Given a suitable definition for Vector2 (i.e., a 2D vector with the appropriate classes), it is delightfully trivial to implement de Casteljau's algorithm: de_Casteljau :: Scalar -> [Vector2] -> [[Vector2]] de_Casteljau t [p] = [[p]] de_Casteljau t ps = ps : de_Casteljau t (zipWith (line t) ps (tail ps)) line :: Scalar -> Vector2 -> Vector2 -> Vector2 line t a b = (1-t) *| a + t *| b Now if you want to compute a given point along a Bezier spline, you can do bezier :: Scalar -> [Vector2] -> Vector2 bezier t ps = head $ last $ de_Casteljau t ps You can chop one in half with split :: Scalar -> [Vector2] -> ([Vector2], [Vector2]) split t ps = let pss = de_Casteljau t ps in (map head pss, map last pss) And any other beautiful incantations. Now, de Boor's algorithm is a generalisation of de Casteljau's algorithm. It draws B-splines instead of Bezier-splines (since B-splines generalise Bezier-splines). But I think I may have ACTUALLY MELTED MY BRAIN attempting to comprehend it. Can anybody supply a straightforward Haskell implementation?