(* To compile this example: ocamlc graphics.cma triangles.ml -o triangles *)
open Graphics;;

let pi = 3.1415926535897932384626433832795
let window_width = 640
let window_height = 480
let sides = 5;

type point = { x: int; y: int}
let average a b = (a + b) / 2
let mid a b = { x = average a.x b.x; y = average a.y b.y }
let distance a b = sqrt(float(b.x-a.x)**2.0 +. float(b.y-a.y)**2.0)
let rotate pt origin angle =
    let r = distance pt origin in
    let rise = pt.y-origin.y in
    let run = pt.x-origin.x in
    let theta = atan (float(rise) /. float(run)) in
    { x = origin.x + truncate(r *. cos(theta +. angle));
      y = origin.y + truncate(r *. sin(theta +. angle)) }
let print_pt pt =
    Printf.printf "%d,%d\n" pt.x pt.y

let round x = int_of_float (x +. 0.5)
let even x = x mod 2 == 0

(* Translate to and from screen co-ordinates. I want the origin to be at
   the centre of the window. *)
let from_screen pt =
    { x = pt.x - window_width/2; y = pt.y - window_height/2 }     
let to_screen pt =
    { x = -pt.x + window_width/2; y = -pt.y + window_height/2 }     

let () =
    let screen_topleft = { x=0; y=0; } in
    let screen_topright = { x=639; y=0 } in
    let screen_bottomleft = { x=0; y=479; } in
    let screen_bottomright = { x=639; y=479 } in
    let topleft = from_screen(screen_topleft) in
    let topright = from_screen(screen_topright) in
    let bottomleft = from_screen(screen_bottomleft) in
    let bottomright = from_screen(screen_bottomright) in
    let o = mid topleft bottomright in
    let deg_to_rad deg = (deg*. pi)/.180.0 in
    let a = mid topleft topright  in
    let points = Array.create sides a in
    for i = 1 to sides - 1 do
        points.(i) <- rotate a o ((deg_to_rad 360.0 /. float(sides)) *. float(i));
    done;
    let screen_o = (to_screen o) in
    let screen_points = Array.map to_screen points in
    open_graph " 640x480";
    let pt_moveto pt = moveto pt.x pt.y in
    let pt_lineto pt = lineto pt.x pt.y in
    (* Draw points, then lines *)
    set_color blue;
    for i = 0 to Array.length screen_points - 1 do
        fill_circle screen_points.(i).x screen_points.(i).y 10
    done;
    set_color black;
    let l = Array.length screen_points in
    for i = 0 to l - 1 do
        pt_moveto screen_points.(i);
        pt_lineto screen_points.((i + 1) mod l);
    done;
    let midpoints = Array.create l o in
    for i = 0 to l - 1 do
        midpoints.(i) <- (mid screen_points.(i) screen_points.((i + 1) mod l));
    done;
    set_color red;
    let f = round (float(sides) /. 2.0) in
    for i = 0 to l - 1 do
        pt_moveto screen_points.((i + f) mod l);
        pt_lineto midpoints.(i);
    done;
    ignore(read_line())