{-# LANGUAGE UndecidableInstances #-}
--------------------------------------------------------------------------------
-- |
-- Module      :  HGeometry.BezierSpline
-- Copyright   :  (C) Frank Staals
-- License     :  see the LICENSE file
-- Maintainer  :  Frank Staals
--
-- Basic Bezier splines.
--
--------------------------------------------------------------------------------
module HGeometry.BezierSpline
  ( BezierSplineF(.., Bezier2, Bezier3)
  , BezierSpline
  , QuadraticBezier
  , CubicBezier
  -- , module HGeometry.BezierSpline.Class
  ) where


import Control.DeepSeq (NFData)
import Control.Lens
-- import qualified Data.Foldable as F
import Data.Functor.Classes
-- import qualified Data.List.NonEmpty as NonEmpty
import Data.Semigroup.Foldable
import Data.Vector.NonEmpty.Internal (NonEmptyVector(..))
import GHC.Generics
import HGeometry.Box
import HGeometry.Point
import HGeometry.Properties
import HGeometry.Transformation
import HGeometry.Vector
import HGeometry.Vector.NonEmpty.Util ()
import Hiraffe.Graph
import Data.Kind (Type)
-- import GHC.TypeLits

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

-- | A Bezier spline.
type BezierSplineF            :: (Type -> Type) -> Type -> Type
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-- | By default we store simple poylline as non-empty vectors.
type BezierSpline = BezierSplineF NonEmptyVector

-- | Quadratic Bezier splines
type QuadraticBezier = BezierSplineF (Vector 3)
-- | Cubic Bezier splines
type CubicBezier     = BezierSplineF (Vector 4)

type instance Dimension (BezierSplineF f point) = 2
type instance NumType   (BezierSplineF f point) = NumType point

-- | Construct a QuadatricBezier
pattern Bezier2       :: point -> point -> point -> QuadraticBezier point
pattern $bBezier2 :: forall point. point -> point -> point -> QuadraticBezier point
$mBezier2 :: forall {r} {point}.
QuadraticBezier point
-> (point -> point -> point -> r) -> ((# #) -> r) -> r
Bezier2 p q r = BezierSpline (Vector3 p q r)
{-# COMPLETE Bezier2 #-}

-- | Construct a cubic bezier
pattern Bezier3         :: point -> point -> point -> point -> CubicBezier point
pattern $bBezier3 :: forall point. point -> point -> point -> point -> CubicBezier point
$mBezier3 :: forall {r} {point}.
CubicBezier point
-> (point -> point -> point -> point -> r) -> ((# #) -> r) -> r
Bezier3 p q r s = BezierSpline (Vector4 p q r s)
{-# COMPLETE Bezier3 #-}


-- | Access the container
_BezierSplineF :: Iso (BezierSplineF f point) (BezierSplineF f' point')
                      (f point)                 (f' point' )
_BezierSplineF :: forall (f :: * -> *) point (f' :: * -> *) point' (p :: * -> * -> *)
       (f :: * -> *).
(Profunctor p, Functor f) =>
p (f point) (f (f' point'))
-> p (BezierSplineF f point) (f (BezierSplineF f' point'))
_BezierSplineF = (BezierSplineF f point -> f point)
-> (f' point' -> BezierSplineF f' point')
-> Iso
     (BezierSplineF f point)
     (BezierSplineF f' point')
     (f point)
     (f' point')
forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso (\(BezierSpline f point
vs) -> f point
vs) f' point' -> BezierSplineF f' point'
forall (f :: * -> *) point. f point -> BezierSplineF f point
BezierSpline

instance Traversable f => Traversable (BezierSplineF f) where
  traverse :: forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> BezierSplineF f a -> f (BezierSplineF f b)
traverse a -> f b
f (BezierSpline f a
vs) = f b -> BezierSplineF f b
forall (f :: * -> *) point. f point -> BezierSplineF f point
BezierSpline (f b -> BezierSplineF f b) -> f (f b) -> f (BezierSplineF f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable t, Applicative f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b.
Applicative f =>
(a -> f b) -> f a -> f (f b)
traverse a -> f b
f f a
vs
instance Traversable1 f => Traversable1 (BezierSplineF f) where
  traverse1 :: forall (f :: * -> *) a b.
Apply f =>
(a -> f b) -> BezierSplineF f a -> f (BezierSplineF f b)
traverse1 a -> f b
f (BezierSpline f a
vs) = f b -> BezierSplineF f b
forall (f :: * -> *) point. f point -> BezierSplineF f point
BezierSpline (f b -> BezierSplineF f b) -> f (f b) -> f (BezierSplineF f b)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (a -> f b) -> f a -> f (f b)
forall (t :: * -> *) (f :: * -> *) a b.
(Traversable1 t, Apply f) =>
(a -> f b) -> t a -> f (t b)
forall (f :: * -> *) a b. Apply f => (a -> f b) -> f a -> f (f b)
traverse1 a -> f b
f f a
vs

instance ( Traversable1 f
         , IxValue (f point) ~ point
         , Index   (f point) ~ Int
         , Ixed    (f point)
         ) => HasVertices (BezierSplineF f point) (BezierSplineF f point') where
  vertices :: IndexedTraversal1
  (VertexIx (BezierSplineF f point))
  (BezierSplineF f point)
  (BezierSplineF f point')
  (Vertex (BezierSplineF f point))
  (Vertex (BezierSplineF f point'))
vertices = (f point -> f (f point'))
-> BezierSplineF f point -> f (BezierSplineF f point')
forall (f :: * -> *) point (f' :: * -> *) point' (p :: * -> * -> *)
       (f :: * -> *).
(Profunctor p, Functor f) =>
p (f point) (f (f' point'))
-> p (BezierSplineF f point) (f (BezierSplineF f' point'))
_BezierSplineF ((f point -> f (f point'))
 -> BezierSplineF f point -> f (BezierSplineF f point'))
-> (p point (f point') -> f point -> f (f point'))
-> p point (f point')
-> BezierSplineF f point
-> f (BezierSplineF f point')
forall b c a. (b -> c) -> (a -> b) -> a -> c
. p point (f point') -> f point -> f (f point')
forall (f :: * -> *) a b.
Traversable1 f =>
IndexedTraversal1 Int (f a) (f b) a b
IndexedTraversal1 Int (f point) (f point') point point'
traversed1

instance ( Traversable1 f
         , IxValue (f point) ~ point
         , Index   (f point) ~ Int
         , Ixed    (f point)
         ) => HasPoints (BezierSplineF f point) (BezierSplineF f point') point point' where
  allPoints :: forall (d :: Nat) r r'.
(Point_ point d r, Point_ point' d r',
 NumType (BezierSplineF f point) ~ r,
 NumType (BezierSplineF f point') ~ r',
 Dimension (BezierSplineF f point) ~ d,
 Dimension (BezierSplineF f point') ~ d) =>
Traversal1
  (BezierSplineF f point) (BezierSplineF f point') point point'
allPoints = (f point -> f (f point'))
-> BezierSplineF f point -> f (BezierSplineF f point')
forall (f :: * -> *) point (f' :: * -> *) point' (p :: * -> * -> *)
       (f :: * -> *).
(Profunctor p, Functor f) =>
p (f point) (f (f' point'))
-> p (BezierSplineF f point) (f (BezierSplineF f' point'))
_BezierSplineF ((f point -> f (f point'))
 -> BezierSplineF f point -> f (BezierSplineF f point'))
-> ((point -> f point') -> f point -> f (f point'))
-> (point -> f point')
-> BezierSplineF f point
-> f (BezierSplineF f point')
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (point -> f point') -> f point -> f (f point')
forall (f :: * -> *) a b.
Traversable1 f =>
IndexedTraversal1 Int (f a) (f b) a b
IndexedTraversal1 Int (f point) (f point') point point'
traversed1

instance ( Traversable1 f
         , IxValue (f point) ~ point
         , Index   (f point) ~ Int
         , Ixed    (f point)
         , DefaultTransformByConstraints (BezierSplineF f point) 2 r
         , Point_ point 2 r
         ) => IsTransformable (BezierSplineF f point)

instance ( Traversable1 f
         , IxValue (f point) ~ point
         , Index   (f point) ~ Int
         , Ixed    (f point)
         , Point_ point 2 r
         ) => IsBoxable (BezierSplineF f point)

instance ( Traversable1 f
         , Ixed (f point)
         , IxValue (f point) ~ point
         , Index (f point) ~ Int
         ) => HasVertices' (BezierSplineF f point) where
  type Vertex   (BezierSplineF f point) = point
  type VertexIx (BezierSplineF f point) = Int
  vertexAt :: VertexIx (BezierSplineF f point)
-> IndexedTraversal'
     (VertexIx (BezierSplineF f point))
     (BezierSplineF f point)
     (Vertex (BezierSplineF f point))
vertexAt VertexIx (BezierSplineF f point)
i = (f point -> f (f point))
-> BezierSplineF f point -> f (BezierSplineF f point)
forall (f :: * -> *) point (f' :: * -> *) point' (p :: * -> * -> *)
       (f :: * -> *).
(Profunctor p, Functor f) =>
p (f point) (f (f' point'))
-> p (BezierSplineF f point) (f (BezierSplineF f' point'))
_BezierSplineF ((f point -> f (f point))
 -> BezierSplineF f point -> f (BezierSplineF f point))
-> (p point (f point) -> f point -> f (f point))
-> p point (f point)
-> BezierSplineF f point
-> f (BezierSplineF f point)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Index (f point)
-> IndexedTraversal'
     (Index (f point)) (f point) (IxValue (f point))
forall m.
Ixed m =>
Index m -> IndexedTraversal' (Index m) m (IxValue m)
iix VertexIx (BezierSplineF f point)
Index (f point)
i