Bitmap/Bézier curves/Cubic

Using the data storage type defined on this page for raster images, and the draw_line function defined in this other one, draw a cubic bezier curves (definition on Wikipedia).

OCaml

<ocaml>let cubic_bezier ~img ~color

       ~p1:(_x1, _y1)
       ~p2:(_x2, _y2)
       ~p3:(_x3, _y3)
       ~p4:(_x4, _y4) =
 let x1, y1, x2, y2, x3, y3, x4, y4 =
   (float _x1, float _y1,
    float _x2, float _y2,
    float _x3, float _y3,
    float _x4, float _y4)
 in
 let bz t =
   let a = (1.0 -. t) ** 3.0
   and b = 3.0 *. t *. ((1.0 -. t) ** 2.0)
   and c = 3.0 *. (t ** 2.0) *. (1.0 -. t)
   and d = t ** 3.0
   in
   let x = a *. x1 +. b *. x2 +. c *. x3 +. d *. x4
   and y = a *. y1 +. b *. y2 +. c *. y3 +. d *. y4
   in
   (int_of_float x, int_of_float y)
 in
 let rec loop _t acc =
   if _t > 20 then acc else
   begin
     let t = (float _t) /. 20.0 in
     let x, y = bz t in
     loop (succ _t) ((x,y)::acc)
   end
 in
 let pts = loop 0 [] in

 (*
 (* draw only points *)
 List.iter (fun (x, y) -> put_pixel img color x y) pts;
 *)

 (* draw segments *)
 let line = draw_line ~img ~color in
 let by_pair li f =
   let rec aux prev = function
     | [] -> ()
     | x::xs ->
         f prev x;
         aux x xs
   in
   aux (List.hd li) (List.tl li)
 in
 by_pair pts (fun p0 p1 -> line ~p0 ~p1);