{-# LANGUAGE UndecidableInstances #-}
{- HLINT ignore "Use camelCase" -}
--------------------------------------------------------------------------------
-- |
-- Module      :  HGeometry.HalfSpace.Type
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--
-- Representing halfspaces
--
--------------------------------------------------------------------------------
module HGeometry.HalfSpace.Type
  ( HalfSpaceF(..), HalfPlaneF
  , HalfSpace
  , Sign(..)
  , module HGeometry.HalfSpace.Class

  , Point_x_HalfSpace_Intersection(..)


  , boundingHyperPlaneLens
  ) where

import Control.Lens
import Data.Bifoldable
import Data.Bifoldable1
import Data.Bitraversable
import Data.Semigroup.Bitraversable
import HGeometry.HalfSpace.Class
import HGeometry.HyperPlane
import HGeometry.Intersection
import HGeometry.Point
import HGeometry.Properties (NumType,Dimension)
import HGeometry.Sign
import HGeometry.Vector
import GHC.TypeNats

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

-- | A HalfSpace bounded by a hyperplane. The sign indicates which
-- side of the bounding hyperplane is indicated. Iff the sign is
-- positive, we mean the points for which onSideTest returns a
-- positive value.
--
-- Half spaces include their bounding hyperplane.
data HalfSpaceF boundingHyperPlane =
    HalfSpace {-# UNPACK #-} !Sign boundingHyperPlane
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         , Dimension boundingHyperPlane ~ d
         ) => HalfSpace_ (HalfSpaceF boundingHyperPlane) d r where
  type BoundingHyperPlane (HalfSpaceF boundingHyperPlane) d r = boundingHyperPlane

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-- | Lens to access the hyperplane bounding the halfspace
--
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-- is useful if you need a lens to change the type of the bounding hyperplane.
boundingHyperPlaneLens :: Lens (HalfSpaceF boundingHyperPlane) (HalfSpaceF boundingHyperPlane')
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{-# INLINE boundingHyperPlaneLens #-}



-- | Arbitrary halfspaces in r^d.
type HalfSpace d r = HalfSpaceF (HyperPlane d r)

-- | A Halfplane (which is just a Halfspace in R^2)
type HalfPlaneF line = HalfSpaceF line

type instance Dimension (HalfSpaceF boundingHyperPlane) = Dimension boundingHyperPlane
type instance NumType   (HalfSpaceF boundingHyperPlane) = NumType boundingHyperPlane

instance ( HyperPlane_ boudingHyperPlane d r, Ord r, Num r
         , Has_ Additive_ d r
         ) => HasIntersectionWith (Point d r) (HalfSpaceF boudingHyperPlane)

type instance Intersection (Point d r) (HalfSpaceF boudingHyperPlane) =
  Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))

-- | Point x HalfSpace intersection
data Point_x_HalfSpace_Intersection boundaryPoint interiorPoint =
    Point_x_HalfSpace_OnBoundary boundaryPoint
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-> Point_x_HalfSpace_Intersection boundaryPoint a -> a
forall boundaryPoint a.
Eq a =>
a -> Point_x_HalfSpace_Intersection boundaryPoint a -> Bool
forall boundaryPoint a.
Num a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
forall boundaryPoint a.
Ord a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
forall boundaryPoint m.
Monoid m =>
Point_x_HalfSpace_Intersection boundaryPoint m -> m
forall m a.
Monoid m =>
(a -> m) -> Point_x_HalfSpace_Intersection boundaryPoint a -> m
forall boundaryPoint a.
Point_x_HalfSpace_Intersection boundaryPoint a -> Bool
forall boundaryPoint a.
Point_x_HalfSpace_Intersection boundaryPoint a -> Int
forall boundaryPoint a.
Point_x_HalfSpace_Intersection boundaryPoint a -> [a]
forall b a.
(b -> a -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
forall a b.
(a -> b -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
forall boundaryPoint a.
(a -> a -> a)
-> Point_x_HalfSpace_Intersection boundaryPoint a -> a
forall boundaryPoint m a.
Monoid m =>
(a -> m) -> Point_x_HalfSpace_Intersection boundaryPoint a -> m
forall boundaryPoint b a.
(b -> a -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
forall boundaryPoint a b.
(a -> b -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
forall (t :: * -> *).
(forall m. Monoid m => t m -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall m a. Monoid m => (a -> m) -> t a -> m)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall a b. (a -> b -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall b a. (b -> a -> b) -> b -> t a -> b)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. (a -> a -> a) -> t a -> a)
-> (forall a. t a -> [a])
-> (forall a. t a -> Bool)
-> (forall a. t a -> Int)
-> (forall a. Eq a => a -> t a -> Bool)
-> (forall a. Ord a => t a -> a)
-> (forall a. Ord a => t a -> a)
-> (forall a. Num a => t a -> a)
-> (forall a. Num a => t a -> a)
-> Foldable t
$cfold :: forall boundaryPoint m.
Monoid m =>
Point_x_HalfSpace_Intersection boundaryPoint m -> m
fold :: forall m.
Monoid m =>
Point_x_HalfSpace_Intersection boundaryPoint m -> m
$cfoldMap :: forall boundaryPoint m a.
Monoid m =>
(a -> m) -> Point_x_HalfSpace_Intersection boundaryPoint a -> m
foldMap :: forall m a.
Monoid m =>
(a -> m) -> Point_x_HalfSpace_Intersection boundaryPoint a -> m
$cfoldMap' :: forall boundaryPoint m a.
Monoid m =>
(a -> m) -> Point_x_HalfSpace_Intersection boundaryPoint a -> m
foldMap' :: forall m a.
Monoid m =>
(a -> m) -> Point_x_HalfSpace_Intersection boundaryPoint a -> m
$cfoldr :: forall boundaryPoint a b.
(a -> b -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
foldr :: forall a b.
(a -> b -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
$cfoldr' :: forall boundaryPoint a b.
(a -> b -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
foldr' :: forall a b.
(a -> b -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
$cfoldl :: forall boundaryPoint b a.
(b -> a -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
foldl :: forall b a.
(b -> a -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
$cfoldl' :: forall boundaryPoint b a.
(b -> a -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
foldl' :: forall b a.
(b -> a -> b)
-> b -> Point_x_HalfSpace_Intersection boundaryPoint a -> b
$cfoldr1 :: forall boundaryPoint a.
(a -> a -> a)
-> Point_x_HalfSpace_Intersection boundaryPoint a -> a
foldr1 :: forall a.
(a -> a -> a)
-> Point_x_HalfSpace_Intersection boundaryPoint a -> a
$cfoldl1 :: forall boundaryPoint a.
(a -> a -> a)
-> Point_x_HalfSpace_Intersection boundaryPoint a -> a
foldl1 :: forall a.
(a -> a -> a)
-> Point_x_HalfSpace_Intersection boundaryPoint a -> a
$ctoList :: forall boundaryPoint a.
Point_x_HalfSpace_Intersection boundaryPoint a -> [a]
toList :: forall a. Point_x_HalfSpace_Intersection boundaryPoint a -> [a]
$cnull :: forall boundaryPoint a.
Point_x_HalfSpace_Intersection boundaryPoint a -> Bool
null :: forall a. Point_x_HalfSpace_Intersection boundaryPoint a -> Bool
$clength :: forall boundaryPoint a.
Point_x_HalfSpace_Intersection boundaryPoint a -> Int
length :: forall a. Point_x_HalfSpace_Intersection boundaryPoint a -> Int
$celem :: forall boundaryPoint a.
Eq a =>
a -> Point_x_HalfSpace_Intersection boundaryPoint a -> Bool
elem :: forall a.
Eq a =>
a -> Point_x_HalfSpace_Intersection boundaryPoint a -> Bool
$cmaximum :: forall boundaryPoint a.
Ord a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
maximum :: forall a.
Ord a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
$cminimum :: forall boundaryPoint a.
Ord a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
minimum :: forall a.
Ord a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
$csum :: forall boundaryPoint a.
Num a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
sum :: forall a.
Num a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
$cproduct :: forall boundaryPoint a.
Num a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
product :: forall a.
Num a =>
Point_x_HalfSpace_Intersection boundaryPoint a -> a
Foldable,Functor (Point_x_HalfSpace_Intersection boundaryPoint)
Foldable (Point_x_HalfSpace_Intersection boundaryPoint)
(Functor (Point_x_HalfSpace_Intersection boundaryPoint),
 Foldable (Point_x_HalfSpace_Intersection boundaryPoint)) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b)
 -> Point_x_HalfSpace_Intersection boundaryPoint a
 -> f (Point_x_HalfSpace_Intersection boundaryPoint b))
-> (forall (f :: * -> *) a.
    Applicative f =>
    Point_x_HalfSpace_Intersection boundaryPoint (f a)
    -> f (Point_x_HalfSpace_Intersection boundaryPoint a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b)
    -> Point_x_HalfSpace_Intersection boundaryPoint a
    -> m (Point_x_HalfSpace_Intersection boundaryPoint b))
-> (forall (m :: * -> *) a.
    Monad m =>
    Point_x_HalfSpace_Intersection boundaryPoint (m a)
    -> m (Point_x_HalfSpace_Intersection boundaryPoint a))
-> Traversable (Point_x_HalfSpace_Intersection boundaryPoint)
forall boundaryPoint.
Functor (Point_x_HalfSpace_Intersection boundaryPoint)
forall boundaryPoint.
Foldable (Point_x_HalfSpace_Intersection boundaryPoint)
forall boundaryPoint (m :: * -> *) a.
Monad m =>
Point_x_HalfSpace_Intersection boundaryPoint (m a)
-> m (Point_x_HalfSpace_Intersection boundaryPoint a)
forall boundaryPoint (f :: * -> *) a.
Applicative f =>
Point_x_HalfSpace_Intersection boundaryPoint (f a)
-> f (Point_x_HalfSpace_Intersection boundaryPoint a)
forall boundaryPoint (m :: * -> *) a b.
Monad m =>
(a -> m b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> m (Point_x_HalfSpace_Intersection boundaryPoint b)
forall boundaryPoint (f :: * -> *) a b.
Applicative f =>
(a -> f b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> f (Point_x_HalfSpace_Intersection boundaryPoint b)
forall (t :: * -> *).
(Functor t, Foldable t) =>
(forall (f :: * -> *) a b.
 Applicative f =>
 (a -> f b) -> t a -> f (t b))
-> (forall (f :: * -> *) a. Applicative f => t (f a) -> f (t a))
-> (forall (m :: * -> *) a b.
    Monad m =>
    (a -> m b) -> t a -> m (t b))
-> (forall (m :: * -> *) a. Monad m => t (m a) -> m (t a))
-> Traversable t
forall (m :: * -> *) a.
Monad m =>
Point_x_HalfSpace_Intersection boundaryPoint (m a)
-> m (Point_x_HalfSpace_Intersection boundaryPoint a)
forall (f :: * -> *) a.
Applicative f =>
Point_x_HalfSpace_Intersection boundaryPoint (f a)
-> f (Point_x_HalfSpace_Intersection boundaryPoint a)
forall (m :: * -> *) a b.
Monad m =>
(a -> m b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> m (Point_x_HalfSpace_Intersection boundaryPoint b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> f (Point_x_HalfSpace_Intersection boundaryPoint b)
$ctraverse :: forall boundaryPoint (f :: * -> *) a b.
Applicative f =>
(a -> f b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> f (Point_x_HalfSpace_Intersection boundaryPoint b)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> f (Point_x_HalfSpace_Intersection boundaryPoint b)
$csequenceA :: forall boundaryPoint (f :: * -> *) a.
Applicative f =>
Point_x_HalfSpace_Intersection boundaryPoint (f a)
-> f (Point_x_HalfSpace_Intersection boundaryPoint a)
sequenceA :: forall (f :: * -> *) a.
Applicative f =>
Point_x_HalfSpace_Intersection boundaryPoint (f a)
-> f (Point_x_HalfSpace_Intersection boundaryPoint a)
$cmapM :: forall boundaryPoint (m :: * -> *) a b.
Monad m =>
(a -> m b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> m (Point_x_HalfSpace_Intersection boundaryPoint b)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b)
-> Point_x_HalfSpace_Intersection boundaryPoint a
-> m (Point_x_HalfSpace_Intersection boundaryPoint b)
$csequence :: forall boundaryPoint (m :: * -> *) a.
Monad m =>
Point_x_HalfSpace_Intersection boundaryPoint (m a)
-> m (Point_x_HalfSpace_Intersection boundaryPoint a)
sequence :: forall (m :: * -> *) a.
Monad m =>
Point_x_HalfSpace_Intersection boundaryPoint (m a)
-> m (Point_x_HalfSpace_Intersection boundaryPoint a)
Traversable)

instance Bifunctor Point_x_HalfSpace_Intersection where
  bimap :: forall a b c d.
(a -> b)
-> (c -> d)
-> Point_x_HalfSpace_Intersection a c
-> Point_x_HalfSpace_Intersection b d
bimap a -> b
f c -> d
g = \case
    Point_x_HalfSpace_OnBoundary a
p -> b -> Point_x_HalfSpace_Intersection b d
forall boundaryPoint interiorPoint.
boundaryPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_OnBoundary (a -> b
f a
p)
    Point_x_HalfSpace_Interior c
p   -> d -> Point_x_HalfSpace_Intersection b d
forall boundaryPoint interiorPoint.
interiorPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_Interior (c -> d
g c
p)

instance Bifoldable Point_x_HalfSpace_Intersection where
  bifoldMap :: forall m a b.
Monoid m =>
(a -> m) -> (b -> m) -> Point_x_HalfSpace_Intersection a b -> m
bifoldMap = (a -> m) -> (b -> m) -> Point_x_HalfSpace_Intersection a b -> m
forall m a b.
Semigroup m =>
(a -> m) -> (b -> m) -> Point_x_HalfSpace_Intersection a b -> m
forall (t :: * -> * -> *) m a b.
(Bifoldable1 t, Semigroup m) =>
(a -> m) -> (b -> m) -> t a b -> m
bifoldMap1

instance Bifoldable1 Point_x_HalfSpace_Intersection where
  bifoldMap1 :: forall m a b.
Semigroup m =>
(a -> m) -> (b -> m) -> Point_x_HalfSpace_Intersection a b -> m
bifoldMap1 a -> m
f b -> m
g = \case
    Point_x_HalfSpace_OnBoundary a
p -> a -> m
f a
p
    Point_x_HalfSpace_Interior b
p   -> b -> m
g b
p

instance Bitraversable Point_x_HalfSpace_Intersection where
  bitraverse :: forall (f :: * -> *) a c b d.
Applicative f =>
(a -> f c)
-> (b -> f d)
-> Point_x_HalfSpace_Intersection a b
-> f (Point_x_HalfSpace_Intersection c d)
bitraverse a -> f c
f b -> f d
g = \case
    Point_x_HalfSpace_OnBoundary a
p -> c -> Point_x_HalfSpace_Intersection c d
forall boundaryPoint interiorPoint.
boundaryPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_OnBoundary (c -> Point_x_HalfSpace_Intersection c d)
-> f c -> f (Point_x_HalfSpace_Intersection c d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f c
f a
p
    Point_x_HalfSpace_Interior b
p   -> d -> Point_x_HalfSpace_Intersection c d
forall boundaryPoint interiorPoint.
interiorPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_Interior   (d -> Point_x_HalfSpace_Intersection c d)
-> f d -> f (Point_x_HalfSpace_Intersection c d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> b -> f d
g b
p

instance Bitraversable1 Point_x_HalfSpace_Intersection where
  bitraverse1 :: forall (f :: * -> *) a b c d.
Apply f =>
(a -> f b)
-> (c -> f d)
-> Point_x_HalfSpace_Intersection a c
-> f (Point_x_HalfSpace_Intersection b d)
bitraverse1 a -> f b
f c -> f d
g = \case
    Point_x_HalfSpace_OnBoundary a
p -> b -> Point_x_HalfSpace_Intersection b d
forall boundaryPoint interiorPoint.
boundaryPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_OnBoundary (b -> Point_x_HalfSpace_Intersection b d)
-> f b -> f (Point_x_HalfSpace_Intersection b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f b
f a
p
    Point_x_HalfSpace_Interior c
p   -> d -> Point_x_HalfSpace_Intersection b d
forall boundaryPoint interiorPoint.
interiorPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_Interior   (d -> Point_x_HalfSpace_Intersection b d)
-> f d -> f (Point_x_HalfSpace_Intersection b d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> c -> f d
g c
p



instance ( HyperPlane_ boudingHyperPlane d r, Ord r, Num r
         , Has_ Additive_ d r
         ) => IsIntersectableWith (Point d r) (HalfSpaceF boudingHyperPlane) where
  Point d r
q intersect :: Point d r
-> HalfSpaceF boudingHyperPlane
-> Intersection (Point d r) (HalfSpaceF boudingHyperPlane)
`intersect` (HalfSpace Sign
s boudingHyperPlane
h) = case Sign
s of
    Sign
Positive -> case Point d r
q Point d r -> boudingHyperPlane -> Ordering
forall point.
(Point_ point d r, Ord r, Num r) =>
point -> boudingHyperPlane -> Ordering
forall hyperPlane (d :: Nat) r point.
(HyperPlane_ hyperPlane d r, Point_ point d r, Ord r, Num r) =>
point -> hyperPlane -> Ordering
`onSideTest` boudingHyperPlane
h of
                  Ordering
LT -> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
Intersection (Point d r) (HalfSpaceF boudingHyperPlane)
forall a. Maybe a
Nothing
                  Ordering
EQ -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a. a -> Maybe a
Just (Point_x_HalfSpace_Intersection (Point d r) (Point d r)
 -> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r)))
-> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a b. (a -> b) -> a -> b
$ Point d r -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
forall boundaryPoint interiorPoint.
boundaryPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_OnBoundary Point d r
q
                  Ordering
GT -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a. a -> Maybe a
Just (Point_x_HalfSpace_Intersection (Point d r) (Point d r)
 -> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r)))
-> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a b. (a -> b) -> a -> b
$ Point d r -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
forall boundaryPoint interiorPoint.
interiorPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_Interior Point d r
q
    Sign
Negative -> case Point d r
q Point d r -> boudingHyperPlane -> Ordering
forall point.
(Point_ point d r, Ord r, Num r) =>
point -> boudingHyperPlane -> Ordering
forall hyperPlane (d :: Nat) r point.
(HyperPlane_ hyperPlane d r, Point_ point d r, Ord r, Num r) =>
point -> hyperPlane -> Ordering
`onSideTest` boudingHyperPlane
h of
                  Ordering
LT -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a. a -> Maybe a
Just (Point_x_HalfSpace_Intersection (Point d r) (Point d r)
 -> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r)))
-> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a b. (a -> b) -> a -> b
$ Point d r -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
forall boundaryPoint interiorPoint.
interiorPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_Interior Point d r
q
                  Ordering
EQ -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a. a -> Maybe a
Just (Point_x_HalfSpace_Intersection (Point d r) (Point d r)
 -> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r)))
-> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
-> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
forall a b. (a -> b) -> a -> b
$ Point d r -> Point_x_HalfSpace_Intersection (Point d r) (Point d r)
forall boundaryPoint interiorPoint.
boundaryPoint
-> Point_x_HalfSpace_Intersection boundaryPoint interiorPoint
Point_x_HalfSpace_OnBoundary Point d r
q
                  Ordering
GT -> Maybe (Point_x_HalfSpace_Intersection (Point d r) (Point d r))
Intersection (Point d r) (HalfSpaceF boudingHyperPlane)
forall a. Maybe a
Nothing

instance ( HasSquaredEuclideanDistance boundingHyperPlane
         , HasIntersectionWith (Point d r) (HalfSpaceF boundingHyperPlane)
         , d ~ Dimension boundingHyperPlane, r ~ NumType boundingHyperPlane
         )
         => HasSquaredEuclideanDistance (HalfSpaceF boundingHyperPlane) where
  pointClosestTo :: forall r (d :: Nat) point.
(r ~ NumType (HalfSpaceF boundingHyperPlane),
 d ~ Dimension (HalfSpaceF boundingHyperPlane), Num r,
 Point_ point d r) =>
point -> HalfSpaceF boundingHyperPlane -> Point d r
pointClosestTo (Getting (Point d r) point (Point d r) -> point -> Point d r
forall s (m :: * -> *) a. MonadReader s m => Getting a s a -> m a
view Getting (Point d r) point (Point d r)
forall point (d :: Nat) r.
Point_ point d r =>
Lens' point (Point d r)
Lens' point (Point d r)
asPoint -> Point d r
q) HalfSpaceF boundingHyperPlane
h
    | Point d r
q Point d r -> HalfSpaceF boundingHyperPlane -> Bool
forall g h. HasIntersectionWith g h => g -> h -> Bool
`intersects` HalfSpaceF boundingHyperPlane
h = Point d r
q
    | Bool
otherwise        = Point d r -> boundingHyperPlane -> Point d r
forall g r (d :: Nat) point.
(HasSquaredEuclideanDistance g, r ~ NumType g, d ~ Dimension g,
 Num r, Point_ point d r) =>
point -> g -> Point d r
forall r (d :: Nat) point.
(r ~ NumType boundingHyperPlane, d ~ Dimension boundingHyperPlane,
 Num r, Point_ point d r) =>
point -> boundingHyperPlane -> Point d r
pointClosestTo Point d r
q (HalfSpaceF boundingHyperPlane
hHalfSpaceF boundingHyperPlane
-> Getting
     boundingHyperPlane
     (HalfSpaceF boundingHyperPlane)
     boundingHyperPlane
-> boundingHyperPlane
forall s a. s -> Getting a s a -> a
^.Getting
  boundingHyperPlane
  (HalfSpaceF boundingHyperPlane)
  boundingHyperPlane
(BoundingHyperPlane (HalfSpaceF boundingHyperPlane) d r
 -> Const
      boundingHyperPlane
      (BoundingHyperPlane (HalfSpaceF boundingHyperPlane) d r))
-> HalfSpaceF boundingHyperPlane
-> Const boundingHyperPlane (HalfSpaceF boundingHyperPlane)
forall halfSpace (d :: Nat) r.
HalfSpace_ halfSpace d r =>
Lens' halfSpace (BoundingHyperPlane halfSpace d r)
Lens'
  (HalfSpaceF boundingHyperPlane)
  (BoundingHyperPlane (HalfSpaceF boundingHyperPlane) d r)
boundingHyperPlane)


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


instance ( HasIntersectionWith line line'
         , HyperPlane_ line 2 r, HyperPlane_ line' 2 r
         , Ord r, Fractional r
         , HasPickInteriorPoint line 2 r, HasPickInteriorPoint line' 2 r
         )
       => HasIntersectionWith (HalfSpaceF line) (HalfSpaceF line') where
  h :: HalfSpaceF line
h@(HalfSpace Sign
_ line
l) intersects :: HalfSpaceF line -> HalfSpaceF line' -> Bool
`intersects` h' :: HalfSpaceF line'
h'@(HalfSpace Sign
_ line'
l') =
    line
l line -> line' -> Bool
forall g h. HasIntersectionWith g h => g -> h -> Bool
`intersects` line'
l' Bool -> Bool -> Bool
|| line -> Point 2 r
forall geom (d :: Nat) r.
HasPickInteriorPoint geom d r =>
geom -> Point d r
pointInteriorTo line
l Point 2 r -> HalfSpaceF line' -> Bool
forall g h. HasIntersectionWith g h => g -> h -> Bool
`intersects`  HalfSpaceF line'
h' Bool -> Bool -> Bool
|| line' -> Point 2 r
forall geom (d :: Nat) r.
HasPickInteriorPoint geom d r =>
geom -> Point d r
pointInteriorTo line'
l' Point 2 r -> HalfSpaceF line -> Bool
forall g h. HasIntersectionWith g h => g -> h -> Bool
`intersects`  HalfSpaceF line
h


instance ( HasPickInteriorPoint hyperPlane d r
         , HyperPlane_ hyperPlane d r
         , 1 <= d, Eq r, Num r
         , Has_ Additive_ d r
         , Has_ Vector_ (1+d) r
         ) => HasPickInteriorPoint (HalfSpaceF hyperPlane) d r where
  pointInteriorTo :: HalfSpaceF hyperPlane -> Point d r
pointInteriorTo HalfSpaceF hyperPlane
h = Point d r
p Point d r -> Vector d r -> Point d r
forall point (d :: Nat) r.
(Affine_ point d r, Num r) =>
point -> Vector d r -> point
.+^ Vector d r -> Vector d r
f (hyperPlane -> Vector d r
forall hyperPlane (d :: Nat) r.
(HyperPlane_ hyperPlane d r, Num r, Eq r, 1 <= d) =>
hyperPlane -> Vector d r
normalVector hyperPlane
l)
    where
      l :: hyperPlane
l = HalfSpaceF hyperPlane
hHalfSpaceF hyperPlane
-> Getting hyperPlane (HalfSpaceF hyperPlane) hyperPlane
-> hyperPlane
forall s a. s -> Getting a s a -> a
^.Getting hyperPlane (HalfSpaceF hyperPlane) hyperPlane
(BoundingHyperPlane (HalfSpaceF hyperPlane) d r
 -> Const
      hyperPlane (BoundingHyperPlane (HalfSpaceF hyperPlane) d r))
-> HalfSpaceF hyperPlane
-> Const hyperPlane (HalfSpaceF hyperPlane)
forall halfSpace (d :: Nat) r.
HalfSpace_ halfSpace d r =>
Lens' halfSpace (BoundingHyperPlane halfSpace d r)
Lens'
  (HalfSpaceF hyperPlane)
  (BoundingHyperPlane (HalfSpaceF hyperPlane) d r)
boundingHyperPlane
      p :: Point d r
p = hyperPlane -> Point d r
forall geom (d :: Nat) r.
HasPickInteriorPoint geom d r =>
geom -> Point d r
pointInteriorTo hyperPlane
l
      f :: Vector d r -> Vector d r
f = case HalfSpaceF hyperPlane
hHalfSpaceF hyperPlane
-> Getting Sign (HalfSpaceF hyperPlane) Sign -> Sign
forall s a. s -> Getting a s a -> a
^.Getting Sign (HalfSpaceF hyperPlane) Sign
forall halfSpace (d :: Nat) r.
HalfSpace_ halfSpace d r =>
Lens' halfSpace Sign
Lens' (HalfSpaceF hyperPlane) Sign
halfSpaceSign of
            Sign
Positive -> Vector d r -> Vector d r
forall a. a -> a
id
            Sign
Negative -> Vector d r -> Vector d r
forall r vector (d :: Nat).
(Num r, Vector_ vector d r) =>
vector -> vector
negated
      -- the normalVector of l should point towards the positive halfspace of l


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