{-# OPTIONS_GHC -Wno-orphans #-}
{-# LANGUAGE UndecidableInstances #-}
{- HLINT ignore "Use camelCase" -}
--------------------------------------------------------------------------------
-- |
-- Module      :  HGeometry.HyperPlane.Intersection
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--
-- Intersection between hyperplanes in R^3
--
--------------------------------------------------------------------------------
module HGeometry.HyperPlane.Intersection
  ( PlanePlaneIntersection(..)
  , planePlaneIntersection
  ) where

import Data.Bifoldable
import Data.Bifunctor
import Data.Bitraversable
import Data.Type.Ord
import GHC.TypeNats
import HGeometry.HyperPlane.Class
import HGeometry.HyperPlane.Internal
import HGeometry.HyperPlane.NonVertical
import HGeometry.Intersection
import HGeometry.Line.General
import HGeometry.Line.LineEQ
import HGeometry.Vector

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

type instance Intersection (HyperPlane 3 r) (HyperPlane 3 r) =
  Maybe (PlanePlaneIntersection (Plane r) (VerticalOrLineEQ r))

type instance Intersection (Plane r) (Plane r) =
  Maybe (PlanePlaneIntersection (Plane r) (VerticalOrLineEQ r))

-- | The intersection between two planes in R^3.
data PlanePlaneIntersection plane line = Plane_x_Plane_Line line
                                       | Plane_x_Plane_Plane plane
                                       deriving (Int -> PlanePlaneIntersection plane line -> ShowS
[PlanePlaneIntersection plane line] -> ShowS
PlanePlaneIntersection plane line -> String
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PlanePlaneIntersection plane line -> String
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 -> PlanePlaneIntersection plane line -> Bool)
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PlanePlaneIntersection plane line
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fold :: forall m. Monoid m => PlanePlaneIntersection plane m -> m
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(a -> m) -> PlanePlaneIntersection plane a -> m
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(a -> m) -> PlanePlaneIntersection plane a -> m
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(a -> m) -> PlanePlaneIntersection plane a -> m
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(a -> m) -> PlanePlaneIntersection plane a -> m
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(a -> b -> b) -> b -> PlanePlaneIntersection plane a -> b
foldr :: forall a b.
(a -> b -> b) -> b -> PlanePlaneIntersection plane a -> b
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(a -> b -> b) -> b -> PlanePlaneIntersection plane a -> b
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(a -> b -> b) -> b -> PlanePlaneIntersection plane a -> b
$cfoldl :: forall plane b a.
(b -> a -> b) -> b -> PlanePlaneIntersection plane a -> b
foldl :: forall b a.
(b -> a -> b) -> b -> PlanePlaneIntersection plane a -> b
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(a -> a -> a) -> PlanePlaneIntersection plane a -> a
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(a -> a -> a) -> PlanePlaneIntersection plane a -> a
foldl1 :: forall a. (a -> a -> a) -> PlanePlaneIntersection plane a -> a
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toList :: forall a. PlanePlaneIntersection plane a -> [a]
$cnull :: forall plane a. PlanePlaneIntersection plane a -> Bool
null :: forall a. PlanePlaneIntersection plane a -> Bool
$clength :: forall plane a. PlanePlaneIntersection plane a -> Int
length :: forall a. PlanePlaneIntersection plane a -> Int
$celem :: forall plane a. Eq a => a -> PlanePlaneIntersection plane a -> Bool
elem :: forall a. Eq a => a -> PlanePlaneIntersection plane a -> Bool
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maximum :: forall a. Ord a => PlanePlaneIntersection plane a -> a
$cminimum :: forall plane a. Ord a => PlanePlaneIntersection plane a -> a
minimum :: forall a. Ord a => PlanePlaneIntersection plane a -> a
$csum :: forall plane a. Num a => PlanePlaneIntersection plane a -> a
sum :: forall a. Num a => PlanePlaneIntersection plane a -> a
$cproduct :: forall plane a. Num a => PlanePlaneIntersection plane a -> a
product :: forall a. Num a => PlanePlaneIntersection plane a -> a
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 Foldable (PlanePlaneIntersection plane)) =>
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forall (m :: * -> *) a.
Monad m =>
PlanePlaneIntersection plane (m a)
-> m (PlanePlaneIntersection plane a)
forall (f :: * -> *) a.
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PlanePlaneIntersection plane (f a)
-> f (PlanePlaneIntersection plane a)
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forall (f :: * -> *) a b.
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(a -> f b)
-> PlanePlaneIntersection plane a
-> f (PlanePlaneIntersection plane b)
$ctraverse :: forall plane (f :: * -> *) a b.
Applicative f =>
(a -> f b)
-> PlanePlaneIntersection plane a
-> f (PlanePlaneIntersection plane b)
traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b)
-> PlanePlaneIntersection plane a
-> f (PlanePlaneIntersection plane b)
$csequenceA :: forall plane (f :: * -> *) a.
Applicative f =>
PlanePlaneIntersection plane (f a)
-> f (PlanePlaneIntersection plane a)
sequenceA :: forall (f :: * -> *) a.
Applicative f =>
PlanePlaneIntersection plane (f a)
-> f (PlanePlaneIntersection plane a)
$cmapM :: forall plane (m :: * -> *) a b.
Monad m =>
(a -> m b)
-> PlanePlaneIntersection plane a
-> m (PlanePlaneIntersection plane b)
mapM :: forall (m :: * -> *) a b.
Monad m =>
(a -> m b)
-> PlanePlaneIntersection plane a
-> m (PlanePlaneIntersection plane b)
$csequence :: forall plane (m :: * -> *) a.
Monad m =>
PlanePlaneIntersection plane (m a)
-> m (PlanePlaneIntersection plane a)
sequence :: forall (m :: * -> *) a.
Monad m =>
PlanePlaneIntersection plane (m a)
-> m (PlanePlaneIntersection plane a)
Traversable)

instance Bifunctor PlanePlaneIntersection where
  bimap :: forall a b c d.
(a -> b)
-> (c -> d)
-> PlanePlaneIntersection a c
-> PlanePlaneIntersection b d
bimap a -> b
f c -> d
g = \case
    Plane_x_Plane_Line  c
l -> d -> PlanePlaneIntersection b d
forall plane line. line -> PlanePlaneIntersection plane line
Plane_x_Plane_Line (d -> PlanePlaneIntersection b d)
-> d -> PlanePlaneIntersection b d
forall a b. (a -> b) -> a -> b
$ c -> d
g c
l
    Plane_x_Plane_Plane a
h -> b -> PlanePlaneIntersection b d
forall plane line. plane -> PlanePlaneIntersection plane line
Plane_x_Plane_Plane (b -> PlanePlaneIntersection b d)
-> b -> PlanePlaneIntersection b d
forall a b. (a -> b) -> a -> b
$ a -> b
f a
h

instance Bifoldable PlanePlaneIntersection where
  bifoldMap :: forall m a b.
Monoid m =>
(a -> m) -> (b -> m) -> PlanePlaneIntersection a b -> m
bifoldMap a -> m
f b -> m
g = \case
    Plane_x_Plane_Line  b
l -> b -> m
g b
l
    Plane_x_Plane_Plane a
h -> a -> m
f a
h

instance Bitraversable PlanePlaneIntersection where
  bitraverse :: forall (f :: * -> *) a c b d.
Applicative f =>
(a -> f c)
-> (b -> f d)
-> PlanePlaneIntersection a b
-> f (PlanePlaneIntersection c d)
bitraverse a -> f c
f b -> f d
g = \case
    Plane_x_Plane_Line  b
l -> d -> PlanePlaneIntersection c d
forall plane line. line -> PlanePlaneIntersection plane line
Plane_x_Plane_Line (d -> PlanePlaneIntersection c d)
-> f d -> f (PlanePlaneIntersection c d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> b -> f d
g b
l
    Plane_x_Plane_Plane a
h -> c -> PlanePlaneIntersection c d
forall plane line. plane -> PlanePlaneIntersection plane line
Plane_x_Plane_Plane (c -> PlanePlaneIntersection c d)
-> f c -> f (PlanePlaneIntersection c d)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> a -> f c
f a
h

instance ( Has_ Metric_ d r, Num r, Eq r, 2 <= d, d < d + 1 -- this constraint is rather silly
         , Has_ Metric_ (1+d) r
         , 1 <= d, Has_ Metric_ (d + 1) r, Eq (Vector (d + 1) r), d <= d + 1
         ) => HasIntersectionWith (HyperPlane d r) (HyperPlane d r) where
  HyperPlane d r
h intersects :: HyperPlane d r -> HyperPlane d r -> Bool
`intersects` HyperPlane d r
h' = HyperPlane d r
h HyperPlane d r -> HyperPlane d r -> Bool
forall a. Eq a => a -> a -> Bool
== HyperPlane d r
h' Bool -> Bool -> Bool
|| Bool -> Bool
not (HyperPlane d r
h HyperPlane d r -> HyperPlane d r -> Bool
forall hyperPlane (d :: Nat) r hyperPlane'.
(HyperPlane_ hyperPlane d r, HyperPlane_ hyperPlane' d r,
 Has_ Metric_ d r, Num r, Eq r, 1 <= d) =>
hyperPlane -> hyperPlane' -> Bool
`isParallelTo` HyperPlane d r
h')

instance ( Has_ Metric_ d r, Num r, Eq r, 2 <= d, d < d + 1
         , Has_ Metric_ (1+d) r, Has_ Additive_ (d-1) r, Eq (Vector d r)
         , 1 <= d, Has_ Metric_ (d + 1) r, (1 + (d - 1) ~ d), d <= d + 1
         , d -1 <= d, ((d - 1) + 1) ~ d
         ) => HasIntersectionWith (NonVerticalHyperPlane d r) (NonVerticalHyperPlane d r) where
  NonVerticalHyperPlane d r
h intersects :: NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool
`intersects` NonVerticalHyperPlane d r
h' = NonVerticalHyperPlane d r
h NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool
forall a. Eq a => a -> a -> Bool
== NonVerticalHyperPlane d r
h' Bool -> Bool -> Bool
||  Bool -> Bool
not (NonVerticalHyperPlane d r
h NonVerticalHyperPlane d r -> NonVerticalHyperPlane d r -> Bool
forall hyperPlane (d :: Nat) r hyperPlane'.
(HyperPlane_ hyperPlane d r, HyperPlane_ hyperPlane' d r,
 Has_ Metric_ d r, Num r, Eq r, 1 <= d) =>
hyperPlane -> hyperPlane' -> Bool
`isParallelTo` NonVerticalHyperPlane d r
h')


instance (Eq r, Fractional r)
         => IsIntersectableWith (Plane r) (Plane r) where
  intersect :: Plane r -> Plane r -> Intersection (Plane r) (Plane r)
intersect = Plane r
-> Plane r
-> Maybe (PlanePlaneIntersection (Plane r) (VerticalOrLineEQ r))
Plane r -> Plane r -> Intersection (Plane r) (Plane r)
forall plane r.
(Plane_ plane r, Fractional r, Eq r) =>
plane
-> plane
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
planePlaneIntersection


-- | Given two planes, computes the line in which they intersect.
planePlaneIntersection :: (Plane_ plane r, Fractional r, Eq r)
                       => plane -> plane
                       -> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
planePlaneIntersection :: forall plane r.
(Plane_ plane r, Fractional r, Eq r) =>
plane
-> plane
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
planePlaneIntersection h :: plane
h@(Plane_ r
a1 r
b1 r
c1) (Plane_ r
a2 r
b2 r
c2)
    | r
b1 r -> r -> Bool
forall a. Eq a => a -> a -> Bool
/= r
b2  = PlanePlaneIntersection plane (VerticalOrLineEQ r)
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a. a -> Maybe a
Just (PlanePlaneIntersection plane (VerticalOrLineEQ r)
 -> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r)))
-> (LineEQ r -> PlanePlaneIntersection plane (VerticalOrLineEQ r))
-> LineEQ r
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. VerticalOrLineEQ r
-> PlanePlaneIntersection plane (VerticalOrLineEQ r)
forall plane line. line -> PlanePlaneIntersection plane line
Plane_x_Plane_Line (VerticalOrLineEQ r
 -> PlanePlaneIntersection plane (VerticalOrLineEQ r))
-> (LineEQ r -> VerticalOrLineEQ r)
-> LineEQ r
-> PlanePlaneIntersection plane (VerticalOrLineEQ r)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. LineEQ r -> VerticalOrLineEQ r
forall r. LineEQ r -> VerticalOrLineEQ r
NonVertical
                (LineEQ r
 -> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r)))
-> LineEQ r
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a b. (a -> b) -> a -> b
$ r -> r -> LineEQ r
forall r. r -> r -> LineEQ r
LineEQ ((r
a2 r -> r -> r
forall a. Num a => a -> a -> a
- r
a1) r -> r -> r
forall a. Fractional a => a -> a -> a
/ r
diffB) ((r
c2 r -> r -> r
forall a. Num a => a -> a -> a
- r
c1) r -> r -> r
forall a. Fractional a => a -> a -> a
/ r
diffB)
                  -- the two planes intersect in some normal line
    | r
a1 r -> r -> Bool
forall a. Eq a => a -> a -> Bool
/= r
a2  = PlanePlaneIntersection plane (VerticalOrLineEQ r)
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a. a -> Maybe a
Just (PlanePlaneIntersection plane (VerticalOrLineEQ r)
 -> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r)))
-> (VerticalOrLineEQ r
    -> PlanePlaneIntersection plane (VerticalOrLineEQ r))
-> VerticalOrLineEQ r
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall b c a. (b -> c) -> (a -> b) -> a -> c
. VerticalOrLineEQ r
-> PlanePlaneIntersection plane (VerticalOrLineEQ r)
forall plane line. line -> PlanePlaneIntersection plane line
Plane_x_Plane_Line
                (VerticalOrLineEQ r
 -> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r)))
-> VerticalOrLineEQ r
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a b. (a -> b) -> a -> b
$ r -> VerticalOrLineEQ r
forall r. r -> VerticalOrLineEQ r
VerticalLineThrough ((r
c2 r -> r -> r
forall a. Num a => a -> a -> a
-r
c1) r -> r -> r
forall a. Fractional a => a -> a -> a
/ (r
a1 r -> r -> r
forall a. Num a => a -> a -> a
- r
a2))
                  -- the planes intersect in a vertical line
    | r
c1 r -> r -> Bool
forall a. Eq a => a -> a -> Bool
== r
c2  = PlanePlaneIntersection plane (VerticalOrLineEQ r)
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a. a -> Maybe a
Just (PlanePlaneIntersection plane (VerticalOrLineEQ r)
 -> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r)))
-> PlanePlaneIntersection plane (VerticalOrLineEQ r)
-> Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a b. (a -> b) -> a -> b
$ plane -> PlanePlaneIntersection plane (VerticalOrLineEQ r)
forall plane line. plane -> PlanePlaneIntersection plane line
Plane_x_Plane_Plane plane
h
                  -- all others are the same
    | Bool
otherwise = Maybe (PlanePlaneIntersection plane (VerticalOrLineEQ r))
forall a. Maybe a
Nothing
                  -- the planes don't intersect at all
  where
    diffB :: r
diffB = r
b1 r -> r -> r
forall a. Num a => a -> a -> a
- r
b2