/// Types taken from assignment
type point = int * int // a point ( x , y ) in the plane
type colour = int * int * int // ( red , green , blue ), 0..255
type figure =
  | Circle of point * int * colour // defined by center, radius, and colour
  | Rectangle of point * point * colour // defined by corners bottom - left , top - right , and colour
  | Mix of figure * figure // combine figures with mixed colour at overlap

/// 8i0: Create a figure of a circle with a center at (50,50) and radius 45, and a box with the corners (40,40) and (90,110)
let figTest =
  let circleCenter = point (50, 50)
  let circleColour = colour (255, 0, 0)
  let redcircle = Circle (circleCenter, 45, circleColour)
  let boxLowerCorner = point (40,40)
  let boxUpperCorner = point (90, 110)
  let boxColour = colour (0, 0, 255)
  let bluebox = Rectangle (boxLowerCorner, boxUpperCorner, boxColour)
  Mix (redcircle, bluebox)

/// TESTS
/// TEST 1: Is figTest a Mix?
match figTest with
 | Circle _ -> printfn "8i0-1 Failed"
 | Rectangle _ -> printfn "8i0-1 Failed"
 | Mix _ -> printfn "8i0-1 Success"

/// TEST 2: Does figTest contain a circle and a box?
match figTest with
| Mix (f1, f2) ->
  match f1 with
    | Circle (center, r, colour) -> if center = (50,50) && r = 45 && colour = (255,0,0) then printfn "8i0-2-1 Success" else printfn "8i0-2-1 Failed"
    | _ -> printfn "8i0-2-1 Failed"
  match f2 with
    | Rectangle (p1, p2, colour) -> if p1 = (40,40) && p2 = (90, 110) && colour = (0,0,255) then printfn "8i0-2-1 Success" else printfn "8i0-2-1 Failed"
    | _ -> printfn "8i0-2-2 Failed"
| _ -> printfn "8i0-2 Failed"

/// colourAt from assignment
let rec colourAt (x,y) figure =
  match figure with
  | Circle ((cx,cy), r, col) ->
      if (x-cx) * (x-cx) + (y-cy)*(y-cy) <= r*r
      then Some col else None
  | Rectangle ((x0,y0), (x1, y1), col) ->
      if x0 <= x && x <= x1 && y0 <= y && y <= y1
      then Some col else None
  | Mix (f1, f2) ->
      match (colourAt (x,y) f1, colourAt (x,y) f2) with
      | (None, c) -> c
      | (c, None) -> c
      | (Some (r1,g1,b1), Some (r2,g2,b2)) ->
          Some ((r1+r2)/2 , (g1+g2)/2 , (b1+b2)/2)

/// 8i1: makePicture function
/// <summary>Turns a figure into a PNG file</summary>
/// <param name="filename">The filename as a string</param>
/// <param name="fig">The figure to be drawn</param>
/// <param name="b">The width of the output file</param>
/// <param name="h">The height of the output file</param>
/// <returns>Nothing</returns>
let makePicture (filename : string) (fig : figure) (b : int) (h : int) : unit =
  let bmp = ImgUtil.mk h b
  for x in [0..b-1] do
    for y in [0..h-1] do
      let colour =
        match (colourAt (x, y) fig) with
        | Some z -> z
        | _ -> colour (128, 128, 128)
      ImgUtil.setPixel (ImgUtil.fromRgb colour) (x, y) bmp
  ImgUtil.toPngFile filename bmp

/// 8i2: Use makePicture
makePicture "test.png" figTest 100 150