--------------------------------------------------------------------------------
-- |
-- Module      :  HGeometry.Boundary
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--------------------------------------------------------------------------------
module HGeometry.Boundary
  ( Boundary(..)
  , _Boundary
  , PointLocationResult(..)
  , PointLocationResultWith(..)
  , asPointLocationResult
  ) where

import Control.Lens (iso,Iso)
import HGeometry.Properties
-- import HGeometry.Transformation.Internal

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

-- | The boundary of a geometric object.
newtype Boundary g = Boundary g
                   deriving (Int -> Boundary g -> ShowS
[Boundary g] -> ShowS
Boundary g -> String
(Int -> Boundary g -> ShowS)
-> (Boundary g -> String)
-> ([Boundary g] -> ShowS)
-> Show (Boundary g)
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$cshowsPrec :: forall g. Show g => Int -> Boundary g -> ShowS
showsPrec :: Int -> Boundary g -> ShowS
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(Boundary g -> Boundary g -> Bool)
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$cmax :: forall g. Ord g => Boundary g -> Boundary g -> Boundary g
max :: Boundary g -> Boundary g -> Boundary g
$cmin :: forall g. Ord g => Boundary g -> Boundary g -> Boundary g
min :: Boundary g -> Boundary g -> Boundary g
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                            ,(forall a b. (a -> b) -> Boundary a -> Boundary b)
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fold :: forall m. Monoid m => Boundary m -> m
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foldMap :: forall m a. Monoid m => (a -> m) -> Boundary a -> m
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$ctoList :: forall a. Boundary a -> [a]
toList :: forall a. Boundary a -> [a]
$cnull :: forall a. Boundary a -> Bool
null :: forall a. Boundary a -> Bool
$clength :: forall a. Boundary a -> Int
length :: forall a. Boundary a -> Int
$celem :: forall a. Eq a => a -> Boundary a -> Bool
elem :: forall a. Eq a => a -> Boundary a -> Bool
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maximum :: forall a. Ord a => Boundary a -> a
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product :: forall a. Num a => Boundary a -> a
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Boundary (f a) -> f (Boundary a)
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type instance NumType (Boundary g)   = NumType g
type instance Dimension (Boundary g) = Dimension g

-- | Iso for converting between things with a boundary and without its boundary
_Boundary :: Iso g h (Boundary g) (Boundary h)
_Boundary :: forall g h (p :: * -> * -> *) (f :: * -> *).
(Profunctor p, Functor f) =>
p (Boundary g) (f (Boundary h)) -> p g (f h)
_Boundary = (g -> Boundary g)
-> (Boundary h -> h) -> Iso g h (Boundary g) (Boundary h)
forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso g -> Boundary g
forall g. g -> Boundary g
Boundary (\(Boundary h
b) -> h
b)


-- | Result of a query that asks if something is Inside a g, *on* the boundary
-- of the g, or outside.
data PointLocationResult = Inside
                         | OnBoundary
                         | Outside
                         deriving (Int -> PointLocationResult -> ShowS
[PointLocationResult] -> ShowS
PointLocationResult -> String
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-> Show PointLocationResult
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-- | Result of a query that asks if something is Inside a g, *on* the
-- boundary of the g, or outside. This type allows us to provide some
-- sort of proof for the claim.
data PointLocationResultWith edge = StrictlyInside
                                  | OnBoundaryEdge !edge
                                  | StrictlyOutside
                                  deriving (Int -> PointLocationResultWith edge -> ShowS
[PointLocationResultWith edge] -> ShowS
PointLocationResultWith edge -> String
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-- | Forget on which edge the point was.
asPointLocationResult :: PointLocationResultWith edge -> PointLocationResult
asPointLocationResult :: forall edge. PointLocationResultWith edge -> PointLocationResult
asPointLocationResult = \case
  PointLocationResultWith edge
StrictlyInside   -> PointLocationResult
Inside
  OnBoundaryEdge edge
_ -> PointLocationResult
OnBoundary
  PointLocationResultWith edge
StrictlyOutside  -> PointLocationResult
Outside