--------------------------------------------------------------------------------
-- |
-- Module      :  HGeometry.Interval.HalfOpen
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--
-- Half-Open Intervals
--
--------------------------------------------------------------------------------
module HGeometry.Interval.HalfOpen
  ( HalfOpenInterval(HalfOpenInterval)
  ) where


import           Control.Lens
-- import           Data.Foldable1
import           HGeometry.Interval.Class
-- import           HGeometry.Interval.EndPoint
import           HGeometry.Interval.Internal
import           HGeometry.Point
-- import HGeometry.Measured.Class
import           HGeometry.Properties
import           HGeometry.Intersection
-- import qualified Data.List.NonEmpty as NonEmpty
-- import           Data.List.NonEmpty (NonEmpty(..))


--------------------------------------------------------------------------------

-- | An interval that is open on the left and closed on the right
data HalfOpenInterval r = HalfOpenInterval { forall r. HalfOpenInterval r -> EndPoint 'Open r
_left  :: !(EndPoint Open   r)
                                           , forall r. HalfOpenInterval r -> EndPoint 'Closed r
_right :: !(EndPoint Closed r)
                                           }
                        deriving (Int -> HalfOpenInterval r -> ShowS
[HalfOpenInterval r] -> ShowS
HalfOpenInterval r -> String
(Int -> HalfOpenInterval r -> ShowS)
-> (HalfOpenInterval r -> String)
-> ([HalfOpenInterval r] -> ShowS)
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forall a b. (a -> b) -> HalfOpenInterval a -> HalfOpenInterval b
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-> Foldable HalfOpenInterval
forall a. Eq a => a -> HalfOpenInterval a -> Bool
forall a. Num a => HalfOpenInterval a -> a
forall a. Ord a => HalfOpenInterval a -> a
forall m. Monoid m => HalfOpenInterval m -> m
forall a. HalfOpenInterval a -> Bool
forall a. HalfOpenInterval a -> Int
forall a. HalfOpenInterval a -> [a]
forall a. (a -> a -> a) -> HalfOpenInterval a -> a
forall m a. Monoid m => (a -> m) -> HalfOpenInterval a -> m
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forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
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$cfold :: forall m. Monoid m => HalfOpenInterval m -> m
fold :: forall m. Monoid m => HalfOpenInterval m -> m
$cfoldMap :: forall m a. Monoid m => (a -> m) -> HalfOpenInterval a -> m
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$cfoldMap' :: forall m a. Monoid m => (a -> m) -> HalfOpenInterval a -> m
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foldr :: forall a b. (a -> b -> b) -> b -> HalfOpenInterval a -> b
$cfoldr' :: forall a b. (a -> b -> b) -> b -> HalfOpenInterval a -> b
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foldr1 :: forall a. (a -> a -> a) -> HalfOpenInterval a -> a
$cfoldl1 :: forall a. (a -> a -> a) -> HalfOpenInterval a -> a
foldl1 :: forall a. (a -> a -> a) -> HalfOpenInterval a -> a
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$clength :: forall a. HalfOpenInterval a -> Int
length :: forall a. HalfOpenInterval a -> Int
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Foldable,Functor HalfOpenInterval
Foldable HalfOpenInterval
(Functor HalfOpenInterval, Foldable HalfOpenInterval) =>
(forall (f :: * -> *) a b.
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 (a -> f b) -> HalfOpenInterval a -> f (HalfOpenInterval b))
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-> (forall (m :: * -> *) a b.
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    (a -> m b) -> HalfOpenInterval a -> m (HalfOpenInterval b))
-> (forall (m :: * -> *) a.
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-> Traversable HalfOpenInterval
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Traversable)

type instance NumType (HalfOpenInterval r) = r

type instance StartPointOf (HalfOpenInterval r) = EndPoint Open   r
type instance EndPointOf  (HalfOpenInterval r)  = EndPoint Closed r

instance HasStart (HalfOpenInterval r) r where
  start :: Lens' (HalfOpenInterval r) r
start = (EndPoint 'Open r -> f (EndPoint 'Open r))
-> HalfOpenInterval r -> f (HalfOpenInterval r)
forall seg p. HasStartPoint seg p => Lens' seg p
Lens' (HalfOpenInterval r) (EndPoint 'Open r)
startPoint((EndPoint 'Open r -> f (EndPoint 'Open r))
 -> HalfOpenInterval r -> f (HalfOpenInterval r))
-> ((r -> f r) -> EndPoint 'Open r -> f (EndPoint 'Open r))
-> (r -> f r)
-> HalfOpenInterval r
-> f (HalfOpenInterval r)
forall b c a. (b -> c) -> (a -> b) -> a -> c
.(r -> f r) -> EndPoint 'Open r -> f (EndPoint 'Open r)
(IxValue (EndPoint 'Open r) -> f (IxValue (EndPoint 'Open r)))
-> EndPoint 'Open r -> f (EndPoint 'Open r)
forall endPoint endPoint'.
IsEndPoint endPoint endPoint' =>
Lens endPoint endPoint' (IxValue endPoint) (IxValue endPoint')
Lens
  (EndPoint 'Open r)
  (EndPoint 'Open r)
  (IxValue (EndPoint 'Open r))
  (IxValue (EndPoint 'Open r))
_endPoint

instance HasEnd (HalfOpenInterval r) r where
  end :: Lens' (HalfOpenInterval r) r
end = (EndPoint 'Closed r -> f (EndPoint 'Closed r))
-> HalfOpenInterval r -> f (HalfOpenInterval r)
forall seg p. HasEndPoint seg p => Lens' seg p
Lens' (HalfOpenInterval r) (EndPoint 'Closed r)
endPoint((EndPoint 'Closed r -> f (EndPoint 'Closed r))
 -> HalfOpenInterval r -> f (HalfOpenInterval r))
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-> f (HalfOpenInterval r)
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(IxValue (EndPoint 'Closed r) -> f (IxValue (EndPoint 'Closed r)))
-> EndPoint 'Closed r -> f (EndPoint 'Closed r)
forall endPoint endPoint'.
IsEndPoint endPoint endPoint' =>
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  (EndPoint 'Closed r)
  (EndPoint 'Closed r)
  (IxValue (EndPoint 'Closed r))
  (IxValue (EndPoint 'Closed r))
_endPoint

instance HasStartPoint (HalfOpenInterval r) (EndPoint Open r) where
  startPoint :: Lens' (HalfOpenInterval r) (EndPoint 'Open r)
startPoint = (HalfOpenInterval r -> EndPoint 'Open r)
-> (HalfOpenInterval r -> EndPoint 'Open r -> HalfOpenInterval r)
-> Lens' (HalfOpenInterval r) (EndPoint 'Open r)
forall s a b t. (s -> a) -> (s -> b -> t) -> Lens s t a b
lens HalfOpenInterval r -> EndPoint 'Open r
forall r. HalfOpenInterval r -> EndPoint 'Open r
_left (\HalfOpenInterval r
ai EndPoint 'Open r
x -> HalfOpenInterval r
ai { _left = x})

instance HasEndPoint (HalfOpenInterval r) (EndPoint Closed r) where
  endPoint :: Lens' (HalfOpenInterval r) (EndPoint 'Closed r)
endPoint = (HalfOpenInterval r -> EndPoint 'Closed r)
-> (HalfOpenInterval r -> EndPoint 'Closed r -> HalfOpenInterval r)
-> Lens' (HalfOpenInterval r) (EndPoint 'Closed r)
forall s a b t. (s -> a) -> (s -> b -> t) -> Lens s t a b
lens HalfOpenInterval r -> EndPoint 'Closed r
forall r. HalfOpenInterval r -> EndPoint 'Closed r
_right (\HalfOpenInterval r
ai EndPoint 'Closed r
x -> HalfOpenInterval r
ai { _right = x})

instance IntervalLike_ (HalfOpenInterval r) r where

instance Interval_ (HalfOpenInterval r) r where

instance ConstructableInterval_ (HalfOpenInterval r) r where
  mkInterval :: StartPointOf (HalfOpenInterval r)
-> EndPointOf (HalfOpenInterval r) -> HalfOpenInterval r
mkInterval = EndPoint 'Open r -> EndPoint 'Closed r -> HalfOpenInterval r
StartPointOf (HalfOpenInterval r)
-> EndPointOf (HalfOpenInterval r) -> HalfOpenInterval r
forall r.
EndPoint 'Open r -> EndPoint 'Closed r -> HalfOpenInterval r
HalfOpenInterval

instance (Ord r) => Point 1 r `HasIntersectionWith` HalfOpenInterval r where
  (Point1 r
q) intersects :: Point 1 r -> HalfOpenInterval r -> Bool
`intersects` HalfOpenInterval r
i = r
q r -> HalfOpenInterval r -> Bool
forall interval r.
(Ord r, Interval_ interval r) =>
r -> interval -> Bool
`stabsInterval` HalfOpenInterval r
i

instance (Ord r) => ClosedInterval r `HasIntersectionWith` HalfOpenInterval r where
  ClosedInterval r
closedInt intersects :: ClosedInterval r -> HalfOpenInterval r -> Bool
`intersects` HalfOpenInterval r
hoInt = case (ClosedInterval r
closedIntClosedInterval r -> Getting r (ClosedInterval r) r -> r
forall s a. s -> Getting a s a -> a
^.Getting r (ClosedInterval r) r
forall seg p. HasStart seg p => Lens' seg p
Lens' (ClosedInterval r) r
start) r -> HalfOpenInterval r -> Ordering
forall r interval.
(Ord r, Interval_ interval r) =>
r -> interval -> Ordering
`compareInterval` HalfOpenInterval r
hoInt of
    Ordering
LT -> case (ClosedInterval r
closedIntClosedInterval r -> Getting r (ClosedInterval r) r -> r
forall s a. s -> Getting a s a -> a
^.Getting r (ClosedInterval r) r
forall seg p. HasEnd seg p => Lens' seg p
Lens' (ClosedInterval r) r
end) r -> HalfOpenInterval r -> Ordering
forall r interval.
(Ord r, Interval_ interval r) =>
r -> interval -> Ordering
`compareInterval` HalfOpenInterval r
hoInt of
            Ordering
LT -> Bool
False
            Ordering
EQ -> Bool
True
            Ordering
GT -> Bool
True
    Ordering
EQ -> Bool
True
    Ordering
GT -> Bool
False -- by invariant, closedInt^.end > closedInt.start, so they don't intersect