Chaikin's Algorithm

Chaikin's algorithm is a curve subdivision method that George Chaikin introduced in 1974 as the first recursive corner-cutting technique for generating a smooth curve from a polygon. Starting from an initial control polygon, each subdivision step replaces every vertex with two new points, one lying a quarter of the way toward the next vertex and one lying a quarter of the way toward the previous vertex, which has the effect of slicing the corner off at every vertex of the polygon; repeating this corner-cutting step on the resulting polygon, again and again, produces a sequence of increasingly smooth polygons that converges in the limit to a smooth curve. That limit curve is a quadratic uniform B-spline, a result that gives Chaikin's simple geometric procedure a precise mathematical description, and the algorithm's combination of simplicity and numerical stability has made it an influential building block in later subdivision curve and subdivision surface methods used in computer graphics and geometric design.