aero-capable graphics hardware. The effect is less mysterious than it looks. A ribbon is just a smooth curve in space with a flat strip attached to it, and the clever part is deciding which way the strip faces at each point.

In geometry that facing direction is called a frame. At every point along the curve you can compute the tangent, which points the way the curve is heading, and then choose a second direction perpendicular to it to form the ribbon’s width. Rotating that second direction slowly around the tangent as you move along produces the twist. Shading depends on the angle between the surface and a light, so the strip brightens and darkens as it turns, which is what makes the twists read as three-dimensional.

Smooth paths are usually built from splines, such as Bezier curves, which join control points with continuous slopes so that there are no kinks. Adding a little animated randomness to those control points makes the strands wander without ever jumping. The result is a good demonstration that complex-looking motion often comes from a few simple parametric rules.