Implement combined functions

Exercises/exercise-6/Shapes.hs

@@ -41,13 +41,13 @@ unitSq = Shape $ \(x, y) ->
 -}
 translate :: Vector -> Shape -> Shape
 translate (dx, dy) s = Shape $ \(x, y) ->
-    error "Fixme"
+    inside s (x + dx, y + dy)
 
 {- Inverting
     Inverting a shape i.e. switching outside vs inside
 -}
 negate :: Shape -> Shape
-negate s = error "Fixme"
+negate s = Shape $ \ (x, y) -> not (inside s (x, y))
 
 {- General combinator
     Combining two shapes with a parametric boolean function
@@ -66,19 +66,19 @@ combineBool f s1 s2 = Shape $ \p -> f (f1 p) (f2 p)
     All points that are in both shapes
 -}
 intersect :: Shape -> Shape -> Shape
-intersect = error "Fixme"
+intersect s1 s2 = Shape $ \ (x, y) -> all (\ s -> inside s (x, y)) [s1, s2]
 
 {-
     All points that in at least one of the shapes
 -}
 merge :: Shape -> Shape -> Shape
-merge = error "Fixme"
+merge s1 s2 = Shape $ \ (x, y) -> any (\ s -> inside s (x, y)) [s1, s2]
 
 {-
-    All points in the first shape that are not in the secnond shape
+    All points in the first shape that are not in the second shape
 -}
 minus :: Shape -> Shape -> Shape
-minus = error "Fixme"
+minus s1 s2 = Shape $ \ (x, y) -> inside s1 (x, y) && not (inside s1 (x, y))
 
 
 {- Matrix transformations