Revert "Remove almost all 'type' usage to make types more transparent"

This reverts commit 5120a44d0f.

Conflicts:
	Parser/Meshparser.hs

Algebra/Polygon.hs

@@ -4,15 +4,14 @@ module Algebra.Polygon where
 
 import Algebra.Vector
 import Data.Maybe
-import Diagrams.TwoD.Types
 import MyPrelude
 
 
 -- |Split a polygon by a given segment which must be vertices of the
 -- polygon (returns empty array otherwise).
-splitPoly :: [P2]
+splitPoly :: [PT]
-          -> (P2, P2)
+          -> Segment
-          -> [[P2]]
+          -> [[PT]]
 splitPoly pts (a, b)
   | elem a pts && elem b pts =
     [b : takeWhile (/= b) shiftedPoly, a : dropWhile (/= b) shiftedPoly]
@@ -22,7 +21,7 @@ splitPoly pts (a, b)
 
 
 -- |Get all edges of a polygon.
-polySegments :: [P2] -> [(P2, P2)]
+polySegments :: [PT] -> [Segment]
 polySegments p@(x':_:_:_) = go p ++ [(last p, x')]
   where
     go (x:y:xs) = (x, y) : go (y:xs)
@@ -33,7 +32,7 @@ polySegments _ = []
 -- |Check whether the given segment is inside the polygon.
 -- This doesn't check for segments that are completely outside
 -- of the polygon yet.
-isInsidePoly :: [P2] -> (P2, P2) -> Bool
+isInsidePoly :: [PT] -> Segment -> Bool
 isInsidePoly pts seg =
   null
     . catMaybes
@@ -42,21 +41,21 @@ isInsidePoly pts seg =
 
 
 -- |Check whether two points are adjacent vertices of a polygon.
-adjacent :: P2 -> P2 -> [P2] -> Bool
+adjacent :: PT -> PT -> [PT] -> Bool
 adjacent u v = any (\x -> x == (u, v) || x == (v, u)) . polySegments
 
 
 -- |Check whether the polygon is a triangle polygon.
-isTrianglePoly :: [P2] -> Bool
+isTrianglePoly :: [PT] -> Bool
 isTrianglePoly [_, _, _] = True
 isTrianglePoly _         = False
 
 
 -- |Get all triangle polygons.
-triangleOnly :: [[P2]] -> [[P2]]
+triangleOnly :: [[PT]] -> [[PT]]
 triangleOnly = filter isTrianglePoly
 
 
 -- |Get all non-triangle polygons.
-nonTriangleOnly :: [[P2]] -> [[P2]]
+nonTriangleOnly :: [[PT]] -> [[PT]]
 nonTriangleOnly = filter (not . isTrianglePoly)

Algebra/Vector.hs

@@ -13,6 +13,13 @@ import GHC.Float
 import MyPrelude
 
 
+type Vec     = R2
+type PT      = P2
+type Coord   = (Double, Double)
+type Segment = (PT, PT)
+type Square  = (Coord, Coord)
+
+
 data Alignment = CW
                | CCW
                | CL
@@ -24,13 +31,13 @@ data Alignment = CW
 -- ((xmin, ymin), (xmax, ymax))
 dimToSquare :: (Double, Double) -- ^ x dimension
             -> (Double, Double) -- ^ y dimension
-            -> ((Double, Double), (Double, Double)) -- ^ square describing those dimensions
+            -> Square           -- ^ square describing those dimensions
 dimToSquare (x1, x2) (y1, y2) = ((x1, y1), (x2, y2))
 
 
 -- |Checks whether the Point is in a given Square.
-inRange :: ((Double, Double), (Double, Double)) -- ^ the square: ((xmin, ymin), (xmax, ymax))
+inRange :: Square -- ^ the square: ((xmin, ymin), (xmax, ymax))
-        -> P2     -- ^ Coordinate
+        -> PT     -- ^ Coordinate
         -> Bool   -- ^ result
 inRange ((xmin, ymin), (xmax, ymax)) (coords -> x :& y)
   = x >= min xmin xmax
@@ -40,7 +47,7 @@ inRange ((xmin, ymin), (xmax, ymax)) (coords -> x :& y)
 
 
 -- |Get the angle between two vectors.
-getAngle :: R2 -> R2 -> Double
+getAngle :: Vec -> Vec -> Double
 getAngle a b =
   acos
     . flip (/) (vecLength a * vecLength b)
@@ -49,50 +56,48 @@ getAngle a b =
 
 
 -- |Get the length of a vector.
-vecLength :: R2 -> Double
+vecLength :: Vec -> Double
 vecLength v = sqrt (x^(2 :: Int) + y^(2 :: Int))
   where
     (x, y) = unr2 v
 
 
 -- |Compute the scalar product of two vectors.
-scalarProd :: R2 -> R2 -> Double
+scalarProd :: Vec -> Vec -> Double
 scalarProd (R2 a1 a2) (R2 b1 b2) = a1 * b1 + a2 * b2
 
 
 -- |Multiply a scalar with a vector.
-scalarMul :: Double -> R2 -> R2
+scalarMul :: Double -> Vec -> Vec
 scalarMul d (R2 a b) = R2 (a * d) (b * d)
 
 
 -- |Construct a vector that points to a point from the origin.
-pt2Vec :: P2 -> R2
+pt2Vec :: PT -> Vec
 pt2Vec = r2 . unp2
 
 
 -- |Give the point which is at the coordinates the vector
 -- points to from the origin.
-vec2Pt :: R2 -> P2
+vec2Pt :: Vec -> PT
 vec2Pt = p2 . unr2
 
 
 -- |Construct a vector between two points.
-vp2 :: P2  -- ^ vector origin
+vp2 :: PT  -- ^ vector origin
-    -> P2  -- ^ vector points here
+    -> PT  -- ^ vector points here
-    -> R2
+    -> Vec
 vp2 a b = pt2Vec b - pt2Vec a
 
 
 -- |Computes the determinant of 3 points.
-det :: P2 -> P2 -> P2 -> Double
+det :: PT -> PT -> PT -> Double
 det (coords -> ax :& ay) (coords -> bx :& by) (coords -> cx :& cy) =
   (bx - ax) * (cy - ay) - (by - ay) * (cx - ax)
 
 
 -- |Get the point where two lines intesect, if any.
-intersectSeg' :: (P2, P2) -- ^ first segment
+intersectSeg' :: Segment -> Segment -> Maybe PT
-              -> (P2, P2) -- ^ second segment
-              -> Maybe P2
 intersectSeg' (a, b) (c, d) =
   glossToPt <$> intersectSegSeg (ptToGloss a)
                                 (ptToGloss b)
@@ -105,7 +110,7 @@ intersectSeg' (a, b) (c, d) =
 
 -- |Get the point where two lines intesect, if any. Excludes the
 -- case of end-points intersecting.
-intersectSeg'' :: (P2, P2) -> (P2, P2) -> Maybe P2
+intersectSeg'' :: Segment -> Segment -> Maybe PT
 intersectSeg'' (a, b) (c, d) = case intersectSeg' (a, b) (c, d) of
   Just x  -> if x `notElem` [a,b,c,d] then Just a else Nothing
   Nothing -> Nothing
@@ -115,7 +120,7 @@ intersectSeg'' (a, b) (c, d) = case intersectSeg' (a, b) (c, d) of
 -- * clock-wise
 -- * counter-clock-wise
 -- * collinear
-getOrient :: P2 -> P2 -> P2 -> Alignment
+getOrient :: PT -> PT -> PT -> Alignment
 getOrient a b c = case compare (det a b c) 0 of
   LT -> CW
   GT -> CCW
@@ -125,7 +130,7 @@ getOrient a b c = case compare (det a b c) 0 of
 --- |Checks if 3 points a,b,c do not build a clockwise triangle by
 --- connecting a-b-c. This is done by computing the determinant and
 --- checking the algebraic sign.
-notcw :: P2 -> P2 -> P2 -> Bool
+notcw :: PT -> PT -> PT -> Bool
 notcw a b c = case getOrient a b c of
   CW -> False
   _  -> True
@@ -134,22 +139,22 @@ notcw a b c = case getOrient a b c of
 --- |Checks if 3 points a,b,c do build a clockwise triangle by
 --- connecting a-b-c. This is done by computing the determinant and
 --- checking the algebraic sign.
-cw :: P2 -> P2 -> P2 -> Bool
+cw :: PT -> PT -> PT -> Bool
 cw a b c = not . notcw a b $ c
 
 
 -- |Sort X and Y coordinates lexicographically.
-sortedXY :: [P2] -> [P2]
+sortedXY :: [PT] -> [PT]
 sortedXY = fmap p2 . sortLex . fmap unp2
 
 
 -- |Sort Y and X coordinates lexicographically.
-sortedYX :: [P2] -> [P2]
+sortedYX :: [PT] -> [PT]
 sortedYX = fmap p2 . sortLexSwapped . fmap unp2
 
 
 -- |Sort all points according to their X-coordinates only.
-sortedX :: [P2] -> [P2]
+sortedX :: [PT] -> [PT]
 sortedX xs =
   fmap p2
   . sortBy (\(a1, _) (a2, _) -> compare a1 a2)
@@ -157,7 +162,7 @@ sortedX xs =
 
 
 -- |Sort all points according to their Y-coordinates only.
-sortedY :: [P2] -> [P2]
+sortedY :: [PT] -> [PT]
 sortedY xs =
   fmap p2
   . sortBy (\(_, b1) (_, b2) -> compare b1 b2)
@@ -165,25 +170,25 @@ sortedY xs =
 
 
 -- |Apply a function on the coordinates of a point.
-onPT :: ((Double, Double) -> (Double, Double)) -> P2 -> P2
+onPT :: (Coord -> Coord) -> PT -> PT
 onPT f = p2 . f . unp2
 
 
 -- |Compare the y-coordinate of two points.
-ptCmpY :: P2 -> P2 -> Ordering
+ptCmpY :: PT -> PT -> Ordering
 ptCmpY (coords -> _ :& y1) (coords -> _ :& y2) =
   compare y1 y2
 
 
 -- |Compare the x-coordinate of two points.
-ptCmpX :: P2 -> P2 -> Ordering
+ptCmpX :: PT -> PT -> Ordering
 ptCmpX (coords -> x1 :& _) (coords -> x2 :& _) =
   compare x1 x2
 
 
-posInfPT :: P2
+posInfPT :: PT
 posInfPT = p2 (read "Infinity", read "Infinity")
 
 
-negInfPT :: P2
+negInfPT :: PT
 negInfPT = p2 (negate . read $ "Infinity", negate . read $ "Infinity")

Algorithms/GrahamScan.hs

@@ -3,7 +3,6 @@
 module Algorithms.GrahamScan where
 
 import Algebra.Vector
-import Diagrams.TwoD.Types
 import MyPrelude
 
 
@@ -75,18 +74,18 @@ ys = []
 return [(100, 100), (400, 200)]
 =========================================================
 --}
-grahamCH :: [P2] -> [P2]
+grahamCH :: [PT] -> [PT]
 grahamCH vs = grahamUCH vs ++ (tailInit . grahamLCH $ vs)
 
 
 -- |Get the lower part of the convex hull.
-grahamLCH :: [P2] -> [P2]
+grahamLCH :: [PT] -> [PT]
 grahamLCH vs = uncurry (\x y -> last . scanH x $ y)
                        (first reverse . splitAt 3 . sortedXY $ vs)
 
 
 -- |Get the upper part of the convex hull.
-grahamUCH :: [P2] -> [P2]
+grahamUCH :: [PT] -> [PT]
 grahamUCH vs = uncurry (\x y -> last . scanH x $ y)
                        (first reverse . splitAt 3 . reverse . sortedXY $ vs)
 
@@ -96,9 +95,9 @@ grahamUCH vs = uncurry (\x y -> last . scanH x $ y)
 -- If it's the upper or lower half depends on the input.
 -- Also, the first list is expected to be reversed since we only care
 -- about the last 3 elements and want to stay efficient.
-scanH :: [P2]   -- ^ the first 3 starting points in reversed order
+scanH :: [PT]   -- ^ the first 3 starting points in reversed order
-      -> [P2]   -- ^ the rest of the points
+      -> [PT]   -- ^ the rest of the points
-      -> [[P2]] -- ^ all convex hull points iterations for the half
+      -> [[PT]] -- ^ all convex hull points iterations for the half
 scanH hs@(x:y:z:xs) (r':rs')
   |	notcw z y x       = hs : scanH (r':hs) rs'
   | otherwise         = hs : scanH (x:z:xs) (r':rs')
@@ -112,12 +111,12 @@ scanH hs _            = [hs]
 -- |Compute all steps of the graham scan algorithm to allow
 -- visualizing it.
 -- Whether the upper or lower hull is computed depends on the input.
-grahamCHSteps :: Int -> [P2] -> [P2] -> [[P2]]
+grahamCHSteps :: Int -> [PT] -> [PT] -> [[PT]]
 grahamCHSteps c xs' ys' = take c . scanH xs' $ ys'
 
 
 -- |Get all iterations of the upper hull of the graham scan algorithm.
-grahamUHSteps :: [P2] -> [[P2]]
+grahamUHSteps :: [PT] -> [[PT]]
 grahamUHSteps vs =
   (++) [getLastX 2 . sortedXY $ vs]
   . rmdups
@@ -128,7 +127,7 @@ grahamUHSteps vs =
 
 
 -- |Get all iterations of the lower hull of the graham scan algorithm.
-grahamLHSteps :: [P2] -> [[P2]]
+grahamLHSteps :: [PT] -> [[PT]]
 grahamLHSteps vs =
   (++) [take 2 . sortedXY $ vs]
   . rmdups

Algorithms/KDTree.hs

@@ -42,9 +42,9 @@ instance Not Direction where
 
 
 -- |Construct a kd-tree from a list of points in O(n log n).
-kdTree :: [P2]      -- ^ list of points to construct the kd-tree from
+kdTree :: [PT]      -- ^ list of points to construct the kd-tree from
        -> Direction -- ^ initial direction of the root-node
-       -> KDTree P2 -- ^ resulting kd-tree
+       -> KDTree PT -- ^ resulting kd-tree
 kdTree xs' = go (sortedX xs') (sortedY xs')
   where
     go [] _ _ = KTNil
@@ -67,10 +67,10 @@ kdTree xs' = go (sortedX xs') (sortedY xs')
 -- If you want to partition against the pivot of X, then you pass
 --   partition' (pivot xs) (ys, xs)
 -- and get ((y1, y2), (x1, x2)).
-partition' :: P2                           -- ^ the pivot to partition against
+partition' :: PT                           -- ^ the pivot to partition against
-           -> (P2 -> P2 -> Ordering)       -- ^ ptCmpY or ptCmpX
+           -> (PT -> PT -> Ordering)       -- ^ ptCmpY or ptCmpX
-           -> ([P2], [P2])                 -- ^ both lists (X, Y) or (Y, X)
+           -> ([PT], [PT])                 -- ^ both lists (X, Y) or (Y, X)
-           -> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2)) or
+           -> (([PT], [PT]), ([PT], [PT])) -- ^ ((x1, x2), (y1, y2)) or
                                            --   ((y1, y2), (x1, x2))
 partition' piv cmp' (xs, ys) = ((x1, x2), (y1, y2))
   where
@@ -83,16 +83,16 @@ partition' piv cmp' (xs, ys) = ((x1, x2), (y1, y2))
 -- |Partition two sorted lists of points X and Y against the pivot of
 -- Y. This function is unsafe as it does not check if there is a valid
 -- pivot.
-partitionY :: ([P2], [P2])                 -- ^ both lists (X, Y)
+partitionY :: ([PT], [PT])                 -- ^ both lists (X, Y)
-           -> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2))
+           -> (([PT], [PT]), ([PT], [PT])) -- ^ ((x1, x2), (y1, y2))
 partitionY (xs, ys) = partition' (fromJust . pivot $ ys) ptCmpY (xs, ys)
 
 
 -- |Partition two sorted lists of points X and Y against the pivot of
 -- X. This function is unsafe as it does not check if there is a valid
 -- pivot.
-partitionX :: ([P2], [P2])                 -- ^ both lists (X, Y)
+partitionX :: ([PT], [PT])                 -- ^ both lists (X, Y)
-           -> (([P2], [P2]), ([P2], [P2])) -- ^ ((x1, x2), (y1, y2))
+           -> (([PT], [PT]), ([PT], [PT])) -- ^ ((x1, x2), (y1, y2))
 partitionX (xs, ys) = (\(x, y) -> (y, x))
                       . partition' (fromJust . pivot $ xs) ptCmpX $ (ys, xs)
 
@@ -100,9 +100,7 @@ partitionX (xs, ys) = (\(x, y) -> (y, x))
 -- |Execute a range search in O(log n). It returns a tuple
 -- of the points found in the range and also gives back a pretty
 -- rose tree suitable for printing.
-rangeSearch :: KDTree P2                            -- ^ tree to search in
+rangeSearch :: KDTree PT -> Square -> ([PT], Tree String)
-            -> ((Double, Double), (Double, Double)) -- ^ square describing the range
-            -> ([P2], Tree String)
 rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
   where
     -- either y1 or x1 depending on the orientation
@@ -112,7 +110,7 @@ rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
     -- either the second or first of the tuple, depending on the orientation
     cur' dir = if' (dir == Vertical) snd fst
     -- All points in the range.
-    goPt :: KDTree P2 -> ((Double, Double), (Double, Double)) -> [P2]
+    goPt :: KDTree PT -> Square -> [PT]
     goPt KTNil _ = []
     goPt (KTNode ln pt dir rn) sq =
       [pt | inRange sq pt]
@@ -124,7 +122,7 @@ rangeSearch kd' sq' = (goPt kd' sq', goTree kd' sq' True)
               (goPt rn sq)
               [])
     -- A pretty rose tree suitable for printing.
-    goTree :: KDTree P2 -> ((Double, Double), (Double, Double)) -> Bool -> Tree String
+    goTree :: KDTree PT -> Square -> Bool -> Tree String
     goTree KTNil _ _ = Node "nil" []
     goTree (KTNode ln pt dir rn) sq vis
       | ln == KTNil && rn == KTNil = Node treeText []
@@ -181,7 +179,7 @@ getDirection _                  = Nothing
 
 
 -- |Convert a kd-tree to a rose tree, for pretty printing.
-kdTreeToRoseTree :: KDTree P2 -> Tree String
+kdTreeToRoseTree :: KDTree PT -> Tree String
 kdTreeToRoseTree (KTNil) = Node "nil" []
 kdTreeToRoseTree (KTNode ln val _ rn) =
   Node (show . unp2 $ val) [kdTreeToRoseTree ln, kdTreeToRoseTree rn]

Algorithms/PolygonIntersection.hs

@@ -18,14 +18,14 @@ import           QueueEx
 -- successor are saved for convenience.
 data PolyPT =
   PolyA {
-    id'   :: P2
+    id'   :: PT
-    , pre :: P2
+    , pre :: PT
-    , suc :: P2
+    , suc :: PT
     }
   | PolyB {
-    id'   :: P2
+    id'   :: PT
-    , pre :: P2
+    , pre :: PT
-    , suc :: P2
+    , suc :: PT
     }
   deriving (Show, Eq)
 
@@ -42,7 +42,7 @@ isPolyB = not . isPolyA
 -- |Shift a list of sorted convex hull points of a polygon so that
 -- the first element in the list is the one with the highest y-coordinate.
 -- This is done in O(n).
-sortLexPoly :: [P2] -> [P2]
+sortLexPoly :: [PT] -> [PT]
 sortLexPoly ps = maybe [] (`shiftM` ps) (elemIndex (yMax ps) ps)
   where
     yMax       = foldl1 (\x y -> if ptCmpY x y == GT then x else y)
@@ -50,8 +50,8 @@ sortLexPoly ps = maybe [] (`shiftM` ps) (elemIndex (yMax ps) ps)
 
 -- |Make a PolyPT list out of a regular list of points, so
 -- the predecessor and successors are all saved.
-mkPolyPTList :: (P2 -> P2 -> P2 -> PolyPT) -- ^ PolyA or PolyB function
+mkPolyPTList :: (PT -> PT -> PT -> PolyPT) -- ^ PolyA or PolyB function
-             -> [P2]                       -- ^ polygon points
+             -> [PT]                       -- ^ polygon points
              -> [PolyPT]
 mkPolyPTList f' pts@(x':y':_:_) =
   f' x' (last pts) y' : go f' pts
@@ -64,7 +64,7 @@ mkPolyPTList _ _ = []
 
 -- |Sort the points of two polygons according to their y-coordinates,
 -- while saving the origin of that point. This is done in O(n).
-sortLexPolys :: ([P2], [P2]) -> [PolyPT]
+sortLexPolys :: ([PT], [PT]) -> [PolyPT]
 sortLexPolys (pA'@(_:_), pB'@(_:_)) =
   queueToList $ go (Q.fromList . mkPolyPTList PolyA . sortLexPoly $ pA')
                    (Q.fromList . mkPolyPTList PolyB . sortLexPoly $ pB')
@@ -104,7 +104,7 @@ sortLexPolys _ = []
 
 -- |Get all points that intersect between both polygons. This is done
 -- in O(n).
-intersectionPoints :: [PolyPT] -> [P2]
+intersectionPoints :: [PolyPT] -> [PT]
 intersectionPoints xs' = rmdups . go $ xs'
   where
     go [] = []
@@ -113,7 +113,7 @@ intersectionPoints xs' = rmdups . go $ xs'
 
     -- Get the scan line or in other words the
     -- Segment pairs we are going to check for intersection.
-    scanLine :: [PolyPT] -> ([(P2, P2)], [(P2, P2)])
+    scanLine :: [PolyPT] -> ([Segment], [Segment])
     scanLine sp@(_:_) = (,) (getSegment isPolyA) (getSegment isPolyB)
       where
         getSegment f = fromMaybe []
@@ -124,7 +124,7 @@ intersectionPoints xs' = rmdups . go $ xs'
     -- Gets the actual intersections between the segments of
     -- both polygons we currently examine. This is done in O(1)
     -- since we have max 4 segments.
-    segIntersections :: ([(P2, P2)], [(P2, P2)]) -> [P2]
+    segIntersections :: ([Segment], [Segment]) -> [PT]
     segIntersections (a@(_:_), b@(_:_)) =
       catMaybes
       . fmap (\[x, y] -> intersectSeg' x y)

Algorithms/PolygonTriangulation.hs

@@ -6,7 +6,6 @@ import Algebra.Polygon
 import Algebra.Vector
 import qualified Control.Arrow as A
 import Data.Maybe
-import Diagrams.TwoD.Types
 import Safe
 
 
@@ -19,12 +18,12 @@ data VCategory = VStart
 
 
 -- |Classify all vertices on a polygon into five categories (see VCategory).
-classifyList :: [P2] -> [(P2, VCategory)]
+classifyList :: [PT] -> [(PT, VCategory)]
 classifyList p@(x:y:_:_) =
   -- need to handle the first and last element separately
   [classify (last p) x y] ++ go p ++ [classify (last . init $ p) (last p) x]
   where
-    go :: [P2] -> [(P2, VCategory)]
+    go :: [PT] -> [(PT, VCategory)]
     go (x':y':z':xs) = classify x' y' z' : go (y':z':xs)
     go _          = []
 classifyList _ = []
@@ -32,10 +31,10 @@ classifyList _ = []
 
 -- |Classify a vertex on a polygon given it's next and previous vertex
 -- into five categories (see VCategory).
-classify :: P2  -- ^ prev vertex
+classify :: PT  -- ^ prev vertex
-         -> P2  -- ^ classify this one
+         -> PT  -- ^ classify this one
-         -> P2  -- ^ next vertex
+         -> PT  -- ^ next vertex
-         -> (P2, VCategory)
+         -> (PT, VCategory)
 classify prev v next
   | isVStart prev v next = (v, VStart)
   | isVSplit prev v next = (v, VSplit)
@@ -46,9 +45,9 @@ classify prev v next
 
 -- |Whether the vertex, given it's next and previous vertex,
 -- is a start vertex.
-isVStart :: P2  -- ^ previous vertex
+isVStart :: PT  -- ^ previous vertex
-         -> P2  -- ^ vertice to check
+         -> PT  -- ^ vertice to check
-         -> P2  -- ^ next vertex
+         -> PT  -- ^ next vertex
          -> Bool
 isVStart prev v next =
   ptCmpY next v == LT && ptCmpY prev v == LT && cw next v prev
@@ -56,9 +55,9 @@ isVStart prev v next =
 
 -- |Whether the vertex, given it's next and previous vertex,
 -- is a split vertex.
-isVSplit :: P2  -- ^ previous vertex
+isVSplit :: PT  -- ^ previous vertex
-         -> P2  -- ^ vertice to check
+         -> PT  -- ^ vertice to check
-         -> P2  -- ^ next vertex
+         -> PT  -- ^ next vertex
          -> Bool
 isVSplit prev v next =
   ptCmpY prev v == LT && ptCmpY next v == LT && cw prev v next
@@ -66,9 +65,9 @@ isVSplit prev v next =
 
 -- |Whether the vertex, given it's next and previous vertex,
 -- is an end vertex.
-isVEnd :: P2  -- ^ previous vertex
+isVEnd :: PT  -- ^ previous vertex
-       -> P2  -- ^ vertice to check
+       -> PT  -- ^ vertice to check
-       -> P2  -- ^ next vertex
+       -> PT  -- ^ next vertex
        -> Bool
 isVEnd prev v next =
   ptCmpY prev v == GT && ptCmpY next v == GT && cw next v prev
@@ -76,9 +75,9 @@ isVEnd prev v next =
 
 -- |Whether the vertex, given it's next and previous vertex,
 -- is a merge vertex.
-isVMerge :: P2  -- ^ previous vertex
+isVMerge :: PT  -- ^ previous vertex
-         -> P2  -- ^ vertice to check
+         -> PT  -- ^ vertice to check
-         -> P2  -- ^ next vertex
+         -> PT  -- ^ next vertex
          -> Bool
 isVMerge prev v next =
   ptCmpY next v == GT && ptCmpY prev v == GT && cw prev v next
@@ -86,9 +85,9 @@ isVMerge prev v next =
 
 -- |Whether the vertex, given it's next and previous vertex,
 -- is a regular vertex.
-isVRegular :: P2  -- ^ previous vertex
+isVRegular :: PT  -- ^ previous vertex
-           -> P2  -- ^ vertice to check
+           -> PT  -- ^ vertice to check
-           -> P2  -- ^ next vertex
+           -> PT  -- ^ next vertex
            -> Bool
 isVRegular prev v next =
      (not . isVStart prev v $ next)
@@ -99,7 +98,7 @@ isVRegular prev v next =
 
 
 -- |A polygon P is y-monotone, if it has no split and merge vertices.
-isYmonotone :: [P2] -> Bool
+isYmonotone :: [PT] -> Bool
 isYmonotone poly =
   not
   . any (\x -> x == VSplit || x == VMerge)
@@ -108,12 +107,12 @@ isYmonotone poly =
 
 
 -- |Partition P into y-monotone pieces.
-monotonePartitioning :: [P2] -> [[P2]]
+monotonePartitioning :: [PT] -> [[PT]]
 monotonePartitioning pts
   | isYmonotone pts = [pts]
   | otherwise = go (monotoneDiagonals pts) pts
   where
-    go :: [(P2, P2)] -> [P2] -> [[P2]]
+    go :: [Segment] -> [PT] -> [[PT]]
     go (x:xs) pts'@(_:_)
       | isYmonotone a && isYmonotone b = [a, b]
       | isYmonotone b = b : go xs a
@@ -125,37 +124,37 @@ monotonePartitioning pts
 
 -- |Try to eliminate the merge and split vertices by computing the
 -- diagonals we have to use for splitting the polygon.
-monotoneDiagonals :: [P2] -> [(P2, P2)]
+monotoneDiagonals :: [PT] -> [Segment]
 monotoneDiagonals pts = catMaybes . go $ classifyList pts
   where
-    go :: [(P2, VCategory)] -> [Maybe (P2, P2)]
+    go :: [(PT, VCategory)] -> [Maybe Segment]
     go (x:xs) = case snd x of
       VMerge -> getSeg (belowS . fst $ x) (fst x) : go xs
       VSplit -> getSeg (aboveS . fst $ x) (fst x) : go xs
       _      -> [] ++ go xs
     go [] = []
-    getSeg :: [P2] -- all points above/below the current point
+    getSeg :: [PT] -- all points above/below the current point
-           -> P2   -- current point
+           -> PT   -- current point
-           -> Maybe (P2, P2)
+           -> Maybe Segment
     getSeg [] _ = Nothing
     getSeg (z:zs) pt
       | isInsidePoly pts (z, pt) = Just (z, pt)
       | otherwise = getSeg zs pt
-    aboveS :: P2 -> [P2]
+    aboveS :: PT -> [PT]
     aboveS pt = tail . dropWhile (/= pt) $ sortedYX pts
-    belowS :: P2 -> [P2]
+    belowS :: PT -> [PT]
     belowS pt = reverse . takeWhile (/= pt) $ sortedYX pts
 
 
 -- |Triangulate a y-monotone polygon.
-triangulate :: [P2] -> [[P2]]
+triangulate :: [PT] -> [[PT]]
 triangulate pts =
   go pts . A.first reverse . splitAt 3 . reverse . sortedYX $ pts
   where
-    go :: [P2]          -- current polygon
+    go :: [PT]          -- current polygon
-       -> ([P2], [P2])  -- (stack of visited vertices, rest)
+       -> ([PT], [PT])  -- (stack of visited vertices, rest)
                         --  sorted by Y-coordinate
-       -> [[P2]]
+       -> [[PT]]
     go xs (p@[_, _], r:rs) = go xs (r:p, rs)
     go xs (p@(u:vi:vi1:ys), rs)
       -- case 1 and 3

Algorithms/QuadTree.hs

@@ -56,8 +56,7 @@ data Orient = North | South | East | West
 
 
 -- |Get a sub-square of the current square, e.g. nw, ne, sw or se.
-nwSq, neSq, swSq, seSq :: ((Double, Double), (Double, Double)) -- ^ current square
+nwSq, neSq, swSq, seSq :: Square -> Square
-                       -> ((Double, Double), (Double, Double)) -- ^ sub-square
 nwSq ((xl, yl), (xu, yu)) = (,)  (xl, (yl + yu) / 2)  ((xl + xu) / 2, yu)
 neSq ((xl, yl), (xu, yu)) = (,)  ((xl + xu) / 2, (yl + yu) / 2)  (xu, yu)
 swSq ((xl, yl), (xu, yu)) = (,)  (xl, yl)  ((xl + xu) / 2, (yl + yu) / 2)
@@ -80,9 +79,9 @@ isSEchild _                 = False
 -- |Builds a quadtree of a list of points which recursively divides up 2D
 -- space into quadrants, so that every leaf-quadrant stores either zero or one
 -- point.
-quadTree :: [P2]                                 -- ^ the points to divide
+quadTree :: [PT]        -- ^ the points to divide
-         -> ((Double, Double), (Double, Double)) -- ^ the initial square around the points
+         -> Square      -- ^ the initial square around the points
-         -> QuadTree P2                          -- ^ the quad tree
+         -> QuadTree PT -- ^ the quad tree
 quadTree []   _ = TNil
 quadTree [pt] _ = TLeaf pt
 quadTree pts sq = TNode (quadTree nWPT . nwSq $ sq) (quadTree nEPT . neSq $ sq)
@@ -96,9 +95,9 @@ quadTree pts sq = TNode (quadTree nWPT . nwSq $ sq) (quadTree nEPT . neSq $ sq)
 
 
 -- |Get all squares of a quad tree.
-quadTreeSquares :: ((Double, Double), (Double, Double))  -- ^ the initial square around the points
+quadTreeSquares :: Square      -- ^ the initial square around the points
-                -> QuadTree P2                            -- ^ the quad tree
+                -> QuadTree PT -- ^ the quad tree
-                -> [((Double, Double), (Double, Double))] -- ^ all squares of the quad tree
+                -> [Square]    -- ^ all squares of the quad tree
 quadTreeSquares sq (TNil)              = [sq]
 quadTreeSquares sq (TLeaf _)           = [sq]
 quadTreeSquares sq (TNode nw ne sw se) =
@@ -108,9 +107,7 @@ quadTreeSquares sq (TNode nw ne sw se) =
 
 -- |Get the current square of the zipper, relative to the given top
 -- square.
-getSquareByZipper :: ((Double, Double), (Double, Double)) -- ^ top square
+getSquareByZipper :: Square -> QTZipper a -> Square
-                  -> QTZipper a
-                  -> ((Double, Double), (Double, Double)) -- ^ current square
 getSquareByZipper sq z = go sq (reverse . snd $ z)
   where
     go sq' []              = sq'
@@ -203,7 +200,7 @@ lookupByNeighbors :: [Orient] -> QTZipper a -> Maybe (QTZipper a)
 lookupByNeighbors = flip (foldlM (flip findNeighbor))
 
 
-quadTreeToRoseTree :: QTZipper P2 -> Tree String
+quadTreeToRoseTree :: QTZipper PT -> Tree String
 quadTreeToRoseTree z' = go (rootNode z')
   where
     go z = case z of

Graphics/Diagram/AlgoDiags.hs

@@ -2,6 +2,7 @@
 
 module Graphics.Diagram.AlgoDiags where
 
+import Algebra.Vector(PT,Square)
 import Algorithms.GrahamScan
 import Algorithms.QuadTree
 import Algorithms.KDTree
@@ -123,9 +124,7 @@ kdSquares = Diag f
       where
         -- Gets all lines that make up the kdSquares. Every line is
         -- described by two points, start and end respectively.
-        kdLines :: KDTree P2
+        kdLines :: KDTree PT -> Square -> [(PT, PT)]
-                -> ((Double, Double), (Double, Double)) -- ^ square
-                -> [(P2, P2)]
         kdLines (KTNode ln pt Horizontal rn) ((xmin, ymin), (xmax, ymax)) =
           (\(x, _) -> [(p2 (x, ymin), p2 (x, ymax))])
             (unp2 pt)
@@ -180,7 +179,7 @@ kdTreeDiag = Diag f
 
 
 -- |Get the quad tree corresponding to the given points and diagram properties.
-qt :: [P2] -> DiagProp -> QuadTree P2
+qt :: [PT] -> DiagProp -> QuadTree PT
 qt vt p = quadTree vt (diagDimSquare p)
 
 
@@ -193,9 +192,7 @@ quadPathSquare = Diag f
       (uncurry rectByDiagonal # lw thin # lc red)
       (getSquare (stringToQuads (quadPath p)) (qt (mconcat vts) p, []))
       where
-        getSquare :: [Either Quad Orient]
+        getSquare :: [Either Quad Orient] -> QTZipper PT -> Square
-                  -> QTZipper P2
-                  -> ((Double, Double), (Double, Double))
         getSquare [] z = getSquareByZipper (diagDimSquare p) z
         getSquare (q:qs) z = case q of
           Right x -> getSquare qs (fromMaybe z (findNeighbor x z))
@@ -211,9 +208,7 @@ gifQuadPath = GifDiag f
       (uncurry rectByDiagonal # lw thick # lc col)
       <$> getSquares (stringToQuads (quadPath p)) (qt vt p, [])
       where
-        getSquares :: [Either Quad Orient]
+        getSquares :: [Either Quad Orient] -> QTZipper PT -> [Square]
-                   -> QTZipper P2
-                   -> [((Double, Double), (Double, Double))]
         getSquares [] z = [getSquareByZipper (diagDimSquare p) z]
         getSquares (q:qs) z = case q of
           Right x -> getSquareByZipper (diagDimSquare p) z :
@@ -233,7 +228,7 @@ treePretty = Diag f
                       . quadPath
                       $ p)
       where
-        getCurQT :: [Either Quad Orient] -> QTZipper P2 -> QTZipper P2
+        getCurQT :: [Either Quad Orient] -> QTZipper PT -> QTZipper PT
         getCurQT [] z = z
         getCurQT (q:qs) z = case q of
           Right x -> getCurQT qs (fromMaybe z (findNeighbor x z))

Graphics/Diagram/Core.hs

@@ -15,15 +15,15 @@ data Diag =
   Diag
   {
     mkDiag :: DiagProp
-           -> [[P2]]
+           -> [[PT]]
            -> Diagram Cairo R2
   }
   | GifDiag
   {
     mkGifDiag :: DiagProp
               -> Colour Double
-              -> ([P2] -> [[P2]])
+              -> ([PT] -> [[PT]])
-              -> [P2]
+              -> [PT]
               -> [Diagram Cairo R2]
   }
   | EmptyDiag (Diagram Cairo R2)
@@ -49,7 +49,7 @@ data DiagProp = MkProp {
   -- |The path to a quad in the quad tree.
   quadPath :: String,
   -- |The square for the kd-tree range search.
-  rangeSquare :: ((Double, Double), (Double, Double))
+  rangeSquare :: Square
 }
 
 
@@ -134,19 +134,19 @@ maybeDiag b d
   | otherwise = mempty
 
 
-filterValidPT :: DiagProp -> [P2] -> [P2]
+filterValidPT :: DiagProp -> [PT] -> [PT]
 filterValidPT =
   filter
   . inRange
   . diagDimSquare
 
 
-diagDimSquare :: DiagProp -> ((Double, Double), (Double, Double))
+diagDimSquare :: DiagProp -> Square
 diagDimSquare p = dimToSquare (xDimension p) $ yDimension p
 
 
 -- |Draw a list of points.
-drawP :: [P2]              -- ^ the points to draw
+drawP :: [PT]              -- ^ the points to draw
       -> Double            -- ^ dot size
       -> Diagram Cairo R2  -- ^ the resulting diagram
 drawP [] _  = mempty
@@ -172,7 +172,7 @@ rectByDiagonal (xmin, ymin) (xmax, ymax) =
 
 -- |Creates a Diagram from a point that shows the coordinates
 -- in text format, such as "(1.0, 2.0)".
-pointToTextCoord :: P2 -> Diagram Cairo R2
+pointToTextCoord :: PT -> Diagram Cairo R2
 pointToTextCoord pt =
   text ("(" ++ (show . trim') x ++ ", " ++ (show . trim') y ++ ")") # scale 10
   where

Graphics/Diagram/Gtk.hs

@@ -2,6 +2,7 @@
 
 module Graphics.Diagram.Gtk where
 
+import Algebra.Vector(PT)
 import qualified Data.ByteString.Char8 as B
 import Data.List(find)
 import Diagrams.Backend.Cairo
@@ -45,7 +46,7 @@ diagTreAlgos =
 
 
 -- |Create the Diagram from the points.
-diag :: DiagProp -> [DiagAlgo] -> [[P2]] -> Diagram Cairo R2
+diag :: DiagProp -> [DiagAlgo] -> [[PT]] -> Diagram Cairo R2
 diag p das vts = maybe mempty (\x -> mkDiag x p vts)
                   $ mconcat
                       -- get the actual [Diag] array

Parser/Meshparser.hs

@@ -2,6 +2,7 @@
 
 module Parser.Meshparser where
 
+import Algebra.Vector(PT)
 import Control.Applicative
 import Data.Attoparsec.ByteString.Char8
 import Data.Either
@@ -11,7 +12,7 @@ import Diagrams.TwoD.Types
 
 -- |Convert a text String with multiple vertices and faces into
 -- a list of vertices, ordered by the faces specification.
-meshFaceVertices :: B.ByteString -> [[P2]]
+meshFaceVertices :: B.ByteString -> [[PT]]
 meshFaceVertices str = fmap (fmap (\y -> meshVertices str !! (y - 1)))
                             (meshFaces str)
 
@@ -19,7 +20,7 @@ meshFaceVertices str = fmap (fmap (\y -> meshVertices str !! (y - 1)))
 -- |Convert a text String with multiple vertices into
 -- an array of float tuples.
 meshVertices :: B.ByteString -- ^ the string to convert
-          -> [P2]         -- ^ the resulting vertice table
+          -> [PT]         -- ^ the resulting vertice table
 meshVertices
   = fmap p2
     . rights

Test/Vector.hs

@@ -82,40 +82,40 @@ instance Arbitrary P2 where
 
 -- the point describing the lower left corner of the square
 -- must be part of the square
-inRangeProp1 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp1 :: Square -> Bool
 inRangeProp1 sq@((x1, y1), _) =
   inRange sq (p2 (x1, y1))
 
 
 -- the point describing the upper right corner of the square
 -- must be part of the square
-inRangeProp2 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp2 :: Square -> Bool
 inRangeProp2 sq@(_, (x2, y2)) =
   inRange sq (p2 (x2, y2))
 
 
 -- the point describing the upper left corner of the square
 -- must be part of the square
-inRangeProp3 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp3 :: Square -> Bool
 inRangeProp3 sq@((x1, _), (_, y2)) =
   inRange sq (p2 (x1, y2))
 
 
 -- the point describing the lower right corner of the square
 -- must be part of the square
-inRangeProp4 :: ((Double, Double), (Double, Double)) -> Bool
+inRangeProp4 :: Square -> Bool
 inRangeProp4 sq@((_, y1), (x2, _)) =
   inRange sq (p2 (x2, y1))
 
 
 -- generating random points within the square
-inRangeProp5 :: ((Double, Double), (Double, Double)) -> Positive Double -> Positive Double -> Bool
+inRangeProp5 :: Square -> Positive Double -> Positive Double -> Bool
 inRangeProp5 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
   inRange sq (p2 (x1 + ((x2 - x1) / (a + 1)), y1 + ((y2 - y1) / (b + 1))))
 
 
 -- generating random points outside of the square
-inRangeProp6 :: ((Double, Double), (Double, Double)) -> Positive Double -> Positive Double -> Bool
+inRangeProp6 :: Square -> Positive Double -> Positive Double -> Bool
 inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
   (not . inRange sq $ p2 (max x1 x2 + (a + 1), max y1 y2 + (b + 1)))
   && (not . inRange sq $ p2 (max x1 x2 + (a + 1), max y1 y2 - (b + 1)))
@@ -126,51 +126,51 @@ inRangeProp6 sq@((x1, y1), (x2, y2)) (Positive a) (Positive b) =
 
 
 -- apply id function on the point
-onPTProp1 :: P2 -> Bool
+onPTProp1 :: PT -> Bool
 onPTProp1 pt = onPT id pt == pt
 
 
 -- add a random value to the point coordinates
-onPTProp2 :: P2 -> Positive R2 -> Bool
+onPTProp2 :: PT -> Positive R2 -> Bool
 onPTProp2 pt (Positive (R2 rx ry))
   = onPT (\(x, y) -> (x + rx, y + ry)) pt /= pt
 
 
 -- angle between two vectors both on the x-axis must be 0
-getAngleProp1 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp1 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp1 (Positive (R2 x1 _)) (Positive (R2 x2 _))
   = getAngle (R2 x1 0) (R2 x2 0) == 0
 
 
 -- angle between two vectors both on the y-axis must be 0
-getAngleProp2 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp2 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp2 (Positive (R2 _ y1)) (Positive (R2 _ y2))
   = getAngle (R2 0 y1) (R2 0 y2) == 0
 
 
 -- angle between two vectors both on the x-axis but with opposite direction
 -- must be pi
-getAngleProp3 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp3 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp3 (Positive (R2 x1 _)) (Positive (R2 x2 _))
   = getAngle (R2 (negate x1) 0) (R2 x2 0) == pi
 
 
 -- angle between two vectors both on the y-axis but with opposite direction
 -- must be pi
-getAngleProp4 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp4 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp4 (Positive (R2 _ y1)) (Positive (R2 _ y2))
   = getAngle (R2 0 (negate y1)) (R2 0 y2) == pi
 
 
 -- angle between vector in x-axis direction and y-axis direction must be
 -- p/2
-getAngleProp5 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp5 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
   = getAngle (R2 x1 0) (R2 0 y2) == pi / 2
 
 
 -- commutative
-getAngleProp6 :: Positive R2 -> Positive R2 -> Bool
+getAngleProp6 :: Positive Vec -> Positive Vec -> Bool
 getAngleProp6 (Positive v1) (Positive v2)
   = getAngle v1 v2 == getAngle v2 v1
 
@@ -183,7 +183,7 @@ getAngleProp7 (PosRoundR2 v)
 
 
 -- commutative
-scalarProdProp1 :: R2 -> R2 -> Bool
+scalarProdProp1 :: Vec -> Vec -> Bool
 scalarProdProp1 v1 v2 = v1 `scalarProd` v2 == v2 `scalarProd` v1
 
 
@@ -212,7 +212,7 @@ scalarProdProp4 (RoundDouble s1) (RoundDouble s2) (RoundR2 v1) (RoundR2 v2)
 
 
 -- orthogonal
-scalarProdProp5 :: Positive R2 -> Positive R2 -> Bool
+scalarProdProp5 :: Positive Vec -> Positive Vec -> Bool
 scalarProdProp5 (Positive (R2 x1 _)) (Positive (R2 _ y2))
   = scalarProd (R2 x1 0) (R2 0 y2) == 0
 
@@ -226,40 +226,40 @@ dimToSquareProp1 (x1, x2) (y1, y2) =
 -- multiply scalar with result of vecLength or with the vector itself...
 -- both results must be the same. We can't check against 0
 -- because of sqrt in vecLength.
-vecLengthProp1 :: PosRoundDouble -> R2 -> Bool
+vecLengthProp1 :: PosRoundDouble -> Vec -> Bool
 vecLengthProp1 (PosRoundDouble r) v
   = abs (vecLength v * r - vecLength (scalarMul r v)) < 0.0001
 
 
 -- convert to vector and back again
-pt2VecProp1 :: P2 -> Bool
+pt2VecProp1 :: PT -> Bool
 pt2VecProp1 pt = (vec2Pt . pt2Vec $ pt) == pt
 
 
 -- unbox coordinates and check if equal
-pt2VecProp2 :: P2 -> Bool
+pt2VecProp2 :: PT -> Bool
 pt2VecProp2 pt = (unr2 . pt2Vec $ pt) == unp2 pt
 
 
 -- convert to point and back again
-vec2PtProp1 :: R2 -> Bool
+vec2PtProp1 :: Vec -> Bool
 vec2PtProp1 v = (pt2Vec . vec2Pt $ v) == v
 
 
 -- unbox coordinates and check if equal
-vec2PtProp2 :: R2 -> Bool
+vec2PtProp2 :: Vec -> Bool
 vec2PtProp2 v = (unp2 . vec2Pt $ v) == unr2 v
 
 
 -- vector from a to b must not be the same as b to a
-vp2Prop1 :: P2 -> P2 -> Bool
+vp2Prop1 :: PT -> PT -> Bool
 vp2Prop1 p1' p2'
   | p1' == origin && p2' == origin = True
   | otherwise = vp2 p1' p2' /= vp2 p2' p1'
 
 
 -- negating vector from a to be must be the same as vector b to a
-vp2Prop2 :: P2 -> P2 -> Bool
+vp2Prop2 :: PT -> PT -> Bool
 vp2Prop2 p1' p2'
   | p1' == origin && p2' == origin = True
   | otherwise = vp2 p1' p2' == (\(R2 x y) -> negate x ^& negate y)
@@ -270,5 +270,5 @@ vp2Prop2 p1' p2'
 
 
 -- determinant of the 3 same points is always 0
-detProp1 :: P2 -> Bool
+detProp1 :: PT -> Bool
 detProp1 pt' = det pt' pt' pt' == 0