myShapes model = 
  let
    indices = List.map toFloat <| List.range 0 (model.numParts-1)
    numParts = model.numParts
  in
    [square 100 |> filled black]
                 ++ (List.map2 (\ shape angle -> shape |> rotate (degrees angle) ) 
                     (List.map (petal <| toFloat numParts) indices) 
                     (List.map (\ x -> (if model.time < 5 then 0.2*model.time - (toFloat <| floor (0.2*model.time)) else 1)*(360/(toFloat numParts))*x ) indices) 
                 ) ++ (
                   if model.time > 5
                     then List.map showAngle <| List.map (\ x -> 360/(toFloat numParts) * x) indices
                     else []
                 ) ++ ( [ button 2 |> move (60,45)
                        , button 3 |> move (60,27)

                        , button 4 |> move (60,9)

                        , button 6 |> move (60,-9)

                        , button 8 |> move (60,-27)

                        , button 12 |> move (60,-45)


                        ]
                 )
                       
petal parts index = 
  let
    angle = 2*pi/parts
    halfAngle = angle/2
    size = 30
  in
    curve (0,0) [Pull (0,0) (size,0)
                ,Pull (2*size * cos halfAngle,2*size * sin halfAngle)
                      (size * cos angle, size * sin angle)
                ]
       |> filled (hsl (360 * index / parts) 1 0.5)

showAngle angle = group [text (toString angle) |> size 6 |> filled white |> move (40,-2)] |> rotate (degrees angle)

button parts = group [ roundedRect 15 10 3 |> filled (rgb 200 0 0) |> notifyTap (AnimateAngle parts)
                     , text (toString parts) |> centered |> size 8 |> filled white |> move (0,-3) |> notifyTap (AnimateAngle parts)
                     ] 

type Msg = Tick Float GetKeyState
         | AnimateAngle Int

update msg model = case msg of
                     Tick t _ -> { model | savedTime = t, time = t - model.startTime }
                     AnimateAngle parts -> { model | numParts = parts, startTime = model.savedTime, time = 0 }

init = { startTime = 0, savedTime = 0, time = 0, numParts = 0 }