    {-# LANGUAGE ConstraintKinds #-}
    {-# LANGUAGE FlexibleContexts     #-}
    {-# LANGUAGE FlexibleInstances    #-}
    {-# LANGUAGE TypeFamilies         #-}
    {-# LANGUAGE UndecidableInstances #-}
    -----------------------------------------------------------------------------
    -- |
    -- Module      :  Diagrams.TrailLike
    -- Copyright   :  (c) 2013 diagrams-lib team (see LICENSE)
    -- License     :  BSD-style (see LICENSE)
    -- Maintainer  :  diagrams-discuss@googlegroups.com
    --
    -- The 'TrailLike' class abstracts over anything which can be
    -- constructed from a concretely located 'Trail', including
    -- lines, loops, trails, paths, vertex lists, and diagrams.
    --
    -----------------------------------------------------------------------------

    module Diagrams.TrailLike
           (
             -- * The TrailLike class

             TrailLike(..)

             -- * Constructing TrailLikes

           , fromSegments, fromLocSegments, fromOffsets, fromLocOffsets, fromVertices
           , (~~), explodeTrail

           ) where

    import           Control.Lens     (view, _Unwrapped')

    import           Diagrams.Core
    import           Diagrams.Located
    import           Diagrams.Segment
    import           Diagrams.Trail

    import           Linear.Affine
    import           Linear.Metric
    import           Linear.Vector

    ------------------------------------------------------------
    --  TrailLike class
    ------------------------------------------------------------

    -- | A type class for trail-like things, /i.e./ things which can be
    --   constructed from a concretely located 'Trail'.  Instances include
    --   lines, loops, trails, paths, lists of vertices, two-dimensional
    --   'Diagram's, and 'Located' variants of all the above.
    --
    --   Usually, type variables with 'TrailLike' constraints are used as
    --   the /output/ types of functions, like
    --
    --   @
    --   foo :: (TrailLike t) => ... -> t
    --   @
    --
    --   Functions with such a type can be used to construct trails,
    --   paths, diagrams, lists of points, and so on, depending on the
    --   context.
    --
    --   To write a function with a signature like the above, you can of
    --   course call 'trailLike' directly; more typically, one would use
    --   one of the provided functions like 'fromOffsets', 'fromVertices',
    --   'fromSegments', or '~~'.
    class (Metric (V t), OrderedField (N t)) => TrailLike t where

      trailLike
        :: Located (Trail (V t) (N t)) -- ^ The concretely located trail.  Note
                                       --   that some trail-like things
                                       --   (e.g. 'Trail's) may ignore the
                                       --   location.
        -> t

    ------------------------------------------------------------
    --  Instances  ---------------------------------------------

    -- | A list of points is trail-like; this instance simply
    --   computes the vertices of the trail, using 'trailPoints'.
    instance (Metric v, OrderedField n) => TrailLike [Point v n] where
      trailLike = trailPoints

    -- | Lines are trail-like.  If given a 'Trail' which contains a loop,
    --   the loop will be cut with 'cutLoop'.  The location is ignored.
    instance (Metric v, OrderedField n) => TrailLike (Trail' Line v n) where
      trailLike = withTrail id cutLoop . unLoc

    -- | Loops are trail-like.  If given a 'Trail' containing a line, the
    --   line will be turned into a loop using 'glueLine'.  The location
    --   is ignored.
    instance (Metric v, OrderedField n) => TrailLike (Trail' Loop v n) where
      trailLike = withTrail glueLine id . unLoc

    -- | 'Trail's are trail-like; the location is simply ignored.
    instance (Metric v, OrderedField n) => TrailLike (Trail v n) where
      trailLike = unLoc

    -- | Translationally invariant things are trail-like as long as the
    --   underlying type is.
    instance TrailLike t => TrailLike (TransInv t) where
      trailLike = view _Unwrapped' . trailLike

    -- | 'Located' things are trail-like as long as the underlying type
    --   is.  The location is taken to be the location of the input
    --   located trail.
    instance TrailLike t => TrailLike (Located t) where
      trailLike t = trailLike t `at` loc t

    ------------------------------------------------------------
    --  Constructing TrailLike things  -------------------------
    ------------------------------------------------------------

    -- | Construct a trail-like thing from a list of segments, with the
    --   origin as the location.
    --
    --   <<diagrams/src_Diagrams_TrailLike_fromSegmentsEx.svg#diagram=fromSegmentsEx&height=200>>
    --
    --   > fromSegmentsEx = fromSegments
    --   >   [ straight (r2 (1,1))
    --   >   , bézier3  (r2 (1,1)) unitX unit_Y
    --   >   , straight unit_X
    --   >   ]
    --   >   # centerXY # pad 1.1
    fromSegments :: TrailLike t => [Segment Closed (V t) (N t)] -> t
    fromSegments = fromLocSegments . (`at` origin)

    -- | Construct a trail-like thing from a located list of segments.
    fromLocSegments :: TrailLike t => Located [Segment Closed (V t) (N t)] -> t
    fromLocSegments = trailLike . mapLoc trailFromSegments

    -- | Construct a trail-like thing of linear segments from a list
    --   of offsets, with the origin as the location.
    --
    --   <<diagrams/src_Diagrams_TrailLike_fromOffsetsEx.svg#diagram=fromOffsetsEx&width=300>>
    --
    --   > fromOffsetsEx = fromOffsets
    --   >   [ unitX
    --   >   , unitX # rotateBy (1/6)
    --   >   , unitX # rotateBy (-1/6)
    --   >   , unitX
    --   >   ]
    --   >   # centerXY # pad 1.1
    fromOffsets :: TrailLike t => [Vn t] -> t
    fromOffsets = trailLike . (`at` origin) . trailFromOffsets

    -- | Construct a trail-like thing of linear segments from a located
    --   list of offsets.
    fromLocOffsets :: (V t ~ v, N t ~ n, V (v n) ~ v, N (v n) ~ n, TrailLike t) => Located [v n] -> t
    fromLocOffsets = trailLike . mapLoc trailFromOffsets

    -- | Construct a trail-like thing connecting the given vertices with
    --   linear segments, with the first vertex as the location.  If no
    --   vertices are given, the empty trail is used with the origin as
    --   the location.
    --
    --   <<diagrams/src_Diagrams_TrailLike_fromVerticesEx.svg#diagram=fromVerticesEx&width=300>>
    --
    --   > import Data.List (transpose)
    --   >
    --   > fromVerticesEx =
    --   >   ( [ pentagon 1
    --   >     , pentagon 1.3 # rotateBy (1/15)
    --   >     , pentagon 1.5 # rotateBy (2/15)
    --   >     ]
    --   >     # transpose
    --   >     # concat
    --   >   )
    --   >   # fromVertices
    --   >   # closeTrail # strokeTrail
    --   >   # centerXY # pad 1.1
    fromVertices :: TrailLike t => [Point (V t) (N t)] -> t
    fromVertices []       = trailLike (emptyTrail `at` origin)
    fromVertices ps@(p:_) = trailLike (trailFromSegments (segmentsFromVertices ps) `at` p)

    segmentsFromVertices :: (Additive v, Num n) => [Point v n] -> [Segment Closed v n]
    segmentsFromVertices []         = []
    segmentsFromVertices vvs@(_:vs) = map straight (zipWith (flip (.-.)) vvs vs)

    -- | Create a linear trail between two given points.
    --
    --   <<diagrams/src_Diagrams_TrailLike_twiddleEx.svg#diagram=twiddleEx&width=300>>
    --
    --   > twiddleEx
    --   >   = mconcat ((~~) <$> hexagon 1 <*> hexagon 1)
    --   >   # centerXY # pad 1.1
    (~~) :: (V t ~ v, N t ~ n, TrailLike t) => Point v n -> Point v n -> t
    p1 ~~ p2 = fromVertices [p1, p2]

    -- | Given a concretely located trail, \"explode\" it by turning each
    --   segment into its own separate trail.  Useful for (say) applying a
    --   different style to each segment.
    --
    --   <<diagrams/src_Diagrams_TrailLike_explodeTrailEx.svg#diagram=explodeTrailEx&width=300>>
    --
    --   > explodeTrailEx
    --   >   = pentagon 1
    --   >   # explodeTrail  -- generate a list of diagrams
    --   >   # zipWith lc [orange, green, yellow, red, blue]
    --   >   # mconcat # centerXY # pad 1.1
    explodeTrail :: (V t ~ v, N t ~ n, TrailLike t) => Located (Trail v n) -> [t]
    explodeTrail = map (mkTrail . fromFixedSeg) . fixTrail
      where
        mkTrail = trailLike . mapLoc (trailFromSegments . (:[]))