Almost done with ex 2.4

2 files changed, 65 insertions, 10 deletions

diff --git a/ex2/Main.hs b/ex2/Main.hs
index 7e32c4a..74d0054 100644
--- a/ex2/Main.hs
+++ b/ex2/Main.hs
@@ -1,4 +1,28 @@
-import Shape
+import           Shape
 
+main :: IO ()
 main = do
-  putStrLn $ show $ square 5.0
+        putStrLn "Convex Polygon:"
+        putStrLn
+                $ show
+                $ area
+                          (polygon
+                                  [ (550, 450)
+                                  , (455, 519)
+                                  , (491, 631)
+                                  , (609, 631)
+                                  , (645, 519)
+                                  ]
+                          )
+        putStrLn "Concave Polygon:"
+        putStrLn
+                $ show
+                $ area
+                          (polygon
+                                  [ (550, 580)
+                                  , (455, 519)
+                                  , (491, 631)
+                                  , (609, 631)
+                                  , (645, 519)
+                                  ]
+                          )
diff --git a/ex2/Shape.hs b/ex2/Shape.hs
index 0f7c0a9..97916c0 100644
--- a/ex2/Shape.hs
+++ b/ex2/Shape.hs
@@ -3,6 +3,7 @@ module Shape
         , area
         , square
         , circle
+        , polygon
         )
 where
 
@@ -16,30 +17,57 @@ type Radius = Float
 type Side = Float
 type Vertex = (Float, Float)
 
+polygon :: [Vertex] -> Shape
+polygon vs = Polygon vs
+
 area :: Shape -> Float
-area (Rectangle  s1 s2) = s1 * s2
-area (RtTriangle s1 s2) = s1 * s2 / 2
+area (Rectangle  s1 s2 ) = s1 * s2
+area (RtTriangle s1 s2 ) = s1 * s2 / 2
+area (Ellipse    r1 r2 ) = pi * r1 * r2
+area (Polygon (v1 : vs)) = polyArea vs
+    where
+        polyArea :: [Vertex] -> Float
+        polyArea (v2 : v3 : vs') = triArea v1 v2 v3 + polyArea (v3 : vs')
+        polyArea _               = 0
 
-square :: Side -> Shape
-square s = Rectangle s s
+triArea :: Vertex -> Vertex -> Vertex -> Float
+triArea v1 v2 v3 =
+        let a = distBetween v1 v2
+            b = distBetween v2 v3
+            c = distBetween v3 v1
+            s = 0.5 * (a + b + c)
+        in  sqrt (s * (s - a) * (s - b) * (s - c))
+
+distBetween :: Vertex -> Vertex -> Float
+distBetween (x1, y1) (x2, y2) = sqrt ((x1 - x2) ^ 2 + (y1 - y2) ^ 2)
 
 circle :: Radius -> Shape
 circle r = Ellipse r r
 
+convex :: Shape -> Bool
+convex (Rectangle  a  b ) = True
+convex (RtTriangle a  b ) = True
+convex (Ellipse    r1 r2) = True
+convex (Polygon [_, _, _]) = True
+convex (Polygon (vfirst : vsecond : vthird : vs)) = False
+
+crossProduct :: Vertex -> Vertex -> Vertex -> Float
+crossProduct (x1, y1) (x2, y2) (x3, y3) = (x2 - x1) * (y3 - y2) - (y2 - y1) * (x3 - x2)
+
+square :: Side -> Shape
+square s = Rectangle s s
+
 rectangle :: Side -> Side -> Shape
 rectangle s1 s2 = Polygon [(x, y), (-x, y), (-x, -y), (x, -y)]
     where
         x = s1 / 2
         y = s2 / 2
 
-rtTriangle :: Side -> Side -> Shape
-rtTriangle s1 s2 = Polygon [(0, 0), (s1, 0), (0, s2)]
-
 regularPolygon :: Int -> Side -> Shape
 regularPolygon n s =
         let
                 angleinc = (pi * 2) / fromIntegral n
-                radius   = (s * sin ((pi - angleinc) / 2)) / (sin angleinc)
+                radius   = (s * sin ((pi - angleinc) / 2)) / sin angleinc
                 regularVerts 0 _ = []
                 regularVerts n angle =
                         (radius * cos angle, radius * sin angle) : regularVerts
@@ -47,3 +75,6 @@ regularPolygon n s =
                                 (angle + angleinc)
         in
                 Polygon (regularVerts n 0)
+
+rtTriangle :: Side -> Side -> Shape
+rtTriangle s1 s2 = Polygon [(0, 0), (s1, 0), (0, s2)]