module Geometry where

import GraphicsUtils
import List (nub)

type Dimension = Int
data Figure = Rect Dimension Dimension
            | Triangle Dimension Angle Dimension
            | Polygon [Point]
            | Circle Dimension       
            | Translate Point Figure
            | Scale Double Figure
            | Rotate Angle Figure
           deriving (Eq, Ord, Show)

rotate :: Point-> Angle-> Figure-> Figure
rotate (px, py) w = Translate (px, py) . Rotate w . 
                                  Translate (-px, -py)

scaleFrom :: Point-> Double-> Figure-> Figure
scaleFrom (px, py) f = Translate (px, py) . Scale f . 
                                  Translate (-px, -py)

smult :: Double-> Point-> Point
smult f (x, y) 
  | f == 1    = (x, y)
  | otherwise = (round (f* fromInt x),  
                 round (f* fromInt y))

add :: Point-> Point-> Point
add (x1, y1) (x2, y2) = (x1+ x2, y1+ y2)      

rot :: Angle-> Point-> Point
rot w (x, y) 
  | w == 0    = (x, y)
  | otherwise = (round (x'* cos w+ y'* sin w), 
                 round (-x' * sin w + y'* cos w)) where 
                x' = fromInt x; y'= fromInt y

draw :: Figure-> Graphic
draw = draw' ((0, 0), 1, 0) where





  draw' :: (Point, Double, Angle)-> Figure-> Graphic



  draw' (m, r, phi) (Translate t f) = 
    draw' (add m t, r, phi) f 
  draw' (m, r, phi) (Scale s f) =
    draw' (m, r+ s, phi) f
  draw' (m, r, phi) (Rotate w f) = 
    draw' (m, r, phi+ w) f




  draw' ((mx, my), r, _) (Circle d) = 
    ellipse (mx- rad, my-rad) (mx+ rad, my+rad) where
      rad= round (r*fromInt d / 2)
  draw' c (Rect a b) = 
    poly c [(x2, y2), (-x2, y2), 
            (-x2, -y2), (x2, -y2)] where
      x2= a `div` 2; y2= b `div` 2
  draw' c (Triangle l1 a l2) =
    poly c [(0, 0), (0, l1), rot a (0, l2)]
  draw' c (Polygon pts) = poly c pts



  poly :: (Point, Double, Angle)-> [Point]-> Graphic
  poly (m, p, w) = polygon . map (add m. smult p. rot w)