From the rounded strokes of typefaces and the smooth motion of animations to the curved surfaces of car bodies — most curves drawn by computers are made this way. Drag the four points (P0–P3) freely and see how the curve changes.
The principle is simple. As t moves from 0 to 1, take the point that is t of the way along each of P0→P1, P1→P2, and P2→P3, and connect those points. Then take another point that is t of the way along each of those connecting segments and connect them again… Repeat this one more time, and the final point is a point on the curve.
Move t with the slider below and you can see this exact “segment on a segment on a segment” process (the light-green lines). This calculation method is called the de Casteljau algorithm.