-- Paint inside the lines!

-- Example which shows how to test if a point is inside a convex polygon

-- What is a convex polygon?
-- 1) If you roll a convex polygon on flat ground, all of the sides will
--    touch the ground at some point.
-- 2) If two people are inside a convex polygon playground, they can role a
--    ball between them.

myShapes model =
   -- List.map applies the function drawAt to all the positions
   List.map drawAt model.positions ++
   -- draw a polygon with vertices from the list polyList
   [ polygon polyList |> outlined (solid 1) (rgba 0 255 0 0.5)
   , text (String.fromInt model.nonHits ++ " misses")
        |> filled black
        |> move (40,-50)
   ]
   ++
   -- to catch taps everywhere, draw a clear rect above all shapes
   [ rect 192 128 |> filled (rgba 0 0 0 0.01) |> notifyTapAt TapAt ]

-- draw a red spot at a point
drawAt : (Float,Float) -> Shape Msg
drawAt pos = circle 0.5 |> filled red |> move pos

type Msg = Tick Float GetKeyState
         | TapAt (Float,Float)
         | StartAgain

update msg model = case msg of
                     Tick t _ ->
                       { model | time = t }
                     StartAgain ->
                       { model | positions = [] }
                     TapAt pos ->
                       if insideConvexClockwisePoly polyList pos
                         then { model | positions = pos :: model.positions }
                         else { model | nonHits = model.nonHits + 1 }

init : { time : Float, positions : List (Float,Float), nonHits : Int }
init = { time = 0, positions = [], nonHits = 0 }

-- define a region by going clockwise around a convex polygon
-- in a convex polygon, stretching a string between any two points on the perimeter stays inside the triangle
polyList = [(-10,-20),(-10,20),   (20,20), (-10,-20)]


-- geometry helper functions

-- return True if the point (x,y) is on the right of the line going from (x1,y1) to (x2,y2)
onRightOf : (Float,Float) -> (Float,Float) -> (Float,Float) -> Bool
onRightOf (x1,y1) (x2,y2) (x,y) =
  let
    v12 = (y1 - y2, x2 - x1)
    vp2 = (x - x2, y - y2 )
  in
    dot v12 vp2 < 0

-- calculate dot product, it is positive if two vectors are pointing in the same direction
dot : (Float,Float) -> (Float,Float) -> Float
dot (x,y) (u,v) = x*u + y*v

insideConvexClockwisePoly : List (Float,Float) -> (Float,Float) -> Bool
insideConvexClockwisePoly ptList pt =
  case ptList of
    q1 :: q2 :: qs -> if onRightOf q1 q2 pt
                        then insideConvexClockwisePoly (q2 :: qs) pt
                        else False
    otherwise -> True -- impossible