packages feed

geom2d (empty) → 0.1.0.1

raw patch · 21 files changed

+2031/−0 lines, 21 filesdep +QuickCheckdep +basedep +ieee754setup-changed

Dependencies added: QuickCheck, base, ieee754

Files

+ Geom2d.hs view
@@ -0,0 +1,17 @@+module Geom2d+  ( module Geom2d.Point+  , module Geom2d.Line+  , module Geom2d.Shape+  , module Geom2d.Intersect+  , module Geom2d.Distance+  , module Geom2d.Translate+  , module Geom2d.Rotation+  ) where++import Geom2d.Point+import Geom2d.Line+import Geom2d.Shape+import Geom2d.Intersect+import Geom2d.Distance+import Geom2d.Translate+import Geom2d.Rotation
+ Geom2d/Distance.hs view
@@ -0,0 +1,12 @@+{-# LANGUAGE MultiParamTypeClasses #-}++module Geom2d.Distance where++import Geom2d.Point.Internal++class Distance p q where+  distance :: (Ord a, Floating a) => p a -> q a -> a++instance Distance Point' Point' where+  distance (Point' (a1,a2)) (Point' (b1,b2)) =+    sqrt $ (a1 - b1)^(2::Int) + (a2 - b2)^(2::Int)
+ Geom2d/Intersect.hs view
@@ -0,0 +1,71 @@+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}++module Geom2d.Intersect++where++import Geom2d.Point+import Geom2d.Line+import Geom2d.Line.Internal++class Intersect a b where+  intersect :: a -> b -> Bool++instance (Eq a) => Intersect (Point' a) (Point' a) where+  intersect p q = p == q++instance (Eq (p a), Num (p a), Num a, RealFloat a, Point p) =>+         Intersect (InfLine p a) (InfLine p a) where+  intersect a b | a == b = True+                | a `parallel` b = False+                | otherwise = True++instance (Point p, Eq a, Fractional a) =>+         Intersect (InfLine p a) (p a) where+  intersect line@(InfLine a _) q =+    maybe+    ( x a == x q )+    ( \f -> f (x q) == y q )+    ( lineF line )++instance (Point p, Eq a, Fractional a) =>+         Intersect (p a) (InfLine p a) where+  intersect = flip intersect++instance (Eq (p a), Point p, Num (p a), RealFloat a) =>+         Intersect (FinLine p a) (FinLine p a) where+  intersect (FinLine a1 b1) (FinLine a2 b2) =+    case intersection (InfLine a1 b1) (InfLine a2 b2) of+      Nothing -> False+      Just p ->+        let minx = max (min (x a1) (x b1)) (min (x a2) (x b2))+            maxx = min (max (x a1) (x b1)) (max (x a2) (x b2))+            miny = max (min (y a1) (y b1)) (min (y a2) (y b2))+            maxy = min (max (y a1) (y b1)) (max (y a2) (y b2))+        in and [ x p <= maxx+               , x p >= minx+               , y p <= maxy+               , y p >= miny+               ]++instance (Eq (p a), Point p, Num (p a), RealFloat a) =>+         Intersect (InfLine p a) (FinLine p a) where+  intersect infLine (FinLine f1 f2) =+    case intersection infLine (InfLine f1 f2) of+      Nothing -> False+      Just p ->+        let minx = min (x f1) (x f2)+            maxx = max (x f1) (x f2)+            miny = min (y f1) (y f2)+            maxy = max (y f1) (y f2)+        in and [ x p <= maxx+               , x p >= minx+               , y p <= maxy+               , y p >= miny+               ]++instance (Eq (p a), Point p, Num (p a), RealFloat a) =>+         Intersect (FinLine p a) (InfLine p a) where+  intersect = flip intersect
+ Geom2d/Line.hs view
@@ -0,0 +1,101 @@+-- | This module describes what lines are defines functions to work+-- with lines.+module Geom2d.Line+    ( -- * Infinite lines+      InfLine+    , mkInfLine+    , lineF+    , parallel+    , slope+    , root+    , intersection+    -- * Finite lines+    , FinLine+    , mkFinLine+    , lineLength+    )++where++import Geom2d.Point+import Geom2d.Line.Internal++-- | Construct an infinit line by specifiying two points.  We won't+-- get a line when the given points are equal.+mkInfLine :: (Eq (p a)) => p a -> p a -> Maybe (InfLine p a)+mkInfLine a b+    | a == b = Nothing+    | otherwise = Just $ InfLine a b++-- | Get a function describing the line.  We won't get a function if+-- the line is vertical.+lineF :: (Eq a, Fractional a, Point p) =>+         InfLine p a -> Maybe (a -> a)+lineF l@(InfLine p _) =+    ( \m -> case root l of+        Just x0 -> \arg -> m * (arg - x0)+        Nothing -> const (y p) ) <$>+    slope l++-- | Check if two lines are paralllel to each other.  This function+-- assumes lines parallel to themselves.+parallel :: (Num a, Num (p a), Point p, Eq a) =>+            InfLine p a -> InfLine p a -> Bool+parallel (InfLine a b) (InfLine p q) = (b - a) `cross` (q - p) == 0++-- | Calculate the slope of a line.  We won't get a value for the+-- slope if, and only if, the line is vertical.+slope :: (Fractional a, Point p, Eq a) =>+         InfLine p a -> Maybe a+slope (InfLine p q)+  | x p == x q = Nothing+  | otherwise = Just $ (y q - y p) / (x q - x p)++-- | Calculate the point where a line meets the x-axis.  We won't get+-- a value if, and only if the line is parallel to the x-axis.+root :: (Eq a, Fractional a, Point p) =>+        InfLine p a -> Maybe a+root l@(InfLine p _) =+  case slope l of+    Nothing -> Just $ x p+    Just m ->+      if m == 0+      then Nothing+      else Just $ x p - (y p * m)++-- | Calculate the point where two lines intersect.+intersection :: (Eq (p a), Num (p a), RealFloat a, Point p) =>+                InfLine p a -> InfLine p a -> Maybe (p a)+intersection l1@(InfLine a1 _) l2@(InfLine b1 _)+  | l1 == l2 = Nothing+  | l1 `parallel` l2 = Nothing+  | otherwise =+      case slope l1 of+        Nothing -> do+          x0 <- root l1+          f <- lineF l2+          return (fromCoords x0 (f x0))+        Just ma ->+          case slope l2 of+            Nothing -> do+              x0 <- root l2+              f <- lineF l1+              return (fromCoords x0 (f x0))+            Just mb -> do+              let na = y a1 - ma * x a1+                  nb = y b1 - mb * x b1+                  safeDiv num denom | denom == 0 = Nothing+                                    | otherwise = Just (num/denom)+              x' <- (nb - na) `safeDiv` (ma - mb)+              f <- lineF l1+              return (fromCoords x' (f x'))++-- | mkFinLine returns a valid finite line, if any.+mkFinLine :: (Eq (p a)) => p a -> p a -> Maybe (FinLine p a)+mkFinLine a b+  | a == b = Nothing+  | otherwise = Just (FinLine a b)++-- | Get the length of a finite line.+lineLength :: (Point p, Num (p a), Floating a) => FinLine p a -> a+lineLength (FinLine a b) = magnitude (b - a)
+ Geom2d/Line/Internal.hs view
@@ -0,0 +1,111 @@+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE MultiParamTypeClasses #-}++-- | This module defines the internals of a line.  You probably won't+-- need this module when using the geomtry libary.++module Geom2d.Line.Internal where++import Test.QuickCheck+import Data.Maybe+import Data.AEq+import Geom2d.Point+import Geom2d.Translate+import Geom2d.Distance+import Control.Monad++-- | This type modells a infinite line.+data InfLine p a = InfLine (p a) (p a) deriving (Show, Read)++-- | `InfLine` is a `Functor` where the function is mapped over both+-- points which define the `InfLine`.+instance Functor p => Functor (InfLine p) where+  fmap f (InfLine a b) = InfLine (fmap f a) (fmap f b)++-- | This `Arbitrary` instance should only produce valid `InfLine`s.+instance (Eq (p a), Arbitrary (p a)) => Arbitrary (InfLine p a) where+  arbitrary = do p1 <- arbitrary+                 p2 <- arbitrary `suchThat` (/= p1)+                 return $ InfLine p1 p2++-- | Two lines are equal when they have the same root and the same+-- slope.  If the two lines do not have a root, that means that the+-- lines are parallel to the x-axis.  In this case we compare their+-- y-value.+instance (Eq (p a), Eq a, RealFloat a, Num (p a), Point p) =>+         Eq (InfLine p a) where+  a@(InfLine a1 _) == b@(InfLine b1 _)+      -- If the slopes of the lines are not equal they cannot be the+      -- equal themselves+      | slope a /= slope b = False+      -- When the slopes are vertical they should have the same x+      -- component+      | isNothing (slope a) = x a1 == x b1+      | otherwise = case root a of+                      Just _ -> fromMaybe False ( (==) <$> root a <*> root b )+                      Nothing -> y a1 == y b1+      where slope (InfLine m n) | x (n - m) == 0 = Nothing+                                | otherwise = Just $ y (n - m) / x (n - m)+            root l@(InfLine p q) | y p == y q = Nothing+                                 | otherwise = +                                     (do dy <- slope l+                                         return (x q - (y q / dy))) `mplus`+                                     Just (x p)++-- | Translate a line by a given vector.+instance Translate p => Translate (InfLine p) where+  translate m (InfLine p q) = InfLine (m `translate` p) (m `translate` q)++-- | Modells a finite line stretching between two points.+data FinLine p a = -- | We expect the two points to be different+                   FinLine (p a) (p a) deriving (Show,Read)++-- | Two lines are equal if their end points are equal.+--+-- prop> FinLine a b == FinLine b a+instance (Eq (p a)) => Eq (FinLine p a) where+  (FinLine a1 b1) == (FinLine a2 b2) =+    (a1 == a2 && b1 == b2) ||+    (a1 == b2 && b1 == a2)++-- | This `Arbitrary` instance should only produce valid `FinLine`s.+instance (Eq (p a), Arbitrary (p a)) => Arbitrary (FinLine p a) where+  arbitrary = do p1 <- arbitrary+                 p2 <- arbitrary `suchThat` (/= p1)+                 return $ FinLine p1 p2++-- | Translate a `FinLine` by a fiven vector+instance Translate p => Translate (FinLine p) where+  translate v (FinLine p q) = FinLine (v `translate` p) (v `translate` q)++-- | Two lines are almost equal if their ending points are almost+-- equal.+instance AEq (p a) => AEq (FinLine p a) where+  (FinLine a1 b1) ~== (FinLine a2 b2) =+    (a1 ~== a2 && b1 ~== b2) ||+    (a1 ~== b2 && b1 ~== a2)++instance (Point p) =>+         Distance (FinLine p) p where+  distance (FinLine a b) p =+    sqrt (dx*dx + dy*dy)+    where dx = ax + (u * qx) - px+          dy = ay + (u * qy) - py+          qx = bx - ax+          qy = by - ay+          s = qx^(2::Int) + qy^(2::Int)+          u' = ((px - ax)*qx + (py - ay)*qy)/s+          u | u' > 1    = 1+            | u' < 0    = 0+            | otherwise = u'+          py = y p+          px = x p+          ax = x a+          ay = y a+          bx = x b+          by = y b++instance (Point p) =>+         Distance p (FinLine p) where+  distance = flip distance
+ Geom2d/Point.hs view
@@ -0,0 +1,62 @@+module Geom2d.Point+    ( Point (..)+    , Point'+    , Triangle+    , Scale (..)+    , normalize+    , magnitude+    , dot+    , cross+    , triArea+    , pointInTriangle+    )++where++import Geom2d.Point.Internal++type Triangle p = (p,p,p)++infixl 7 `dot`,`cross`++dot :: (Num a, Point p) => p a -> p a -> a+dot a b = x a * x b + y a * y b++cross :: (Num a, Point p) => p a -> p a -> a+cross a b = x a * y b - y a * x b++triArea :: (Point p, Num (p a), Fractional a) => Triangle (p a) -> a+triArea (a,b,c) = abs $ ((b - a) `cross` (c - a)) / 2++pointInTriangle :: (Eq (p a), Num (p a), Fractional a, Point p, Ord a) =>+                   Triangle (p a) -> p a -> Bool+pointInTriangle (a,b,c) p+    -- barycentric coordinates+    | b == a || c == a || b == c = False+    | p == a = True+    | otherwise = u >= 0 && v >= 0 && u + v <= 1+    where+      u = ( v1Square * v2v0 - v1v0 * v2v1 ) / denom+      v = ( v0Square * v2v1 - v0v1 * v2v0 ) / denom+      denom = v0Square * v1Square - v0v1 * v1v0+      v1Square = v1 `dot` v1+      v0Square = v0 `dot` v0+      v1v0 = v1 `dot` v0+      v0v1 = v0 `dot` v1+      v2v0 = v2 `dot` v0+      v2v1 = v2 `dot` v1+      v0 = c-a+      v1 = b-a+      v2 = p-a++class Scale p where+  scale :: (Num a) => a -> p a -> p a++instance Scale Point' where+  scale s (Point' (a,b)) = Point' (a * s, b * s)++-- | Normalizes a scaleable point to length 1.+normalize :: (Scale p, Point p, Fractional a, Eq a, Floating a) =>+             p a -> Maybe (p a)+normalize v | magnitude v == 0 = Nothing+            | otherwise = Just $ scale (1/magnitude v) v
+ Geom2d/Point/Internal.hs view
@@ -0,0 +1,62 @@+module Geom2d.Point.Internal+    ( Point' (..)+    , Point (..)+    , magnitude+    )++where++import Data.AEq+import Data.Fixed+import Geom2d.Rotation+import qualified Prelude ((^))+import Prelude hiding ((^))+import Test.QuickCheck++(^) :: Num a => a -> Int -> a+(^) = (Prelude.^)++newtype Point' a = Point' (a,a) deriving (Show, Read, Eq)++class Point p where+  x :: p a -> a+  y :: p a -> a+  fromCoords :: a -> a -> p a++magnitude :: (Point p, Floating a, Num a) => p a -> a+magnitude p =+  sqrt (x p ^ (2::Int) + y p ^ (2::Int))++instance Point Point' where+  x (Point' p) = fst p+  y (Point' p) = snd p+  fromCoords a b = Point' (a, b)++instance (Eq a, Num a, Fractional a, RealFloat a) => Num (Point' a) where+  (Point' (p1,p2)) + (Point' (q1,q2)) = Point' (p1+q1, p2+q2)+  (Point' (p1,p2)) - (Point' (q1,q2)) = Point' (p1-q1, p2-q2)+  (Point' (m,n)) * (Point' (p,q)) = Point' (m*p - n*q, m*q + n*p)+  abs (Point' (m,n)) = Point' (sqrt (m^2 + n^2), 0)+  signum p@(Point' (m,n))+      | m == fromIntegral (0::Int) && n == fromIntegral (0::Int) =+          Point' (m,n)+      | otherwise = Point' (m*l,n*l)+      where l = 1 / x (abs p)+  fromInteger n = Point' (fromInteger n, 0)+  negate (Point' (a,b)) = Point' (negate a, negate b)++instance (Arbitrary a) => Arbitrary (Point' a) where+  arbitrary = curry Point' <$> arbitrary <*> arbitrary++instance (Num a, AEq a, RealFloat a) => AEq (Point' a) where+  (Point' (m,n)) ~== (Point' (p,q)) =+    m^2 + n^2 ~== p^2 + q^2 &&+    atan2 n m ~== atan2 q p++instance Functor Point' where+  fmap f (Point' (a,b)) = Point' (f a, f b)++instance Rotation Point' where+  angle p | magnitude p == 0 = Nothing+          | otherwise = Just $ atan2 (y p) (x p)+  rotate r (Point' (a,b)) = Point' (a * cos r - b * sin r, a * sin r + b * cos r)
+ Geom2d/Rotation.hs view
@@ -0,0 +1,25 @@+module Geom2d.Rotation++where++-- | Modells data that has an angle and can be rotated.  +class Rotation p where+  -- | An object can return the orientation in space.  If the object+  -- returns its orientation it should hold the following law:+  --+  -- prop> fromMaybe True $ (==) <$> angle (r `rotate` x) <*> ((subtract pi).((`mod'` (2*pi)).(+pi).(+r)) <$> angle x)+  --+  -- Also angle should never return a value bigger than `pi` and+  -- smaller than `- pi`+  --+  -- prop> fromMaybe True (fmap (\a -> a >= (- pi) && a <= pi) (angle x))+  --+  -- The default implementation is+  -- +  -- @+  -- angle _ = Nothing+  -- @+  angle :: (Floating a, RealFloat a, Ord a) => p a -> Maybe a+  angle _ = Nothing+  -- | Should rotate an object by a given angle.+  rotate :: (Floating a) => a -> p a -> p a
+ Geom2d/Shape.hs view
@@ -0,0 +1,19 @@+module Geom2d.Shape+    ( Shape+    , circle+    , rectangle+    )++where++import Geom2d.Point+import Geom2d.Rotation+import Geom2d.Shape.Internal+import Geom2d.Translate++circle :: Num a => p a -> a -> Shape p a+circle m r = ShapeCircle $ mkCircleInt m r++rectangle :: (Translate p, Eq a, RealFloat a, Point p, Rotation p) =>+             p a -> a -> a -> Maybe (Shape p a)+rectangle m a b = ShapePolygon <$> rectangleInt m a b
+ Geom2d/Shape/Internal.hs view
@@ -0,0 +1,214 @@+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE FlexibleContexts #-}+{-# LANGUAGE ScopedTypeVariables #-}++module Geom2d.Shape.Internal+    ( Circle (..)+    , mkCircleInt+    , radius+    , center+    , Polygon (..)+    , convexHull'+    , rectangleInt+    , Shape (..)+    )++       where++import Data.Function+import Data.List hiding (intersect)+import Data.Maybe+import Geom2d.Distance+import Geom2d.Intersect+import Geom2d.Line.Internal+import Geom2d.Point+import Geom2d.Point.Internal+import Geom2d.Rotation+import Geom2d.Translate+import Test.QuickCheck++data Circle p a = Circle (p a) a deriving (Show,Read,Eq)++instance (Point p, Distance p p) => Distance (Circle p) p where+  distance (Circle m r) p =+    max (distance m p - r) 0++instance (Point p, Distance p p) => Distance p (Circle p) where+  distance = flip distance++instance (Floating a, Ord a, Distance p p) =>+         Intersect (Circle p a) (p a) where+  intersect (Circle m r) p+    | distance m p <= r = True+    | otherwise = False++instance (Floating a, Ord a, Distance p p) =>+         Intersect (p a) (Circle p a) where+  intersect = flip intersect++instance (Floating a, Ord a, Distance p p) =>+         Intersect (Circle p a) (Circle p a) where+  intersect (Circle m1 r1) (Circle m2 r2) =+    distance m1 m2 <= r1 + r2++instance (Arbitrary a, Arbitrary (p a), Ord a, Num a) =>+         Arbitrary (Circle p a) where+  arbitrary = Circle <$> arbitrary <*>+              (arbitrary `suchThat`(>0))++instance (Rotation p, Point p) => Rotation (Circle p) where+  angle (Circle m _) = angle m+  rotate ang (Circle m r) = Circle (rotate ang m) r++mkCircleInt :: (Num a) => p a -> a -> Circle p a+mkCircleInt m r' = Circle m (abs r')++radius :: Circle p a -> a+radius (Circle _ r) = r++center :: Circle p a -> p a+center (Circle m _) = m++-- | A Polygon is meant to describe a convex 2-dimensional shape.+data Polygon p a =  -- | The point (first argument) should be inside+                    -- the polygon, otherwise weird stuff will happen.+                    -- Also you must not specify the same vector+                    -- (second argument) twice.+                   Polygon (p a) [p a]+                   deriving (Show,Read,Eq)++instance (Point p, Fractional a, Num (p a), Eq (p a), Ord a) =>+         Intersect (p a) (Polygon p a) where+  intersect p (Polygon m vs) =+    any (`pointInTriangle` p) triangles+    where triangles = map (\(a,b) -> (m,a,b))+                      ( zip verteces (tail verteces ++ [head verteces]))+          verteces = map (+ m) vs++instance (Point p, Fractional a, Num (p a), Eq (p a), Ord a) =>+         Intersect (Polygon p a) (p a) where+  intersect = flip intersect++instance ( Arbitrary (p a), Num (p a), RealFloat a, Point p, Scale p+         , Eq (p a)) =>+         Arbitrary (Polygon p a) where+  arbitrary = do+    vs' <- listOf1 (arbitrary `suchThat` (\a -> magnitude a > 0)) `suchThat`+           ((>= 4).length)+    (return.fromJust.convexHull') vs'++instance (Eq (p a), Floating a, Num (p a), Ord a, Point p) =>+         Intersect (Polygon p a) (Circle p a) where+  intersect poly@(Polygon p vs') (Circle m r)+    | m `intersect` poly = True+    | otherwise =+          any ((r >=). distance m)+          verteces+    where verteces = zipWith FinLine+                     vs+                     (tail vs ++ [head vs])+          vs = map (p+) vs'++instance (Eq (p a), Num (p a), RealFloat a, Point p) =>+         Intersect (Polygon p a) (Polygon p a) where+  intersect poly1@(Polygon p1 vs1) poly2@(Polygon p2 vs2) =+    let verts1 = map (p1+) vs1+        verts2 = map (p2+) vs2+        edges1 = zipWith FinLine verts1 (tail verts1 ++ [head verts1])+        edges2 = zipWith FinLine verts2 (tail verts2 ++ [head verts2])+    in any (uncurry intersect)+       [ (v1,v2) | v1 <- edges1, v2 <- edges2 ] ||+       any (intersect poly2) verts1 ||+       any (intersect poly1) verts2++instance (Eq (p a), Floating a, Num (p a), Ord a, Point p) =>+         Intersect (Circle p a) (Polygon p a) where+  intersect = flip intersect++instance (Rotation p) => Rotation (Polygon p) where+  rotate r (Polygon m vs) = Polygon (rotate r m) (map (rotate r) vs)+  angle (Polygon m _) = angle m++-- | Calculate the convex hull of an arbitrary number of points.+convexHull' :: forall p a.+               (Num (p a), Fractional a, Ord a, Scale p, Point p) =>+               [p a] -> Maybe (Polygon p a)+convexHull' [] = Nothing+convexHull' [_] = Nothing+convexHull' [_,_] = Nothing+convexHull' ps = Just $+    Polygon middle (map (subtract middle) hull)+    where middle :: p a+          middle = (1 / (fromIntegral.length) hull) `scale`+                   sum hull+          hull :: [p a]+          hull = chain sortedPs+          chain :: [p a] -> [p a]+          chain xs = lower ++ upper+              where lower = go [] xs+                    upper = go [] (reverse xs)+          go :: [p a] -> [p a] -> [p a]+          go acc@(r1:r2:rs) (x:xs)+              | clockwise r2 r1 x = go (r2:rs) (x:xs)+              | otherwise = go (x:acc) xs+          go acc (x:xs) = go (x:acc) xs+          go acc [] = reverse $ tail acc+          sortedPs :: [p a]+          sortedPs = sortBy+                     (\p q ->+                         case compare (x p) (x q) of+                           EQ -> compare (y p) (y q)+                           c -> c+                     ) ps+          clockwise :: p a -> p a -> p a -> Bool+          clockwise o a b = (a - o) `cross` (b - o) <= 0++rectangleInt :: forall p a. (Point p, RealFloat a, Eq a, Translate p+                            , Rotation p) =>+             p a+          -> a -- ^ length of one side+          -> a -- ^ length of the other side+          -> Maybe (Polygon p a)+rectangleInt m a b+  | a == 0 || b == 0 = Nothing+  | otherwise =+      Just $+        Polygon+        m+        ( sortBy+          (compare `on` angle)+          [ fromCoords (negate a/2) (negate b/2) :: p a+          , fromCoords (a/2) (negate b/2) :: p a+          , fromCoords (a/2) (b/2) :: p a+          , fromCoords (negate a/2) (b/2) :: p a+          ]+        )++-- | `Shape` describes geometric shapes in the euklidean plain.+data Shape p a = ShapeCircle (Circle p a)+               | ShapePolygon (Polygon p a)+               deriving (Show,Read,Eq)++instance ( Ord a, Distance p p, Eq (p a)+         , Num (p a), Point p, RealFloat a) =>+         Intersect (Shape p a) (Shape p a) where+  intersect (ShapeCircle c) (ShapePolygon p) = c `intersect` p+  intersect (ShapePolygon p) (ShapeCircle c) = c `intersect` p+  intersect (ShapeCircle a) (ShapeCircle b) = a `intersect` b+  intersect (ShapePolygon a) (ShapePolygon b) = a `intersect` b++instance ( Floating a, Eq (p a), Num (p a), Ord a, Point p, Distance p p ) =>+         Intersect (Shape p a) (p a) where+  intersect (ShapeCircle c) p = c `intersect` p+  intersect (ShapePolygon c) p = c `intersect` p++instance ( Floating a, Eq (p a), Num (p a), Ord a, Point p, Distance p p ) =>+         Intersect (p a) (Shape p a) where+  intersect = flip intersect++instance (Rotation p, Point p) => Rotation (Shape p) where+  rotate a (ShapeCircle s) = ShapeCircle (rotate a s)+  rotate a (ShapePolygon s) = ShapePolygon (rotate a s)+  angle (ShapeCircle s) = angle s+  angle (ShapePolygon s) = angle s
+ Geom2d/Translate.hs view
@@ -0,0 +1,12 @@+module Geom2d.Translate++where++import Geom2d.Point+import Geom2d.Point.Internal+  +class Translate t where+  translate :: (Point p, Num a) => p a -> t a -> t a++instance Translate Point' where+  translate p (Point' (a,b)) = Point' (x p + a, y p + b)
+ LICENSE view
@@ -0,0 +1,674 @@+              GNU GENERAL PUBLIC LICENSE+                Version 3, 29 June 2007++ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>+ Everyone is permitted to copy and distribute verbatim copies+ of this license document, but changing it is not allowed.++                     Preamble++  The GNU General Public License is a free, copyleft license for+software and other kinds of works.++  The licenses for most software and other practical works are designed+to take away your freedom to share and change the works.  By contrast,+the GNU General Public License is intended to guarantee your freedom to+share and change all versions of a program--to make sure it remains free+software for all its users.  We, the Free Software Foundation, use the+GNU General Public License for most of our software; it applies also to+any other work released this way by its authors.  You can apply it to+your programs, too.++  When we speak of free software, we are referring to freedom, not+price.  Our General Public Licenses are designed to make sure that you+have the freedom to distribute copies of free software (and charge for+them if you wish), that you receive source code or can get it if you+want it, that you can change the software or use pieces of it in new+free programs, and that you know you can do these things.++  To protect your rights, we need to prevent others from denying you+these rights or asking you to surrender the rights.  Therefore, you have+certain responsibilities if you distribute copies of the software, or if+you modify it: responsibilities to respect the freedom of others.++  For example, if you distribute copies of such a program, whether+gratis or for a fee, you must pass on to the recipients the same+freedoms that you received.  You must make sure that they, too, receive+or can get the source code.  And you must show them these terms so they+know their rights.++  Developers that use the GNU GPL protect your rights with two steps:+(1) assert copyright on the software, and (2) offer you this License+giving you legal permission to copy, distribute and/or modify it.++  For the developers' and authors' protection, the GPL clearly explains+that there is no warranty for this free software.  For both users' and+authors' sake, the GPL requires that modified versions be marked as+changed, so that their problems will not be attributed erroneously to+authors of previous versions.++  Some devices are designed to deny users access to install or run+modified versions of the software inside them, although the manufacturer+can do so.  This is fundamentally incompatible with the aim of+protecting users' freedom to change the software.  The systematic+pattern of such abuse occurs in the area of products for individuals to+use, which is precisely where it is most unacceptable.  Therefore, we+have designed this version of the GPL to prohibit the practice for those+products.  If such problems arise substantially in other domains, we+stand ready to extend this provision to those domains in future versions+of the GPL, as needed to protect the freedom of users.++  Finally, every program is threatened constantly by software patents.+States should not allow patents to restrict development and use of+software on general-purpose computers, but in those that do, we wish to+avoid the special danger that patents applied to a free program could+make it effectively proprietary.  To prevent this, the GPL assures that+patents cannot be used to render the program non-free.++  The precise terms and conditions for copying, distribution and+modification follow.++                TERMS AND CONDITIONS++  0. Definitions.++  "This License" refers to version 3 of the GNU General Public License.++  "Copyright" also means copyright-like laws that apply to other kinds of+works, such as semiconductor masks.++  "The Program" refers to any copyrightable work licensed under this+License.  Each licensee is addressed as "you".  "Licensees" and+"recipients" may be individuals or organizations.++  To "modify" a work means to copy from or adapt all or part of the work+in a fashion requiring copyright permission, other than the making of an+exact copy.  The resulting work is called a "modified version" of the+earlier work or a work "based on" the earlier work.++  A "covered work" means either the unmodified Program or a work based+on the Program.++  To "propagate" a work means to do anything with it that, without+permission, would make you directly or secondarily liable for+infringement under applicable copyright law, except executing it on a+computer or modifying a private copy.  Propagation includes copying,+distribution (with or without modification), making available to the+public, and in some countries other activities as well.++  To "convey" a work means any kind of propagation that enables other+parties to make or receive copies.  Mere interaction with a user through+a computer network, with no transfer of a copy, is not conveying.++  An interactive user interface displays "Appropriate Legal Notices"+to the extent that it includes a convenient and prominently visible+feature that (1) displays an appropriate copyright notice, and (2)+tells the user that there is no warranty for the work (except to the+extent that warranties are provided), that licensees may convey the+work under this License, and how to view a copy of this License.  If+the interface presents a list of user commands or options, such as a+menu, a prominent item in the list meets this criterion.++  1. Source Code.++  The "source code" for a work means the preferred form of the work+for making modifications to it.  "Object code" means any non-source+form of a work.++  A "Standard Interface" means an interface that either is an official+standard defined by a recognized standards body, or, in the case of+interfaces specified for a particular programming language, one that+is widely used among developers working in that language.++  The "System Libraries" of an executable work include anything, other+than the work as a whole, that (a) is included in the normal form of+packaging a Major Component, but which is not part of that Major+Component, and (b) serves only to enable use of the work with that+Major Component, or to implement a Standard Interface for which an+implementation is available to the public in source code form.  A+"Major Component", in this context, means a major essential component+(kernel, window system, and so on) of the specific operating system+(if any) on which the executable work runs, or a compiler used to+produce the work, or an object code interpreter used to run it.++  The "Corresponding Source" for a work in object code form means all+the source code needed to generate, install, and (for an executable+work) run the object code and to modify the work, including scripts to+control those activities.  However, it does not include the work's+System Libraries, or general-purpose tools or generally available free+programs which are used unmodified in performing those activities but+which are not part of the work.  For example, Corresponding Source+includes interface definition files associated with source files for+the work, and the source code for shared libraries and dynamically+linked subprograms that the work is specifically designed to require,+such as by intimate data communication or control flow between those+subprograms and other parts of the work.++  The Corresponding Source need not include anything that users+can regenerate automatically from other parts of the Corresponding+Source.++  The Corresponding Source for a work in source code form is that+same work.++  2. Basic Permissions.++  All rights granted under this License are granted for the term of+copyright on the Program, and are irrevocable provided the stated+conditions are met.  This License explicitly affirms your unlimited+permission to run the unmodified Program.  The output from running a+covered work is covered by this License only if the output, given its+content, constitutes a covered work.  This License acknowledges your+rights of fair use or other equivalent, as provided by copyright law.++  You may make, run and propagate covered works that you do not+convey, without conditions so long as your license otherwise remains+in force.  You may convey covered works to others for the sole purpose+of having them make modifications exclusively for you, or provide you+with facilities for running those works, provided that you comply with+the terms of this License in conveying all material for which you do+not control copyright.  Those thus making or running the covered works+for you must do so exclusively on your behalf, under your direction+and control, on terms that prohibit them from making any copies of+your copyrighted material outside their relationship with you.++  Conveying under any other circumstances is permitted solely under+the conditions stated below.  Sublicensing is not allowed; section 10+makes it unnecessary.++  3. Protecting Users' Legal Rights From Anti-Circumvention Law.++  No covered work shall be deemed part of an effective technological+measure under any applicable law fulfilling obligations under article+11 of the WIPO copyright treaty adopted on 20 December 1996, or+similar laws prohibiting or restricting circumvention of such+measures.++  When you convey a covered work, you waive any legal power to forbid+circumvention of technological measures to the extent such circumvention+is effected by exercising rights under this License with respect to+the covered work, and you disclaim any intention to limit operation or+modification of the work as a means of enforcing, against the work's+users, your or third parties' legal rights to forbid circumvention of+technological measures.++  4. Conveying Verbatim Copies.++  You may convey verbatim copies of the Program's source code as you+receive it, in any medium, provided that you conspicuously and+appropriately publish on each copy an appropriate copyright notice;+keep intact all notices stating that this License and any+non-permissive terms added in accord with section 7 apply to the code;+keep intact all notices of the absence of any warranty; and give all+recipients a copy of this License along with the Program.++  You may charge any price or no price for each copy that you convey,+and you may offer support or warranty protection for a fee.++  5. Conveying Modified Source Versions.++  You may convey a work based on the Program, or the modifications to+produce it from the Program, in the form of source code under the+terms of section 4, provided that you also meet all of these conditions:++    a) The work must carry prominent notices stating that you modified+    it, and giving a relevant date.++    b) The work must carry prominent notices stating that it is+    released under this License and any conditions added under section+    7.  This requirement modifies the requirement in section 4 to+    "keep intact all notices".++    c) You must license the entire work, as a whole, under this+    License to anyone who comes into possession of a copy.  This+    License will therefore apply, along with any applicable section 7+    additional terms, to the whole of the work, and all its parts,+    regardless of how they are packaged.  This License gives no+    permission to license the work in any other way, but it does not+    invalidate such permission if you have separately received it.++    d) If the work has interactive user interfaces, each must display+    Appropriate Legal Notices; however, if the Program has interactive+    interfaces that do not display Appropriate Legal Notices, your+    work need not make them do so.++  A compilation of a covered work with other separate and independent+works, which are not by their nature extensions of the covered work,+and which are not combined with it such as to form a larger program,+in or on a volume of a storage or distribution medium, is called an+"aggregate" if the compilation and its resulting copyright are not+used to limit the access or legal rights of the compilation's users+beyond what the individual works permit.  Inclusion of a covered work+in an aggregate does not cause this License to apply to the other+parts of the aggregate.++  6. Conveying Non-Source Forms.++  You may convey a covered work in object code form under the terms+of sections 4 and 5, provided that you also convey the+machine-readable Corresponding Source under the terms of this License,+in one of these ways:++    a) Convey the object code in, or embodied in, a physical product+    (including a physical distribution medium), accompanied by the+    Corresponding Source fixed on a durable physical medium+    customarily used for software interchange.++    b) Convey the object code in, or embodied in, a physical product+    (including a physical distribution medium), accompanied by a+    written offer, valid for at least three years and valid for as+    long as you offer spare parts or customer support for that product+    model, to give anyone who possesses the object code either (1) a+    copy of the Corresponding Source for all the software in the+    product that is covered by this License, on a durable physical+    medium customarily used for software interchange, for a price no+    more than your reasonable cost of physically performing this+    conveying of source, or (2) access to copy the+    Corresponding Source from a network server at no charge.++    c) Convey individual copies of the object code with a copy of the+    written offer to provide the Corresponding Source.  This+    alternative is allowed only occasionally and noncommercially, and+    only if you received the object code with such an offer, in accord+    with subsection 6b.++    d) Convey the object code by offering access from a designated+    place (gratis or for a charge), and offer equivalent access to the+    Corresponding Source in the same way through the same place at no+    further charge.  You need not require recipients to copy the+    Corresponding Source along with the object code.  If the place to+    copy the object code is a network server, the Corresponding Source+    may be on a different server (operated by you or a third party)+    that supports equivalent copying facilities, provided you maintain+    clear directions next to the object code saying where to find the+    Corresponding Source.  Regardless of what server hosts the+    Corresponding Source, you remain obligated to ensure that it is+    available for as long as needed to satisfy these requirements.++    e) Convey the object code using peer-to-peer transmission, provided+    you inform other peers where the object code and Corresponding+    Source of the work are being offered to the general public at no+    charge under subsection 6d.++  A separable portion of the object code, whose source code is excluded+from the Corresponding Source as a System Library, need not be+included in conveying the object code work.++  A "User Product" is either (1) a "consumer product", which means any+tangible personal property which is normally used for personal, family,+or household purposes, or (2) anything designed or sold for incorporation+into a dwelling.  In determining whether a product is a consumer product,+doubtful cases shall be resolved in favor of coverage.  For a particular+product received by a particular user, "normally used" refers to a+typical or common use of that class of product, regardless of the status+of the particular user or of the way in which the particular user+actually uses, or expects or is expected to use, the product.  A product+is a consumer product regardless of whether the product has substantial+commercial, industrial or non-consumer uses, unless such uses represent+the only significant mode of use of the product.++  "Installation Information" for a User Product means any methods,+procedures, authorization keys, or other information required to install+and execute modified versions of a covered work in that User Product from+a modified version of its Corresponding Source.  The information must+suffice to ensure that the continued functioning of the modified object+code is in no case prevented or interfered with solely because+modification has been made.++  If you convey an object code work under this section in, or with, or+specifically for use in, a User Product, and the conveying occurs as+part of a transaction in which the right of possession and use of the+User Product is transferred to the recipient in perpetuity or for a+fixed term (regardless of how the transaction is characterized), the+Corresponding Source conveyed under this section must be accompanied+by the Installation Information.  But this requirement does not apply+if neither you nor any third party retains the ability to install+modified object code on the User Product (for example, the work has+been installed in ROM).++  The requirement to provide Installation Information does not include a+requirement to continue to provide support service, warranty, or updates+for a work that has been modified or installed by the recipient, or for+the User Product in which it has been modified or installed.  Access to a+network may be denied when the modification itself materially and+adversely affects the operation of the network or violates the rules and+protocols for communication across the network.++  Corresponding Source conveyed, and Installation Information provided,+in accord with this section must be in a format that is publicly+documented (and with an implementation available to the public in+source code form), and must require no special password or key for+unpacking, reading or copying.++  7. Additional Terms.++  "Additional permissions" are terms that supplement the terms of this+License by making exceptions from one or more of its conditions.+Additional permissions that are applicable to the entire Program shall+be treated as though they were included in this License, to the extent+that they are valid under applicable law.  If additional permissions+apply only to part of the Program, that part may be used separately+under those permissions, but the entire Program remains governed by+this License without regard to the additional permissions.++  When you convey a copy of a covered work, you may at your option+remove any additional permissions from that copy, or from any part of+it.  (Additional permissions may be written to require their own+removal in certain cases when you modify the work.)  You may place+additional permissions on material, added by you to a covered work,+for which you have or can give appropriate copyright permission.++  Notwithstanding any other provision of this License, for material you+add to a covered work, you may (if authorized by the copyright holders of+that material) supplement the terms of this License with terms:++    a) Disclaiming warranty or limiting liability differently from the+    terms of sections 15 and 16 of this License; or++    b) Requiring preservation of specified reasonable legal notices or+    author attributions in that material or in the Appropriate Legal+    Notices displayed by works containing it; or++    c) Prohibiting misrepresentation of the origin of that material, or+    requiring that modified versions of such material be marked in+    reasonable ways as different from the original version; or++    d) Limiting the use for publicity purposes of names of licensors or+    authors of the material; or++    e) Declining to grant rights under trademark law for use of some+    trade names, trademarks, or service marks; or++    f) Requiring indemnification of licensors and authors of that+    material by anyone who conveys the material (or modified versions of+    it) with contractual assumptions of liability to the recipient, for+    any liability that these contractual assumptions directly impose on+    those licensors and authors.++  All other non-permissive additional terms are considered "further+restrictions" within the meaning of section 10.  If the Program as you+received it, or any part of it, contains a notice stating that it is+governed by this License along with a term that is a further+restriction, you may remove that term.  If a license document contains+a further restriction but permits relicensing or conveying under this+License, you may add to a covered work material governed by the terms+of that license document, provided that the further restriction does+not survive such relicensing or conveying.++  If you add terms to a covered work in accord with this section, you+must place, in the relevant source files, a statement of the+additional terms that apply to those files, or a notice indicating+where to find the applicable terms.++  Additional terms, permissive or non-permissive, may be stated in the+form of a separately written license, or stated as exceptions;+the above requirements apply either way.++  8. Termination.++  You may not propagate or modify a covered work except as expressly+provided under this License.  Any attempt otherwise to propagate or+modify it is void, and will automatically terminate your rights under+this License (including any patent licenses granted under the third+paragraph of section 11).++  However, if you cease all violation of this License, then your+license from a particular copyright holder is reinstated (a)+provisionally, unless and until the copyright holder explicitly and+finally terminates your license, and (b) permanently, if the copyright+holder fails to notify you of the violation by some reasonable means+prior to 60 days after the cessation.++  Moreover, your license from a particular copyright holder is+reinstated permanently if the copyright holder notifies you of the+violation by some reasonable means, this is the first time you have+received notice of violation of this License (for any work) from that+copyright holder, and you cure the violation prior to 30 days after+your receipt of the notice.++  Termination of your rights under this section does not terminate the+licenses of parties who have received copies or rights from you under+this License.  If your rights have been terminated and not permanently+reinstated, you do not qualify to receive new licenses for the same+material under section 10.++  9. Acceptance Not Required for Having Copies.++  You are not required to accept this License in order to receive or+run a copy of the Program.  Ancillary propagation of a covered work+occurring solely as a consequence of using peer-to-peer transmission+to receive a copy likewise does not require acceptance.  However,+nothing other than this License grants you permission to propagate or+modify any covered work.  These actions infringe copyright if you do+not accept this License.  Therefore, by modifying or propagating a+covered work, you indicate your acceptance of this License to do so.++  10. Automatic Licensing of Downstream Recipients.++  Each time you convey a covered work, the recipient automatically+receives a license from the original licensors, to run, modify and+propagate that work, subject to this License.  You are not responsible+for enforcing compliance by third parties with this License.++  An "entity transaction" is a transaction transferring control of an+organization, or substantially all assets of one, or subdividing an+organization, or merging organizations.  If propagation of a covered+work results from an entity transaction, each party to that+transaction who receives a copy of the work also receives whatever+licenses to the work the party's predecessor in interest had or could+give under the previous paragraph, plus a right to possession of the+Corresponding Source of the work from the predecessor in interest, if+the predecessor has it or can get it with reasonable efforts.++  You may not impose any further restrictions on the exercise of the+rights granted or affirmed under this License.  For example, you may+not impose a license fee, royalty, or other charge for exercise of+rights granted under this License, and you may not initiate litigation+(including a cross-claim or counterclaim in a lawsuit) alleging that+any patent claim is infringed by making, using, selling, offering for+sale, or importing the Program or any portion of it.++  11. Patents.++  A "contributor" is a copyright holder who authorizes use under this+License of the Program or a work on which the Program is based.  The+work thus licensed is called the contributor's "contributor version".++  A contributor's "essential patent claims" are all patent claims+owned or controlled by the contributor, whether already acquired or+hereafter acquired, that would be infringed by some manner, permitted+by this License, of making, using, or selling its contributor version,+but do not include claims that would be infringed only as a+consequence of further modification of the contributor version.  For+purposes of this definition, "control" includes the right to grant+patent sublicenses in a manner consistent with the requirements of+this License.++  Each contributor grants you a non-exclusive, worldwide, royalty-free+patent license under the contributor's essential patent claims, to+make, use, sell, offer for sale, import and otherwise run, modify and+propagate the contents of its contributor version.++  In the following three paragraphs, a "patent license" is any express+agreement or commitment, however denominated, not to enforce a patent+(such as an express permission to practice a patent or covenant not to+sue for patent infringement).  To "grant" such a patent license to a+party means to make such an agreement or commitment not to enforce a+patent against the party.++  If you convey a covered work, knowingly relying on a patent license,+and the Corresponding Source of the work is not available for anyone+to copy, free of charge and under the terms of this License, through a+publicly available network server or other readily accessible means,+then you must either (1) cause the Corresponding Source to be so+available, or (2) arrange to deprive yourself of the benefit of the+patent license for this particular work, or (3) arrange, in a manner+consistent with the requirements of this License, to extend the patent+license to downstream recipients.  "Knowingly relying" means you have+actual knowledge that, but for the patent license, your conveying the+covered work in a country, or your recipient's use of the covered work+in a country, would infringe one or more identifiable patents in that+country that you have reason to believe are valid.++  If, pursuant to or in connection with a single transaction or+arrangement, you convey, or propagate by procuring conveyance of, a+covered work, and grant a patent license to some of the parties+receiving the covered work authorizing them to use, propagate, modify+or convey a specific copy of the covered work, then the patent license+you grant is automatically extended to all recipients of the covered+work and works based on it.++  A patent license is "discriminatory" if it does not include within+the scope of its coverage, prohibits the exercise of, or is+conditioned on the non-exercise of one or more of the rights that are+specifically granted under this License.  You may not convey a covered+work if you are a party to an arrangement with a third party that is+in the business of distributing software, under which you make payment+to the third party based on the extent of your activity of conveying+the work, and under which the third party grants, to any of the+parties who would receive the covered work from you, a discriminatory+patent license (a) in connection with copies of the covered work+conveyed by you (or copies made from those copies), or (b) primarily+for and in connection with specific products or compilations that+contain the covered work, unless you entered into that arrangement,+or that patent license was granted, prior to 28 March 2007.++  Nothing in this License shall be construed as excluding or limiting+any implied license or other defenses to infringement that may+otherwise be available to you under applicable patent law.++  12. No Surrender of Others' Freedom.++  If conditions are imposed on you (whether by court order, agreement or+otherwise) that contradict the conditions of this License, they do not+excuse you from the conditions of this License.  If you cannot convey a+covered work so as to satisfy simultaneously your obligations under this+License and any other pertinent obligations, then as a consequence you may+not convey it at all.  For example, if you agree to terms that obligate you+to collect a royalty for further conveying from those to whom you convey+the Program, the only way you could satisfy both those terms and this+License would be to refrain entirely from conveying the Program.++  13. Use with the GNU Affero General Public License.++  Notwithstanding any other provision of this License, you have+permission to link or combine any covered work with a work licensed+under version 3 of the GNU Affero General Public License into a single+combined work, and to convey the resulting work.  The terms of this+License will continue to apply to the part which is the covered work,+but the special requirements of the GNU Affero General Public License,+section 13, concerning interaction through a network will apply to the+combination as such.++  14. Revised Versions of this License.++  The Free Software Foundation may publish revised and/or new versions of+the GNU General Public License from time to time.  Such new versions will+be similar in spirit to the present version, but may differ in detail to+address new problems or concerns.++  Each version is given a distinguishing version number.  If the+Program specifies that a certain numbered version of the GNU General+Public License "or any later version" applies to it, you have the+option of following the terms and conditions either of that numbered+version or of any later version published by the Free Software+Foundation.  If the Program does not specify a version number of the+GNU General Public License, you may choose any version ever published+by the Free Software Foundation.++  If the Program specifies that a proxy can decide which future+versions of the GNU General Public License can be used, that proxy's+public statement of acceptance of a version permanently authorizes you+to choose that version for the Program.++  Later license versions may give you additional or different+permissions.  However, no additional obligations are imposed on any+author or copyright holder as a result of your choosing to follow a+later version.++  15. Disclaimer of Warranty.++  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.++  16. Limitation of Liability.++  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF+SUCH DAMAGES.++  17. Interpretation of Sections 15 and 16.++  If the disclaimer of warranty and limitation of liability provided+above cannot be given local legal effect according to their terms,+reviewing courts shall apply local law that most closely approximates+an absolute waiver of all civil liability in connection with the+Program, unless a warranty or assumption of liability accompanies a+copy of the Program in return for a fee.++              END OF TERMS AND CONDITIONS++     How to Apply These Terms to Your New Programs++  If you develop a new program, and you want it to be of the greatest+possible use to the public, the best way to achieve this is to make it+free software which everyone can redistribute and change under these terms.++  To do so, attach the following notices to the program.  It is safest+to attach them to the start of each source file to most effectively+state the exclusion of warranty; and each file should have at least+the "copyright" line and a pointer to where the full notice is found.++    <one line to give the program's name and a brief idea of what it does.>+    Copyright (C) <year>  <name of author>++    This program is free software: you can redistribute it and/or modify+    it under the terms of the GNU General Public License as published by+    the Free Software Foundation, either version 3 of the License, or+    (at your option) any later version.++    This program is distributed in the hope that it will be useful,+    but WITHOUT ANY WARRANTY; without even the implied warranty of+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the+    GNU General Public License for more details.++    You should have received a copy of the GNU General Public License+    along with this program.  If not, see <http://www.gnu.org/licenses/>.++Also add information on how to contact you by electronic and paper mail.++  If the program does terminal interaction, make it output a short+notice like this when it starts in an interactive mode:++    <program>  Copyright (C) <year>  <name of author>+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.+    This is free software, and you are welcome to redistribute it+    under certain conditions; type `show c' for details.++The hypothetical commands `show w' and `show c' should show the appropriate+parts of the General Public License.  Of course, your program's commands+might be different; for a GUI interface, you would use an "about box".++  You should also get your employer (if you work as a programmer) or school,+if any, to sign a "copyright disclaimer" for the program, if necessary.+For more information on this, and how to apply and follow the GNU GPL, see+<http://www.gnu.org/licenses/>.++  The GNU General Public License does not permit incorporating your program+into proprietary programs.  If your program is a subroutine library, you+may consider it more useful to permit linking proprietary applications with+the library.  If this is what you want to do, use the GNU Lesser General+Public License instead of this License.  But first, please read+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ Test/Distance.hs view
@@ -0,0 +1,21 @@+{-# LANGUAGE TemplateHaskell #-}++import Data.AEq+import Geom2d.Point+import Geom2d.Distance+import Test.QuickCheck+import Test.Utils++prop_distance_point_point :: Point' Float -> Point' Float -> Bool+prop_distance_point_point p q =+  distance p q ~==+  sqrt ( (x p - x q)^(2::Int) + (y p - y q)^(2::Int) )++return []+runTests = $quickCheckAll++main :: IO ()+main = do+  putStrLn "Test Distance"+  runTests >>= doExit+
+ Test/Intersect.hs view
@@ -0,0 +1,49 @@+{-# LANGUAGE TemplateHaskell #-}++import Geom2d.Intersect+import Geom2d.Point+import Geom2d.Line+import Test.QuickCheck.All+import Test.QuickCheck+import Test.Utils+import Data.AEq++prop_intersect_point_point :: Point' Float -> Point' Float -> Bool+prop_intersect_point_point a b =+  (a == b) == (a `intersect` b)++prop_intersect_infline_infline_xaxis :: Float -> Float -> Bool+prop_intersect_infline_infline_xaxis a b = maybe True id $ do+  l <- mkInfLine+       (fromCoords a 0)+       (fromCoords a b) :: Maybe (InfLine Point' Float)+  xAxis <- mkInfLine+           (fromCoords 0 0)+           (fromCoords 1 0) :: Maybe (InfLine Point' Float)+  return (l `intersect` xAxis)+  +prop_intersect_infline_infline_yaxis :: Float -> Float -> Bool+prop_intersect_infline_infline_yaxis a b = maybe True id $ do+  l <- mkInfLine+       (fromCoords 0 a)+       (fromCoords b a) :: Maybe (InfLine Point' Float)+  yAxis <- mkInfLine+           (fromCoords 0 0)+           (fromCoords 0 1) :: Maybe (InfLine Point' Float)+  return (l `intersect` yAxis)++prop_intersect_infline_point :: InfLine Point' Float -> Point' Float -> Bool+prop_intersect_infline_point line p =+  (line `intersect` p) `implies`+  ( maybe True id $ do+      f <- lineF line+      return (y p ~== f (x p)))+  where True `implies` False = False+        _ `implies` _ = True+  +return []+runTests = $quickCheckAll++main = do+  putStrLn "Test Intersect.hs"+  runTests >>= doExit
+ Test/Line.hs view
@@ -0,0 +1,168 @@+{-# LANGUAGE TemplateHaskell #-}++import Geom2d.Line+import Geom2d.Point+import Geom2d.Translate+import Geom2d.Distance+import Geom2d.Intersect+import Test.QuickCheck.All+import Test.QuickCheck+import Data.AEq+import Data.Maybe+import Test.Utils++prop_infline_translate :: InfLine Point' Float+                       -> InfLine Point' Float+                       -> Point' Float+                       -> Bool+prop_infline_translate l1 l2 v =+  parallel l1 l2 == parallel l1 (translate v l2)++prop_line_function_vertical :: Float -> Bool+prop_line_function_vertical xarg =+  maybe False (not.isJust.lineF) $+    mkInfLine (fromCoords xarg 0 :: Point' Float) (fromCoords xarg 1)++prop_line_function_linear :: Float -> Bool+prop_line_function_linear xarg = maybe False (\f -> f xarg ~== xarg) $ do+  line <- mkInfLine (fromCoords 0 0) (fromCoords 1 1 :: Point' Float)+  lineF line++prop_parallel :: Float -> Bool+prop_parallel n = maybe True id $ do+  yAxis <- mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 0 1)+  line <- mkInfLine (fromCoords 1 0) (fromCoords 1 n)+  return (parallel yAxis line)++prop_slope :: Float -> Float -> Bool+prop_slope ax ay = maybe True id $ do+  l <- mkInfLine+       (fromCoords 0 0 :: Point' Float)+       (fromCoords ax ay)+  s <- slope l+  return $ s == ay / ax++prop_root :: InfLine Point' Float -> Bool+prop_root l+  | slope l == Just 0 = isNothing (root l)+  | isNothing (slope l) = True+  | otherwise = maybe False id $ do+      x0 <- root l+      f <- lineF l+      return (f x0 ~== 0)++prop_line_equal :: Bool+prop_line_equal = maybe False (\l -> l == l) $+  mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 1 0)++prop_intersection_equal :: Bool+prop_intersection_equal = maybe False id $ do+  xAxis <- mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 1 0)+  return $ (not.isJust) (xAxis `intersection` xAxis)++prop_intersection_parallel :: Bool+prop_intersection_parallel = maybe False id $ do+  xAxis <- mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 1 0)+  let line = translate (fromCoords 0 1 :: Point' Float) xAxis+  return $ (not.isJust) (xAxis `intersection` line)++prop_intersection_origin :: Bool+prop_intersection_origin = maybe False id $ do+  xAxis <- mkLine (fromCoords 0 0) (fromCoords 1 0)+  yAxis <- mkLine (fromCoords 0 0) (fromCoords 0 1)+  (~== origin) <$> (xAxis `intersection` yAxis)+  where mkLine :: Point' Float -> Point' Float -> Maybe (InfLine Point' Float)+        mkLine = mkInfLine+        origin = fromCoords 0 0++prop_intersection_onYAxis :: Float -> Float -> Bool+prop_intersection_onYAxis m1 m2 = maybe (m1 == m2) (== fromCoords 0 0) $ do+  l1 <- mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 1 m1)+  l2 <- mkInfLine (fromCoords 0 0) (fromCoords 1 m2)+  intersection l1 l2++prop_intersection_yaxis :: Bool+prop_intersection_yaxis = fromMaybe False $ do+  l1 <- mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 0 1)+  l2 <- mkInfLine (fromCoords 0 0 :: Point' Float) (fromCoords 1 0)+  (~== fromCoords 0 0) <$> intersection l1 l2++prop_finline_translate_constant_length :: FinLine Point' Float+                                       -> Point' Float+                                       -> Bool+prop_finline_translate_constant_length l v =+  lineLength l ~==+  lineLength (translate v l)++prop_finline_translate_notequal :: FinLine Point' Float+                                -> Point' Float+                                -> Bool+prop_finline_translate_notequal l v+  | not (magnitude v ~== 0) =+      not (l ~== (translate v l))+  | otherwise = (l ~== (translate v l))++prop_finline_distance_1 :: Bool+prop_finline_distance_1 = maybe False id $ do+  line <- mkFinLine (fromCoords 0 0 :: Point' Float)+                    (fromCoords 1 0)+  return (distance (fromCoords 1 1 :: Point' Float) line ~==+          1)++prop_finline_distance_2 :: Bool+prop_finline_distance_2 = maybe False id $ do+  line <- mkFinLine (fromCoords 0 0 :: Point' Float)+                    (fromCoords 1 0)+  return (distance (fromCoords 2 0 :: Point' Float) line ~==+          1)++prop_finline_distance_3 :: Bool+prop_finline_distance_3 = maybe False id $ do+  line <- mkFinLine (fromCoords (-10) 0 :: Point' Float)+                    (fromCoords 10 0)+  return (distance (fromCoords 0 1 :: Point' Float) line ~==+          1)++prop_finline_distance_4 :: Bool+prop_finline_distance_4 = maybe False id $ do+  line <- mkFinLine (fromCoords (-10) 0 :: Point' Float)+                    (fromCoords 10 0)+  return (distance (fromCoords 0 0 :: Point' Float) line ~==+          0)++prop_intersect_infline_infline_1 :: Bool+prop_intersect_infline_infline_1 =+  maybe False+  ( \(l1,l2) -> l1 `intersect` l2 )+  ( (,) <$>+    mkInfLine (fromCoords (-1) 0 :: Point' Float)+              (fromCoords 1 0) <*>+    mkInfLine (fromCoords 0 (-1) :: Point' Float)+              (fromCoords 0 1))++prop_intersect_finline_finline_1 :: Bool+prop_intersect_finline_finline_1 =+  maybe False+  ( \(l1,l2) -> l1 `intersect` l2 )+  ( (,) <$>+    mkFinLine (fromCoords (-1) 0 :: Point' Float)+              (fromCoords 1 0) <*>+    mkFinLine (fromCoords 0 (-1) :: Point' Float)+              (fromCoords 0 1))++prop_intersect_infline_finline_1 :: Bool+prop_intersect_infline_finline_1 =+  maybe False+  ( \(l1,l2) -> l1 `intersect` l2 )+  ( (,) <$>+    mkInfLine (fromCoords (-1) 0 :: Point' Float)+              (fromCoords 1 0) <*>+    mkFinLine (fromCoords 0 (-1) :: Point' Float)+              (fromCoords 0 1))++return []+runTests = $quickCheckAll++main = do+  putStrLn "Line.hs"+  runTests >>= doExit
+ Test/Point.hs view
@@ -0,0 +1,141 @@+{-# LANGUAGE TemplateHaskell #-}+{-# LANGUAGE ScopedTypeVariables #-}++import Data.AEq+import Data.Maybe+import Geom2d.Point+import Geom2d.Rotation+import Test.QuickCheck+import Test.QuickCheck.All+import Test.Utils+import Data.Fixed++mkpropPoint :: forall a p. (Arbitrary (p a), Point p, Eq a) =>+                 p a -> Bool+mkpropPoint p =+  and [ prop_identity+      ]+  where prop_identity = x p == x idPoint &&+                        y p == y idPoint+        idPoint :: p a+        idPoint = fromCoords (x p) (y p)++mkpropNum :: (Arbitrary a, Num a) => (a -> a -> Bool) -> a -> Bool+mkpropNum isEqual x =+    x `isEqual` (signum x * abs x)++mkpropFunctor :: (Arbitrary (f a), Eq (f a), Functor f) =>+                  f a -> Bool+mkpropFunctor x =+  fmap id x == x++mkpropScale :: (Arbitrary (p a), Scale p, Floating a, Point p) =>+                (a -> a -> Bool) -> p a -> a -> Bool+mkpropScale comparison p a =+  (magnitude p * abs a) `comparison`+  magnitude (a `scale` p)++mkpropNormalize :: (Arbitrary (p a), Point p, Scale p, Floating a, AEq a+                    , Num a) =>+                p a -> Bool+mkpropNormalize v =+  maybe (magnitude v ~== 0)+  ( (~== 1).magnitude )+  ( normalize v)++prop_point_point' :: Point' Integer -> Bool+prop_point_point' = mkpropPoint++prop_num_point' :: Point' Float -> Bool+prop_num_point' = mkpropNum (~==)++prop_functor_point' :: Point' Integer -> Bool+prop_functor_point' = mkpropFunctor++prop_point'_magnitude :: Point' Float -> Bool+prop_point'_magnitude p =+  sqrt ( x p ^ 2 + y p ^ 2 ) ~== magnitude p++prop_triarea :: Float -> Float -> Bool+prop_triarea a b =+  triArea triangle ~== abs ((a * b) / 2)+  where triangle :: Triangle (Point' Float)+        triangle = ( fromCoords 0 0+                   , fromCoords a 0+                   , fromCoords 0 b+                   )++prop_point_scale :: Point' Float -> Float -> Bool+prop_point_scale = mkpropScale (~==)++prop_point_normalize :: Point' Float -> Bool+prop_point_normalize = mkpropNormalize++prop_pointInTriangle :: Bool+prop_pointInTriangle =+  pointInTriangle tri p+  where tri = ( fromCoords (-1) (-1)+              , fromCoords 1 (-1)+              , fromCoords 0 1+              )+        p :: Point' Float+        p = fromCoords 0 0++prop_pointInTriangle_onVert :: Bool+prop_pointInTriangle_onVert =+  pointInTriangle tri p+  where p = fromCoords 0 0+        tri :: Triangle (Point' Float)+        tri = (p, fromCoords 1 1, fromCoords 1 (-1))++prop_angle_zero :: Bool+prop_angle_zero =+  angle (fromCoords 1 0 :: Point' Float) == Just 0++prop_point_show_read :: Point' Float -> Bool+prop_point_show_read p =+  p == (read.show) p++prop_point_add :: Point' Float -> Point' Float -> Bool+prop_point_add p q =+  x (p + q) == x p + x q &&+  y (p + q) == y p + y q++prop_point_negate :: Point' Float -> Bool+prop_point_negate p =+  x (negate p) == negate (x p) &&+  y (negate p) == negate (y p)++prop_triangle_invalid :: Bool+prop_triangle_invalid =+  let tri :: Triangle (Point' Float)+      tri = ( fromCoords 0 0+            , fromCoords 1 1+            , fromCoords 1 1+            )+  in not (pointInTriangle tri (fromCoords 0 0))++prop_rotation_point_linear :: Point' Float -> Bool+prop_rotation_point_linear x =+  fromMaybe True+  ( (~==) <$>+    angle (r `rotate` x) <*>+    ((subtract pi).((`mod'` (2*pi)).(+pi).(+r)) <$> angle x)+  )+  where r = 1.2++prop_rotation_point_bounds :: Point' Float -> Bool+prop_rotation_point_bounds x =+  fromMaybe True+  ( fmap+    (\a -> a >= (- pi) && a <= pi)+    (angle x)+  )++return []+runTests = $quickCheckAll++main :: IO ()+main = do+  putStrLn "Test Point"+  runTests >>= doExit
+ Test/Shape.hs view
@@ -0,0 +1,168 @@+{-# LANGUAGE TemplateHaskell #-}++import Data.AEq+import Data.Fixed+import Data.Maybe+import Geom2d.Distance+import Geom2d.Intersect+import Geom2d.Point+import Geom2d.Rotation+import Geom2d.Shape+import Geom2d.Shape.Internal+import Test.QuickCheck+import Test.Utils++prop_circle_radius :: Point' Float -> Float -> Bool+prop_circle_radius m r =+  radius (mkCircleInt m r) ~== abs r++prop_circle_rotate_1 :: Bool+prop_circle_rotate_1 =+  rotate 5 circ == circ+  where circ :: Shape Point' Float+        circ = circle (fromCoords 0 0) 4++prop_circle_rotate_2 :: Point' Float -> Bool+prop_circle_rotate_2 m =+  let circ = circle m 1+  in angle circ ~== angle m++prop_circle_center :: Point' Float -> Float -> Bool+prop_circle_center m r =+  center (mkCircleInt m r) ~== m++prop_distance_circle_point :: Bool+prop_distance_circle_point =+  distance+  (mkCircleInt (fromCoords 0 0 :: Point' Float) 1)+  (fromCoords 5 0 :: Point' Float) ~== 4++prop_point_in_circle :: Bool+prop_point_in_circle =+  let circ :: Circle Point' Float+      circ = mkCircleInt (fromCoords 0 0) 1+      p :: Point' Float+      p = fromCoords 0 0+  in circ `intersect` p &&+     p `intersect` circ++prop_intersect_circle_circle :: Circle Point' Float+                             -> Circle Point' Float+                             -> Bool+prop_intersect_circle_circle a b =+  intersect a b ==+  ( distance (center a) (center b) <= radius a + radius b )++prop_point_outside_circle :: Bool+prop_point_outside_circle =+  let circ :: Shape Point' Float+      circ = circle (fromCoords 0 0) 1+      p :: Point' Float+      p = fromCoords 2 0+  in not (circ `intersect` p) ||+     not (p `intersect` circ)++prop_point_in_polygon :: Bool+prop_point_in_polygon =+  maybe+  False+  ( intersect (fromCoords 0 0::Point' Float) )+  ( rectangle (fromCoords 0 0::Point' Float) 1 1 )++prop_point_outside_polygon :: Bool+prop_point_outside_polygon =+  maybe+  False+  ( not.intersect (fromCoords 10 0::Point' Float) )+  ( rectangle (fromCoords 0 0::Point' Float) 1 1 )++prop_point_outside_polygon_1 :: Bool+prop_point_outside_polygon_1 =+  maybe+  False+  ( not.intersect (fromCoords (-5) 0 :: Point' Float))+  ( rectangle (fromCoords 0 5 :: Point' Float) 4 4)++prop_intersect_polygon_circle_1 :: Bool+prop_intersect_polygon_circle_1 =+  maybe False+  ( intersect (circle (fromCoords 0 0 :: Point' Float) 1 ))+  ( rectangle (fromCoords 0 0 :: Point' Float) 4 4 )++prop_intersect_polygon_circle_2 :: Bool+prop_intersect_polygon_circle_2 =+  maybe False+  ( (intersect :: Shape Point' Float -> Shape Point' Float -> Bool)+    (circle (fromCoords 0 5 :: Point' Float) 4 ))+  ( rectangle (fromCoords 0 0 :: Point' Float) 4 4 )++-- | This test make a rectangleInt (-9,-9) (11,11) and a circle (10,15)+-- with radius 2.  so these shapes should not intersect.+prop_intersect_polygon_circle_3 :: Bool+prop_intersect_polygon_circle_3 =+  maybe False+  ( not.+    (intersect :: Shape Point' Float -> Shape Point' Float -> Bool)+    (circle (fromCoords 10 15 :: Point' Float) 2 ))+  ( rectangle (fromCoords 10 10 :: Point' Float) 1 1 )++prop_intersect_polygon_1 :: Bool+prop_intersect_polygon_1 =+  fromMaybe False $+    intersect <$>+    rectangle (fromCoords 0 0 :: Point' Float) 1 3 <*>+    rectangle (fromCoords 1 2 :: Point' Float) 3 1++prop_intersect_polygon_eq :: Polygon Point' Float -> Bool+prop_intersect_polygon_eq p = p `intersect` p++prop_polygon_convexHull_1 :: Bool+prop_polygon_convexHull_1 =+  fromMaybe False $ do+    shape <- convexHull' [ fromCoords (-1) (-1) :: Point' Float+                         , fromCoords 1 (-1)+                         , fromCoords 1 1+                         , fromCoords (-1) 1+                         ]+    return ( shape `intersect` point 1 1 &&+             shape `intersect` point (-1) 1 &&+             shape `intersect` point 1 (-1) &&+             shape `intersect` point (-1) (-1))+  where point :: Float -> Float -> Point' Float+        point = fromCoords++prop_polygon_convexHull_2 :: Bool+prop_polygon_convexHull_2 =+  fromMaybe False $ do+    shape <- convexHull' points+    return (all (intersect shape) points)+  where points = [ point 5 5+                 , point 7 4+                 , point 8 3+                 , point 10 20+                 , point 2 20+                 , point 5 5+                 ]+        point :: Float -> Float -> Point' Float+        point = fromCoords++prop_polygon_rotate :: Polygon Point' Float -> Bool+prop_polygon_rotate p =+  fromMaybe True $ do+    angBefore <- angle p+    angAfter <- angle (rotate rotAng p)+    return (normalize (angBefore + rotAng) ~== angAfter)+  where rotAng = 1+        normalize = subtract pi.(`mod'` (2*pi)).(+pi)++prop_polygon_rotate_defined :: Bool+prop_polygon_rotate_defined =+  fromMaybe False $ do+    rect <- rectangle (fromCoords 1 0 :: Point' Float) 1 1+    ang <- angle rect+    return (ang ~== 0)++return []+runTests = $quickCheckAll++main = runTests >>= doExit
+ Test/Translate.hs view
@@ -0,0 +1,21 @@+{-# LANGUAGE TemplateHaskell #-}++import Geom2d.Translate+import Geom2d.Point+import Test.Utils+import Test.QuickCheck.All+import Test.QuickCheck+import Data.AEq++prop_point_translate_identity :: Point' Float -> Bool+prop_point_translate_identity p =+  translate (fromCoords 0 0 :: Point' Float) p == p++prop_point_translate_addition :: Point' Float -> Point' Float -> Bool+prop_point_translate_addition p q = p `translate` q ~== p + q++return []+runTests = $quickCheckAll++main = do+  runTests >>= doExit
+ Test/Utils.hs view
@@ -0,0 +1,9 @@+module Test.Utils++where++import System.Exit++doExit :: Bool -> IO ()+doExit True = exitSuccess+doExit False = exitFailure
+ geom2d.cabal view
@@ -0,0 +1,72 @@+name:                geom2d+version:             0.1.0.1+synopsis:            package for geometry in euklidean 2d space+description:         This package provides tools for dealing with geometric+                     objects in 2D space.+license:             GPL-3+license-file:        LICENSE+author:              Sebastian Jordan+maintainer:          sebastian.jordan.mail@googlemail.com+category:            Math+build-type:          Simple+cabal-version:       >=1.10+extra-source-files:  Test/Utils.hs++source-repository head+  type:      darcs+  location:  http://hub.darcs.net/seppeljordan/geom2d/++library+  exposed-modules:     Geom2d.Intersect, Geom2d.Point, Geom2d.Distance+                     , Geom2d.Line, Geom2d.Point.Internal+                     , Geom2d.Line.Internal, Geom2d.Shape+                     , Geom2d.Translate, Geom2d.Shape.Internal+                     , Geom2d.Rotation, Geom2d+  other-extensions:    MultiParamTypeClasses, FlexibleContexts, TemplateHaskell+                     , ScopedTypeVariables+  build-depends:       base >=4.8 && <4.9, QuickCheck >=2.7 && <2.8+                     , ieee754 >=0.7 && <0.8+  default-language:    Haskell2010+  ghc-options:         -Wall++Test-Suite point+  default-language:    Haskell2010+  type:                exitcode-stdio-1.0+  main-is:             Test/Point.hs+  build-depends:       base >= 4.8 && < 4.9, ieee754 >= 0.7 && < 0.8+                     , QuickCheck >= 2.7 && < 2.8++Test-Suite line+  default-language:    Haskell2010+  type:                exitcode-stdio-1.0+  main-is:             Test/Line.hs+  build-depends:       base >= 4.8 && < 4.9, ieee754 >= 0.7 && < 0.8+                     , QuickCheck >= 2.7 && < 2.8++Test-Suite intersect+  default-language:    Haskell2010+  type:                exitcode-stdio-1.0+  main-is:             Test/Intersect.hs+  build-depends:       base >= 4.8 && < 4.9, ieee754 >= 0.7 && < 0.8+                     , QuickCheck >= 2.7 && < 2.8++Test-Suite distance+  default-language:    Haskell2010+  type:                exitcode-stdio-1.0+  main-is:             Test/Distance.hs+  build-depends:       base >= 4.8 && < 4.9, ieee754 >= 0.7 && < 0.8+                     , QuickCheck >= 2.7 && < 2.8++Test-Suite translate+  default-language:    Haskell2010+  type:                exitcode-stdio-1.0+  main-is:             Test/Translate.hs+  build-depends:       base >= 4.8 && < 4.9, ieee754 >= 0.7 && < 0.8+                     , QuickCheck >= 2.7 && < 2.8++Test-Suite shape+  default-language:    Haskell2010+  type:                exitcode-stdio-1.0+  main-is:             Test/Shape.hs+  build-depends:       base >= 4.8 && < 4.9, ieee754 >= 0.7 && < 0.8+                     , QuickCheck >= 2.7 && < 2.8