Add files for Exercise 6

Exercises/exercise-6/Matrix.hs

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+module Matrix (Matrix (..), Point, Vector, scale, invert, apply) where
+
+type Point = (Float, Float)
+
+type Vector = Point
+
+data Matrix = Matrix (Float, Float) (Float, Float)
+  deriving (Show)
+
+scale :: Float -> Matrix -> Matrix
+scale r (Matrix (a, b) (c, d)) = Matrix (r * a, r * b) (r * c, r * d)
+
+invert :: Matrix -> Matrix
+invert (Matrix (a, b) (c, d)) =
+  scale
+    (1 / (a * d - b * c))
+    (Matrix (d, -b) (-c, a))
+
+apply :: Matrix -> Vector -> Vector
+apply (Matrix (a, b) (c, d)) (x, y) =
+  ( a * x + b * y,
+    c * x + d * y
+  )

Exercises/exercise-6/Shapes.hs

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+module Shape where
+
+import Data.List
+import Matrix (Matrix (Matrix), Vector, Point, invert, apply)
+
+{- Definition of 'Shape'
+    Shapes are things that discriminate between outside and inside
+-}
+newtype Shape = Shape { inside :: Point -> Bool }
+
+{- Basic Shapes
+    These are the basic shapes used to construct more complicated shapes
+-}
+
+{-
+    A simple empty shape
+-}
+empty :: Shape
+empty = Shape $ const False
+
+{-
+    A disc with radius 1 located at (0,0)
+-}
+unitDisc :: Shape
+unitDisc = Shape $ \(x, y) ->
+    x^2 + y^2 <= 1
+
+{-
+    A square with length/width 1 located at (0,0)
+-}
+unitSq :: Shape
+unitSq = Shape $ \(x, y) ->
+    abs x <= 1 && abs y <= 1
+
+{- Manipulations
+   Functions to change and combine existing shapes into new shapes
+-}
+
+{- Translation
+    Moving a shape along a vector
+-}
+translate :: Vector -> Shape -> Shape
+translate (dx, dy) s = Shape $ \(x, y) ->
+    error "Fixme"
+
+{- Inverting
+    Inverting a shape i.e. switching outside vs inside
+-}
+negate :: Shape -> Shape
+negate s = error "Fixme"
+
+{- General combinator
+    Combining two shapes with a parametric boolean function
+-}
+combineBool
+    :: (Bool -> Bool -> Bool)
+    -> Shape
+    -> Shape
+    -> Shape
+combineBool f s1 s2 = Shape $ \p -> f (f1 p) (f2 p)
+    where
+        f1 = inside s1
+        f2 = inside s2
+
+{-
+    All points that are in both shapes
+-}
+intersect :: Shape -> Shape -> Shape
+intersect = error "Fixme"
+
+{-
+    All points that in at least one of the shapes
+-}
+merge :: Shape -> Shape -> Shape
+merge = error "Fixme"
+
+{-
+    All points in the first shape that are not in the secnond shape
+-}
+minus :: Shape -> Shape -> Shape
+minus = error "Fixme"
+
+
+{- Matrix transformations
+    Applying a matrix/linear transformation to a shape
+-}
+transformM :: Matrix -> Shape -> Shape
+transformM m s = Shape $ \p ->
+    inside s $ apply m' p
+    where
+        m' = invert m
+
+{-
+    Stretch a shape along the X axis
+-}
+stretchX :: Float -> Shape -> Shape
+stretchX r = transformM $ Matrix (r, 0) (0, 1)
+
+{-
+    Stretch a shape along the Y axis
+-}
+stretchY :: Float -> Shape -> Shape
+stretchY r = transformM $ Matrix (1, 0) (0, r)
+
+{-
+    Stretch a shape
+-}
+stretch :: Float -> Shape -> Shape
+stretch r = transformM $ Matrix (r, 0) (0, r)
+
+{-
+    Mirror a shape at the X-axis
+-}
+flipX :: Shape -> Shape
+flipX = transformM (Matrix (1, 0) (0, -1))
+
+{-
+    Mirror a shape at the Y-axis
+-}
+flipY :: Shape -> Shape
+flipY = transformM (Matrix (-1, 0) (0, 1))
+
+
+flip45 :: Shape -> Shape
+flip45 = transformM (Matrix (0, 1) (1, 0))
+
+{-
+    Mirror a shape at the origin
+-}
+flip0 :: Shape -> Shape
+flip0 = transformM (Matrix (-1, 0) (0, -1))
+
+
+{-
+    Rotate a shape around the origin
+-}
+rotate :: Float -> Shape -> Shape
+rotate a = transformM $ Matrix
+        (cos a, -(sin a))
+        (sin a, cos a)
+
+{- Semantics
+    Here we render/interpret shapes in terms of "ASCII-Art" text files
+-}
+
+render :: Float -> Float -> Shape -> IO ()
+render length height shape = writeFile "shape.txt" lines
+    where
+        draw p
+            | inside shape p = ('#', p)
+            | otherwise = (' ', p)
+
+        breakLn (d, (x,y))
+            | x == length = [d,'\n']
+            | otherwise = [d]
+
+        pixels = [draw (x,y) | y <- [(-height)..height],  x <- [(-length)..length]]
+
+        lines = concatMap breakLn pixels
+
+{- Examples
+--}
+
+shape1 = translate (100, 100) $ stretch 10 unitDisc
+shape2 = rotate 1 unitSq
+
+shape3 = translate (100, 100) $ merge shape1 shape2
+
+iShape = flipX $ merge
+    (stretchY 2 unitSq)
+    (translate (0, 5) unitDisc)
+
+disc50 = stretch 50 unitDisc