ALGO: improve readability

Algorithms/ConvexHull/GrahamScan.hs

@@ -14,14 +14,14 @@ grahamGetCH :: [PT] -> [PT]
 grahamGetCH vs =
         -- merge upper hull with lower hull while discarding
         -- the duplicated points from the lower hull
-        f (reverse uH) uHRest ++ tailInit (f (reverse lH) lHRest)
+        scan uH uHRest ++ tailInit (scan lH lHRest)
   where
     -- sort lexicographically by x values (ties are resolved by y values)
-    sortedVs = fmap p2 . sortLex . fmap unp2 $ vs
+    sortedXY     = fmap p2 . sortLex . fmap unp2 $ vs
     -- lists for lower hull
-    (lH, lHRest) = splitAt 2 sortedVs
+    (lH, lHRest) = first reverse . splitAt 2 $ sortedXY
     -- lists for upper hull
-    (uH, uHRest) = splitAt 2 . reverse $ sortedVs
+    (uH, uHRest) = first reverse . splitAt 2 . reverse $ sortedXY
     -- This is the actual algorithm.
     -- If we have a list say:
     -- [(100, 100), (200, 450), (250, 250), (300, 400), (400, 200)]
@@ -31,42 +31,45 @@ grahamGetCH vs =
     --
     -- The first list is reversed since we only care about the last
     -- 3 elements and want to stay efficient.
-    f (y:z:xs) (x:ys)
+    scan :: [PT] -- ^ the starting convex hull points
+         -> [PT] -- ^ the rest of the points
+         -> [PT] -- ^ all convex hull points
+    scan (y:z:xs) (x:ys)
       -- last 3 elements are ccw, but there are elements left to check
-      |	ccw z y x   = f (x:y:z:xs) ys
+      |	ccw z y x   = scan (x:y:z:xs) ys
       -- not ccw, pop one out
-      | otherwise   = f (x:z:xs) ys
-    f (x:y:z:xs) []
+      | otherwise   = scan (x:z:xs) ys
+    scan (x:y:z:xs) []
       -- nothing left and last 3 elements are ccw, so return
       |	ccw z y x   = x:y:z:xs
       -- not ccw, pop one out
-      | otherwise   = f (x:z:xs) []
-    f xs _ = xs
+      | otherwise   = scan (x:z:xs) []
+    scan xs _ = xs
 
 
 -- |Compute all steps of the graham scan algorithm to allow
 -- visualizing it.
 grahamGetCHSteps :: [PT] -> [[PT]]
 grahamGetCHSteps vs =
-  (++)  (reverse . g (length vs) (reverse lH) $ lHRest) .
-    fmap (\x -> (last . reverse . g (length vs) (reverse lH) $ lHRest)
+  (++)  (reverse . g (length vs) lH $ lHRest) .
+    fmap (\x -> (last . reverse . g (length vs) lH $ lHRest)
           ++ x) $
-    (init . reverse . g (length vs) (reverse uH) $ uHRest)
+    (init . reverse . g (length vs) uH $ uHRest)
   where
-    sortedVs = fmap p2 . sortLex . fmap unp2 $ vs
-    (lH, lHRest) = splitAt 2 sortedVs
-    (uH, uHRest) = splitAt 2 . reverse $ sortedVs
+    sortedXY = fmap p2 . sortLex . fmap unp2 $ vs
+    (lH, lHRest) = first reverse . splitAt 2 $ sortedXY
+    (uH, uHRest) = first reverse . splitAt 2 . reverse $ sortedXY
     g c xs' ys'
-      | c >= 0    = f 0 xs' ys' : g (c - 1) xs' ys'
+      | c >= 0    = scan 0 xs' ys' : g (c - 1) xs' ys'
       | otherwise = []
       where
-        f c' (y:z:xs) (x:ys)
+        scan c' (y:z:xs) (x:ys)
           | c' >= c     = reverse (y:z:xs)
-          |	ccw z y x   = f (c' + 1) (x:y:z:xs) ys
-          | otherwise   = f (c' + 1) (x:z:xs) ys
-        f _ [x,y] []    = [y,x]
-        f c' (x:y:z:xs) []
+          |	ccw z y x   = scan (c' + 1) (x:y:z:xs) ys
+          | otherwise   = scan (c' + 1) (x:z:xs) ys
+        scan _ [x,y] []    = [y,x]
+        scan c' (x:y:z:xs) []
           | c' >= c     = reverse (x:y:z:xs)
           |	ccw z y x   = x:y:z:xs
-          | otherwise   = f (c' + 1) (x:z:xs) []
-        f _ xs _        = reverse xs
+          | otherwise   = scan (c' + 1) (x:z:xs) []
+        scan _ xs _        = reverse xs