The same simple explanation in the animation leads to a nice simple Haskell implementation. Assuming you already have a parametric line function `line p q t` t

The same simple explanation in the animation leads to a nice simple Haskell implementation. Assuming you already have a parametric line function `line p q t` that interpolates between two points p and q on t in [0,1], you can recursively implement parametric Bézier on a list of control points as: bezier [p] t = p bezier ps t = line (bezier (init ps) t) (bezier (tail ps) t) t It's exponential in the number of points though ;) (Full source at https://github.com/hrldcpr/Bezier.hs/blob/master/Bezier.hs https://github.com/hrldcpr/Bezier.hs/blob/master/Bezier.hs)