Bitmap/Bézier curves/Quadratic

Using the data storage type defined on this page, draw a quadratic bezier curves (definition on Wikipedia).

OCaml

<ocaml>let quad_bezier ~img ~color

       ~p1:(_x1, _y1)
       ~p2:(_x2, _y2)
       ~p3:(_x3, _y3) =
 let (x1, y1, x2, y2, x3, y3) =
   (float _x1, float _y1, float _x2, float _y2, float _x3, float _y3)
 in
 let bz t =
   let a = (1.0 -. t) ** 2.0
   and b = 2.0 *. t *. (1.0 -. t)
   and c = t ** 2.0
   in
   let x = a *. x1 +. b *. x2 +. c *. x3
   and y = a *. y1 +. b *. y2 +. c *. y3
   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);

</ocaml>