{-# LANGUAGE ConstraintKinds            #-}
{-# LANGUAGE DeriveDataTypeable         #-}
{-# LANGUAGE FlexibleContexts           #-}
{-# LANGUAGE FlexibleInstances          #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses      #-}
{-# LANGUAGE Rank2Types                 #-}
{-# LANGUAGE StandaloneDeriving         #-}
{-# LANGUAGE TemplateHaskell            #-}
{-# LANGUAGE TypeFamilies               #-}
{-# LANGUAGE TypeOperators              #-}
{-# LANGUAGE UndecidableInstances       #-}
{-# LANGUAGE ViewPatterns               #-}

{-# OPTIONS_GHC -fno-warn-orphans #-}

-----------------------------------------------------------------------------
-- |
-- Module      :  Diagrams.TwoD.Path
-- Copyright   :  (c) 2011-2015 diagrams-lib team (see LICENSE)
-- License     :  BSD-style (see LICENSE)
-- Maintainer  :  diagrams-discuss@googlegroups.com
--
-- Paths in two dimensions are special since we may stroke them to
-- create a 2D diagram, and (eventually) perform operations such as
-- intersection and union.  They also have a trace, whereas paths in
-- higher dimensions do not.
--
-----------------------------------------------------------------------------

module Diagrams.TwoD.Path
  ( -- * Constructing path-based diagrams

    stroke, stroke'
  , strokePath, strokeP, strokePath', strokeP'
  , strokeTrail, strokeT, strokeTrail', strokeT'
  , strokeLine, strokeLoop
  , strokeLocTrail, strokeLocT, strokeLocLine, strokeLocLoop

    -- ** Stroke options

  , FillRule(..)
  , getFillRule, fillRule, _fillRule
  , StrokeOpts(..), vertexNames, queryFillRule

    -- ** Inside/outside testing

  , Crossings (..)
  , isInsideWinding
  , isInsideEvenOdd

    -- * Clipping

  , Clip(..), _Clip, _clip
  , clipBy, clipTo, clipped

    -- * Intersections

  , intersectPoints, intersectPoints'
  , intersectPointsP, intersectPointsP'
  , intersectPointsT, intersectPointsT'
  ) where

import           Control.Applicative       (liftA2)
import           Control.Lens              hiding (at, transform)
import qualified Data.Foldable             as F
import           Data.Semigroup
import           Data.Typeable

import           Data.Default.Class

import           Diagrams.Angle
import           Diagrams.Combinators      (withEnvelope, withTrace)
import           Diagrams.Core
import           Diagrams.Core.Trace
import           Diagrams.Located          (Located, mapLoc, unLoc)
import           Diagrams.Parametric
import           Diagrams.Path
import           Diagrams.Query
import           Diagrams.Segment
import           Diagrams.Solve.Polynomial
import           Diagrams.Trail
import           Diagrams.TrailLike
import           Diagrams.TwoD.Segment
import           Diagrams.TwoD.Types
import           Diagrams.TwoD.Vector
import           Diagrams.Util             (tau)

import           Linear.Affine
import           Linear.Vector

------------------------------------------------------------
--  Trail and path traces  ---------------------------------
------------------------------------------------------------

-- Only 2D trails and paths have a trace.

-- XXX can the efficiency of this be improved?  See the comment in
-- Diagrams.Path on the Enveloped instance for Trail.
instance RealFloat n => Traced (Trail V2 n) where
  getTrace :: Trail V2 n -> Trace (V (Trail V2 n)) (N (Trail V2 n))
getTrace = forall (v :: * -> *) n r.
(Metric v, OrderedField n) =>
(Trail' Line v n -> r) -> Trail v n -> r
withLine forall a b. (a -> b) -> a -> b
$
      forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr
        (\Segment Closed V2 n
seg Trace V2 n
bds -> forall t (v :: * -> *) n.
(V t ~ v, N t ~ n, HasOrigin t) =>
v n -> t -> t
moveOriginBy (forall (f :: * -> *) a. (Functor f, Num a) => f a -> f a
negated forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall p. EndValues p => p -> Codomain p (N p)
atEnd forall a b. (a -> b) -> a -> b
$ Segment Closed V2 n
seg) Trace V2 n
bds forall a. Semigroup a => a -> a -> a
<> forall a. Traced a => a -> Trace (V a) (N a)
getTrace Segment Closed V2 n
seg)
        forall a. Monoid a => a
mempty
    forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n. Trail' Line v n -> [Segment Closed v n]
lineSegments

instance RealFloat n => Traced (Path V2 n) where
  getTrace :: Path V2 n -> Trace (V (Path V2 n)) (N (Path V2 n))
getTrace = forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
F.foldMap forall a. Traced a => a -> Trace (V a) (N a)
getTrace forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall s. Wrapped s => (Unwrapped s -> s) -> s -> Unwrapped s
op forall (v :: * -> *) n. [Located (Trail v n)] -> Path v n
Path

------------------------------------------------------------
--  Constructing path-based diagrams  ----------------------
------------------------------------------------------------

-- | Enumeration of algorithms or \"rules\" for determining which
--   points lie in the interior of a (possibly self-intersecting)
--   path.
data FillRule
  = Winding  -- ^ Interior points are those with a nonzero
             --   /winding/ /number/.  See
             --   <http://en.wikipedia.org/wiki/Nonzero-rule>.
  | EvenOdd  -- ^ Interior points are those where a ray
             --   extended infinitely in a particular direction crosses
             --   the path an odd number of times. See
             --   <http://en.wikipedia.org/wiki/Even-odd_rule>.
    deriving (Int -> FillRule -> ShowS
[FillRule] -> ShowS
FillRule -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [FillRule] -> ShowS
$cshowList :: [FillRule] -> ShowS
show :: FillRule -> String
$cshow :: FillRule -> String
showsPrec :: Int -> FillRule -> ShowS
$cshowsPrec :: Int -> FillRule -> ShowS
Show, Typeable, FillRule -> FillRule -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: FillRule -> FillRule -> Bool
$c/= :: FillRule -> FillRule -> Bool
== :: FillRule -> FillRule -> Bool
$c== :: FillRule -> FillRule -> Bool
Eq, Eq FillRule
FillRule -> FillRule -> Bool
FillRule -> FillRule -> Ordering
FillRule -> FillRule -> FillRule
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
min :: FillRule -> FillRule -> FillRule
$cmin :: FillRule -> FillRule -> FillRule
max :: FillRule -> FillRule -> FillRule
$cmax :: FillRule -> FillRule -> FillRule
>= :: FillRule -> FillRule -> Bool
$c>= :: FillRule -> FillRule -> Bool
> :: FillRule -> FillRule -> Bool
$c> :: FillRule -> FillRule -> Bool
<= :: FillRule -> FillRule -> Bool
$c<= :: FillRule -> FillRule -> Bool
< :: FillRule -> FillRule -> Bool
$c< :: FillRule -> FillRule -> Bool
compare :: FillRule -> FillRule -> Ordering
$ccompare :: FillRule -> FillRule -> Ordering
Ord)

instance AttributeClass FillRule
instance Semigroup FillRule where
  FillRule
_ <> :: FillRule -> FillRule -> FillRule
<> FillRule
b = FillRule
b

instance Default FillRule where
  def :: FillRule
def = FillRule
Winding

-- | A record of options that control how a path is stroked.
--   @StrokeOpts@ is an instance of 'Default', so a @StrokeOpts@
--   records can be created using @'with' { ... }@ notation.
data StrokeOpts a
  = StrokeOpts
    { forall a. StrokeOpts a -> [[a]]
_vertexNames   :: [[a]]

    , forall a. StrokeOpts a -> FillRule
_queryFillRule :: FillRule

    }

makeLensesWith (generateSignatures .~ False $ lensRules) ''StrokeOpts

-- | Atomic names that should be assigned to the vertices of the path so that
--   they can be referenced later.  If there are not enough names, the extra
--   vertices are not assigned names; if there are too many, the extra names
--   are ignored.  Note that this is a /list of lists/ of names, since paths
--   can consist of multiple trails.  The first list of names are assigned to
--   the vertices of the first trail, the second list to the second trail, and
--   so on.
--
--   The default value is the empty list.

vertexNames :: Lens (StrokeOpts a) (StrokeOpts a') [[a]] [[a']]

-- | The fill rule used for determining which points are inside the path.
--   The default is 'Winding'.  NOTE: for now, this only affects the resulting
--   diagram's 'Query', /not/ how it will be drawn!  To set the fill rule
--   determining how it is to be drawn, use the 'fillRule' function.
queryFillRule :: Lens' (StrokeOpts a) FillRule

instance Default (StrokeOpts a) where
  def :: StrokeOpts a
def = StrokeOpts
        { _vertexNames :: [[a]]
_vertexNames    = []
        , _queryFillRule :: FillRule
_queryFillRule = forall a. Default a => a
def
        }

-- | Convert a 'ToPath' object into a diagram.  The resulting diagram has the
--   names 0, 1, ... assigned to each of the path's vertices.
--
--   See also 'stroke'', which takes an extra options record allowing
--   its behaviour to be customized.
--
-- @
-- 'stroke' :: 'Path' 'V2' 'Double'                  -> 'Diagram' b
-- 'stroke' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Diagram' b
-- 'stroke' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Diagram' b
-- 'stroke' :: 'Located' ('Trail'' 'Line' 'V2' 'Double') -> 'Diagram' b
-- @
stroke :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b)
       => t -> QDiagram b V2 n Any
stroke :: forall n t b.
(InSpace V2 n t, ToPath t, TypeableFloat n,
 Renderable (Path V2 n) b) =>
t -> QDiagram b V2 n Any
stroke = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t.
(ToPath t, Metric (V t), OrderedField (N t)) =>
t -> Path (V t) (N t)
toPath

-- | A variant of 'stroke' that takes an extra record of options to
--   customize its behaviour.  In particular:
--
--     * Names can be assigned to the path's vertices
--
--   'StrokeOpts' is an instance of 'Default', so @stroke' ('with' &
--   ... )@ syntax may be used.
stroke' :: (InSpace V2 n t, ToPath t, TypeableFloat n, Renderable (Path V2 n) b, IsName a)
       => StrokeOpts a -> t -> QDiagram b V2 n Any
stroke' :: forall n t b a.
(InSpace V2 n t, ToPath t, TypeableFloat n,
 Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> t -> QDiagram b V2 n Any
stroke' StrokeOpts a
opts = forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokeP' StrokeOpts a
opts forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t.
(ToPath t, Metric (V t), OrderedField (N t)) =>
t -> Path (V t) (N t)
toPath

-- | 'stroke' specialised to 'Path'.
strokeP :: (TypeableFloat n, Renderable (Path V2 n) b)
        => Path V2 n -> QDiagram b V2 n Any
strokeP :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP = forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokeP' (forall a. Default a => a
def :: StrokeOpts ())

-- | 'stroke' specialised to 'Path'.
strokePath :: (TypeableFloat n, Renderable (Path V2 n) b)
        => Path V2 n -> QDiagram b V2 n Any
strokePath :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokePath = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP

instance (TypeableFloat n, Renderable (Path V2 n) b)
    => TrailLike (QDiagram b V2 n Any) where
  trailLike :: Located (Trail (V (QDiagram b V2 n Any)) (N (QDiagram b V2 n Any)))
-> QDiagram b V2 n Any
trailLike = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t. TrailLike t => Located (Trail (V t) (N t)) -> t
trailLike

-- | 'stroke'' specialised to 'Path'.
strokeP' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
    => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokeP' :: forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokeP' StrokeOpts a
opts Path V2 n
path
  | forall (t :: * -> *) a. Foldable t => t a -> Bool
null (Path V2 n
pLines forall s a. s -> Getting a s a -> a
^. forall s. Wrapped s => Iso' s (Unwrapped s)
_Wrapped') = Path V2 n -> QDiagram b V2 n Any
mkP Path V2 n
pLoops
  | forall (t :: * -> *) a. Foldable t => t a -> Bool
null (Path V2 n
pLoops forall s a. s -> Getting a s a -> a
^. forall s. Wrapped s => Iso' s (Unwrapped s)
_Wrapped') = Path V2 n -> QDiagram b V2 n Any
mkP Path V2 n
pLines
  | Bool
otherwise                  = Path V2 n -> QDiagram b V2 n Any
mkP Path V2 n
pLines forall a. Semigroup a => a -> a -> a
<> Path V2 n -> QDiagram b V2 n Any
mkP Path V2 n
pLoops
  where
    (Path V2 n
pLines,Path V2 n
pLoops) = forall (v :: * -> *) n.
(Located (Trail v n) -> Bool) -> Path v n -> (Path v n, Path v n)
partitionPath (forall (v :: * -> *) n. Trail v n -> Bool
isLine forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Located a -> a
unLoc) Path V2 n
path
    mkP :: Path V2 n -> QDiagram b V2 n Any
mkP Path V2 n
p
      = forall b (v :: * -> *) n m.
Prim b v n
-> Envelope v n
-> Trace v n
-> SubMap b v n m
-> Query v n m
-> QDiagram b v n m
mkQD (forall p b.
(Transformable p, Typeable p, Renderable p b) =>
p -> Prim b (V p) (N p)
Prim Path V2 n
p)
         (forall a. Enveloped a => a -> Envelope (V a) (N a)
getEnvelope Path V2 n
p)
         (forall a. Traced a => a -> Trace (V a) (N a)
getTrace Path V2 n
p)
         (forall a b (v :: * -> *) n m.
IsName a =>
[(a, Subdiagram b v n m)] -> SubMap b v n m
fromNames forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (t :: * -> *) a. Foldable t => t [a] -> [a]
concat forall a b. (a -> b) -> a -> b
$
           forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith forall a b. [a] -> [b] -> [(a, b)]
zip (StrokeOpts a
optsforall s a. s -> Getting a s a -> a
^.forall a a'. Lens (StrokeOpts a) (StrokeOpts a') [[a]] [[a']]
vertexNames) ((forall a b. (a -> b) -> [a] -> [b]
map forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> [a] -> [b]
map) forall (v :: * -> *) n b m.
(Metric v, OrderedField n) =>
Point v n -> Subdiagram b v n m
subPoint (forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Path v n -> [[Point v n]]
pathVertices Path V2 n
p))
         )
         (forall (v :: * -> *) n m. (Point v n -> m) -> Query v n m
Query forall a b. (a -> b) -> a -> b
$ Bool -> Any
Any forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall n.
RealFloat n =>
FillRule -> Path V2 n -> Point V2 n -> Bool
runFillRule (StrokeOpts a
optsforall s a. s -> Getting a s a -> a
^.forall a. Lens' (StrokeOpts a) FillRule
queryFillRule)) Path V2 n
p)

-- | 'stroke'' specialised to 'Path'.
strokePath' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
    => StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokePath' :: forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokePath' = forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Path V2 n -> QDiagram b V2 n Any
strokeP'

-- | 'stroke' specialised to 'Trail'.
strokeTrail :: (TypeableFloat n, Renderable (Path V2 n) b)
            => Trail V2 n -> QDiagram b V2 n Any
strokeTrail :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail V2 n -> QDiagram b V2 n Any
strokeTrail = forall n t b.
(InSpace V2 n t, ToPath t, TypeableFloat n,
 Renderable (Path V2 n) b) =>
t -> QDiagram b V2 n Any
stroke forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Trail v n -> Path v n
pathFromTrail

-- | 'stroke' specialised to 'Trail'.
strokeT :: (TypeableFloat n, Renderable (Path V2 n) b)
        => Trail V2 n -> QDiagram b V2 n Any
strokeT :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail V2 n -> QDiagram b V2 n Any
strokeT = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail V2 n -> QDiagram b V2 n Any
strokeTrail

-- | A composition of 'stroke'' and 'pathFromTrail' for conveniently
--   converting a trail directly into a diagram.
strokeTrail' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
             => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeTrail' :: forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeTrail' StrokeOpts a
opts = forall n t b a.
(InSpace V2 n t, ToPath t, TypeableFloat n,
 Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> t -> QDiagram b V2 n Any
stroke' StrokeOpts a
opts forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Trail v n -> Path v n
pathFromTrail

-- | Deprecated synonym for 'strokeTrail''.
strokeT' :: (TypeableFloat n, Renderable (Path V2 n) b, IsName a)
         => StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeT' :: forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeT' = forall n b a.
(TypeableFloat n, Renderable (Path V2 n) b, IsName a) =>
StrokeOpts a -> Trail V2 n -> QDiagram b V2 n Any
strokeTrail'

-- | A composition of 'strokeT' and 'wrapLine' for conveniently
--   converting a line directly into a diagram.
strokeLine :: (TypeableFloat n, Renderable (Path V2 n) b)
           => Trail' Line V2 n -> QDiagram b V2 n Any
strokeLine :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail' Line V2 n -> QDiagram b V2 n Any
strokeLine = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail V2 n -> QDiagram b V2 n Any
strokeT forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n. Trail' Line v n -> Trail v n
wrapLine

-- | A composition of 'strokeT' and 'wrapLoop' for conveniently
--   converting a loop directly into a diagram.
strokeLoop :: (TypeableFloat n, Renderable (Path V2 n) b)
           => Trail' Loop V2 n -> QDiagram b V2 n Any
strokeLoop :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail' Loop V2 n -> QDiagram b V2 n Any
strokeLoop = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Trail V2 n -> QDiagram b V2 n Any
strokeT forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n. Trail' Loop v n -> Trail v n
wrapLoop

-- | A convenience function for converting a @Located Trail@ directly
--   into a diagram; @strokeLocTrail = stroke . trailLike@.
strokeLocTrail :: (TypeableFloat n, Renderable (Path V2 n) b)
               => Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLocTrail :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLocTrail = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t. TrailLike t => Located (Trail (V t) (N t)) -> t
trailLike

-- | Deprecated synonym for 'strokeLocTrail'.
strokeLocT :: (TypeableFloat n, Renderable (Path V2 n) b)
           => Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLocT :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLocT = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Located (Trail V2 n) -> QDiagram b V2 n Any
strokeLocTrail

-- | A convenience function for converting a @Located@ line directly
--   into a diagram; @strokeLocLine = stroke . trailLike . mapLoc wrapLine@.
strokeLocLine :: (TypeableFloat n, Renderable (Path V2 n) b)
              => Located (Trail' Line V2 n) -> QDiagram b V2 n Any
strokeLocLine :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Located (Trail' Line V2 n) -> QDiagram b V2 n Any
strokeLocLine = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t. TrailLike t => Located (Trail (V t) (N t)) -> t
trailLike forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. SameSpace a b => (a -> b) -> Located a -> Located b
mapLoc forall (v :: * -> *) n. Trail' Line v n -> Trail v n
wrapLine

-- | A convenience function for converting a @Located@ loop directly
--   into a diagram; @strokeLocLoop = stroke . trailLike . mapLoc wrapLoop@.
strokeLocLoop :: (TypeableFloat n, Renderable (Path V2 n) b)
              => Located (Trail' Loop V2 n) -> QDiagram b V2 n Any
strokeLocLoop :: forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Located (Trail' Loop V2 n) -> QDiagram b V2 n Any
strokeLocLoop = forall n b.
(TypeableFloat n, Renderable (Path V2 n) b) =>
Path V2 n -> QDiagram b V2 n Any
strokeP forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t. TrailLike t => Located (Trail (V t) (N t)) -> t
trailLike forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. SameSpace a b => (a -> b) -> Located a -> Located b
mapLoc forall (v :: * -> *) n. Trail' Loop v n -> Trail v n
wrapLoop

------------------------------------------------------------
--  Inside/outside testing
------------------------------------------------------------

runFillRule :: RealFloat n => FillRule -> Path V2 n -> Point V2 n -> Bool
runFillRule :: forall n.
RealFloat n =>
FillRule -> Path V2 n -> Point V2 n -> Bool
runFillRule FillRule
Winding = forall t. HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideWinding
runFillRule FillRule
EvenOdd = forall t. HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideEvenOdd

-- | Extract the fill rule from a 'FillRuleA' attribute.
getFillRule :: FillRule -> FillRule
getFillRule :: FillRule -> FillRule
getFillRule = forall a. a -> a
id

-- | Specify the fill rule that should be used for determining which
--   points are inside a path.
fillRule :: HasStyle a => FillRule -> a -> a
fillRule :: forall a. HasStyle a => FillRule -> a -> a
fillRule = forall a d. (AttributeClass a, HasStyle d) => a -> d -> d
applyAttr

-- | Lens onto the fill rule of a style.
_fillRule :: Lens' (Style V2 n) FillRule
_fillRule :: forall n. Lens' (Style V2 n) FillRule
_fillRule = forall a (v :: * -> *) n.
AttributeClass a =>
Lens' (Style v n) (Maybe a)
atAttr forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Eq a => a -> Iso' (Maybe a) a
non forall a. Default a => a
def

-- | The sum of /signed/ crossings of a path as we travel in the
--   positive x direction from a given point.
--
--     - A point is filled according to the 'Winding' fill rule, if the
--       number of 'Crossings' is non-zero (see 'isInsideWinding').
--
--     - A point is filled according to the 'EvenOdd' fill rule, if the
--       number of 'Crossings' is odd (see 'isInsideEvenOdd').
--
--   This is the 'HasQuery' result for 'Path's, 'Located' 'Trail's and
--   'Located' 'Loops'.
--
-- @
-- 'sample' :: 'Path' 'V2' 'Double'                  -> 'Point' 'V2' 'Double' -> 'Crossings'
-- 'sample' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Point' 'V2' 'Double' -> 'Crossings'
-- 'sample' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Point' 'V2' 'Double' -> 'Crossings'
-- @
--
--   Note that 'Line's have no inside or outside, so don't contribute
--   crossings
newtype Crossings = Crossings Int
  deriving (Int -> Crossings -> ShowS
[Crossings] -> ShowS
Crossings -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Crossings] -> ShowS
$cshowList :: [Crossings] -> ShowS
show :: Crossings -> String
$cshow :: Crossings -> String
showsPrec :: Int -> Crossings -> ShowS
$cshowsPrec :: Int -> Crossings -> ShowS
Show, Crossings -> Crossings -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Crossings -> Crossings -> Bool
$c/= :: Crossings -> Crossings -> Bool
== :: Crossings -> Crossings -> Bool
$c== :: Crossings -> Crossings -> Bool
Eq, Eq Crossings
Crossings -> Crossings -> Bool
Crossings -> Crossings -> Ordering
Crossings -> Crossings -> Crossings
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
min :: Crossings -> Crossings -> Crossings
$cmin :: Crossings -> Crossings -> Crossings
max :: Crossings -> Crossings -> Crossings
$cmax :: Crossings -> Crossings -> Crossings
>= :: Crossings -> Crossings -> Bool
$c>= :: Crossings -> Crossings -> Bool
> :: Crossings -> Crossings -> Bool
$c> :: Crossings -> Crossings -> Bool
<= :: Crossings -> Crossings -> Bool
$c<= :: Crossings -> Crossings -> Bool
< :: Crossings -> Crossings -> Bool
$c< :: Crossings -> Crossings -> Bool
compare :: Crossings -> Crossings -> Ordering
$ccompare :: Crossings -> Crossings -> Ordering
Ord, Integer -> Crossings
Crossings -> Crossings
Crossings -> Crossings -> Crossings
forall a.
(a -> a -> a)
-> (a -> a -> a)
-> (a -> a -> a)
-> (a -> a)
-> (a -> a)
-> (a -> a)
-> (Integer -> a)
-> Num a
fromInteger :: Integer -> Crossings
$cfromInteger :: Integer -> Crossings
signum :: Crossings -> Crossings
$csignum :: Crossings -> Crossings
abs :: Crossings -> Crossings
$cabs :: Crossings -> Crossings
negate :: Crossings -> Crossings
$cnegate :: Crossings -> Crossings
* :: Crossings -> Crossings -> Crossings
$c* :: Crossings -> Crossings -> Crossings
- :: Crossings -> Crossings -> Crossings
$c- :: Crossings -> Crossings -> Crossings
+ :: Crossings -> Crossings -> Crossings
$c+ :: Crossings -> Crossings -> Crossings
Num, Int -> Crossings
Crossings -> Int
Crossings -> [Crossings]
Crossings -> Crossings
Crossings -> Crossings -> [Crossings]
Crossings -> Crossings -> Crossings -> [Crossings]
forall a.
(a -> a)
-> (a -> a)
-> (Int -> a)
-> (a -> Int)
-> (a -> [a])
-> (a -> a -> [a])
-> (a -> a -> [a])
-> (a -> a -> a -> [a])
-> Enum a
enumFromThenTo :: Crossings -> Crossings -> Crossings -> [Crossings]
$cenumFromThenTo :: Crossings -> Crossings -> Crossings -> [Crossings]
enumFromTo :: Crossings -> Crossings -> [Crossings]
$cenumFromTo :: Crossings -> Crossings -> [Crossings]
enumFromThen :: Crossings -> Crossings -> [Crossings]
$cenumFromThen :: Crossings -> Crossings -> [Crossings]
enumFrom :: Crossings -> [Crossings]
$cenumFrom :: Crossings -> [Crossings]
fromEnum :: Crossings -> Int
$cfromEnum :: Crossings -> Int
toEnum :: Int -> Crossings
$ctoEnum :: Int -> Crossings
pred :: Crossings -> Crossings
$cpred :: Crossings -> Crossings
succ :: Crossings -> Crossings
$csucc :: Crossings -> Crossings
Enum, Num Crossings
Ord Crossings
Crossings -> Rational
forall a. Num a -> Ord a -> (a -> Rational) -> Real a
toRational :: Crossings -> Rational
$ctoRational :: Crossings -> Rational
Real, Enum Crossings
Real Crossings
Crossings -> Integer
Crossings -> Crossings -> (Crossings, Crossings)
Crossings -> Crossings -> Crossings
forall a.
Real a
-> Enum a
-> (a -> a -> a)
-> (a -> a -> a)
-> (a -> a -> a)
-> (a -> a -> a)
-> (a -> a -> (a, a))
-> (a -> a -> (a, a))
-> (a -> Integer)
-> Integral a
toInteger :: Crossings -> Integer
$ctoInteger :: Crossings -> Integer
divMod :: Crossings -> Crossings -> (Crossings, Crossings)
$cdivMod :: Crossings -> Crossings -> (Crossings, Crossings)
quotRem :: Crossings -> Crossings -> (Crossings, Crossings)
$cquotRem :: Crossings -> Crossings -> (Crossings, Crossings)
mod :: Crossings -> Crossings -> Crossings
$cmod :: Crossings -> Crossings -> Crossings
div :: Crossings -> Crossings -> Crossings
$cdiv :: Crossings -> Crossings -> Crossings
rem :: Crossings -> Crossings -> Crossings
$crem :: Crossings -> Crossings -> Crossings
quot :: Crossings -> Crossings -> Crossings
$cquot :: Crossings -> Crossings -> Crossings
Integral)

instance Semigroup Crossings where
  Crossings Int
a <> :: Crossings -> Crossings -> Crossings
<> Crossings Int
b = Int -> Crossings
Crossings (Int
a forall a. Num a => a -> a -> a
+ Int
b)

instance Monoid Crossings where
  mempty :: Crossings
mempty  = Int -> Crossings
Crossings Int
0
  mappend :: Crossings -> Crossings -> Crossings
mappend = forall a. Semigroup a => a -> a -> a
(<>)

instance RealFloat n => HasQuery (Located (Trail V2 n)) Crossings where
  getQuery :: Located (Trail V2 n)
-> Query
     (V (Located (Trail V2 n))) (N (Located (Trail V2 n))) Crossings
getQuery Located (Trail V2 n)
trail = forall (v :: * -> *) n m. (Point v n -> m) -> Query v n m
Query forall a b. (a -> b) -> a -> b
$ \Point (V (Located (Trail V2 n))) (N (Located (Trail V2 n)))
p -> forall n.
RealFloat n =>
Point V2 n -> Located (Trail V2 n) -> Crossings
trailCrossings Point (V (Located (Trail V2 n))) (N (Located (Trail V2 n)))
p Located (Trail V2 n)
trail

instance RealFloat n => HasQuery (Located (Trail' l V2 n)) Crossings where
  getQuery :: Located (Trail' l V2 n)
-> Query
     (V (Located (Trail' l V2 n)))
     (N (Located (Trail' l V2 n)))
     Crossings
getQuery Located (Trail' l V2 n)
trail' = forall t m. HasQuery t m => t -> Query (V t) (N t) m
getQuery (forall a b. SameSpace a b => (a -> b) -> Located a -> Located b
mapLoc forall l (v :: * -> *) n. Trail' l v n -> Trail v n
Trail Located (Trail' l V2 n)
trail')

instance RealFloat n => HasQuery (Path V2 n) Crossings where
  getQuery :: Path V2 n -> Query (V (Path V2 n)) (N (Path V2 n)) Crossings
getQuery = forall r s a. Getting r s a -> (a -> r) -> s -> r
foldMapOf forall s t a b. Each s t a b => Traversal s t a b
each forall t m. HasQuery t m => t -> Query (V t) (N t) m
getQuery

-- | Test whether the given point is inside the given path,
--   by testing whether the point's /winding number/ is nonzero. Note
--   that @False@ is /always/ returned for paths consisting of lines
--   (as opposed to loops), regardless of the winding number.
--
-- @
-- 'isInsideWinding' :: 'Path' 'V2' 'Double'                  -> 'Point' 'V2' 'Double' -> 'Bool'
-- 'isInsideWinding' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Point' 'V2' 'Double' -> 'Bool'
-- 'isInsideWinding' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Point' 'V2' 'Double' -> 'Bool'
-- @
isInsideWinding :: HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideWinding :: forall t. HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideWinding t
t = (forall a. Eq a => a -> a -> Bool
/= Crossings
0) forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t m. HasQuery t m => t -> Point (V t) (N t) -> m
sample t
t

-- | Test whether the given point is inside the given path,
--   by testing whether a ray extending from the point in the positive
--   x direction crosses the path an even (outside) or odd (inside)
--   number of times.  Note that @False@ is /always/ returned for
--   paths consisting of lines (as opposed to loops), regardless of
--   the number of crossings.
--
-- @
-- 'isInsideEvenOdd' :: 'Path' 'V2' 'Double'                  -> 'Point' 'V2' 'Double' -> 'Bool'
-- 'isInsideEvenOdd' :: 'Located' ('Trail' 'V2' 'Double')       -> 'Point' 'V2' 'Double' -> 'Bool'
-- 'isInsideEvenOdd' :: 'Located' ('Trail'' 'Loop' 'V2' 'Double') -> 'Point' 'V2' 'Double' -> 'Bool'
-- @
isInsideEvenOdd :: HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideEvenOdd :: forall t. HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideEvenOdd t
t = forall a. Integral a => a -> Bool
odd forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t m. HasQuery t m => t -> Point (V t) (N t) -> m
sample t
t

-- | Compute the sum of signed crossings of a trail starting from the
--   given point in the positive x direction.
trailCrossings :: RealFloat n => Point V2 n -> Located (Trail V2 n) -> Crossings

  -- non-loop trails have no inside or outside, so don't contribute crossings
trailCrossings :: forall n.
RealFloat n =>
Point V2 n -> Located (Trail V2 n) -> Crossings
trailCrossings Point V2 n
_ Located (Trail V2 n)
t | Bool -> Bool
not (forall (v :: * -> *) n. Trail v n -> Bool
isLoop (forall a. Located a -> a
unLoc Located (Trail V2 n)
t)) = Crossings
0

trailCrossings p :: Point V2 n
p@(forall n. P2 n -> (n, n)
unp2 -> (n
x,n
y)) Located (Trail V2 n)
tr
  = forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
F.foldMap FixedSegment V2 n -> Crossings
test forall a b. (a -> b) -> a -> b
$ forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Located (Trail v n) -> [FixedSegment v n]
fixTrail Located (Trail V2 n)
tr
  where
    test :: FixedSegment V2 n -> Crossings
test (FLinear a :: Point V2 n
a@(forall n. P2 n -> (n, n)
unp2 -> (n
_,n
ay)) b :: Point V2 n
b@(forall n. P2 n -> (n, n)
unp2 -> (n
_,n
by)))
      | n
ay forall a. Ord a => a -> a -> Bool
<= n
y Bool -> Bool -> Bool
&& n
by forall a. Ord a => a -> a -> Bool
> n
y Bool -> Bool -> Bool
&& Point V2 n -> Point V2 n -> n
isLeft Point V2 n
a Point V2 n
b forall a. Ord a => a -> a -> Bool
> n
0 =  Crossings
1
      | n
by forall a. Ord a => a -> a -> Bool
<= n
y Bool -> Bool -> Bool
&& n
ay forall a. Ord a => a -> a -> Bool
> n
y Bool -> Bool -> Bool
&& Point V2 n -> Point V2 n -> n
isLeft Point V2 n
a Point V2 n
b forall a. Ord a => a -> a -> Bool
< n
0 = -Crossings
1
      | Bool
otherwise                           =  Crossings
0

    test c :: FixedSegment V2 n
c@(FCubic (P x1 :: V2 n
x1@(V2 n
_ n
x1y))
                   (P c1 :: V2 n
c1@(V2 n
_ n
c1y))
                   (P c2 :: V2 n
c2@(V2 n
_ n
c2y))
                   (P x2 :: V2 n
x2@(V2 n
_ n
x2y))
           ) =
        forall (t :: * -> *) a. (Foldable t, Num a) => t a -> a
sum forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b. (a -> b) -> [a] -> [b]
map n -> Crossings
testT forall a b. (a -> b) -> a -> b
$ [n]
ts
      where ts :: [n]
ts = forall a. (a -> Bool) -> [a] -> [a]
filter (forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 Bool -> Bool -> Bool
(&&) (forall a. Ord a => a -> a -> Bool
>=n
0) (forall a. Ord a => a -> a -> Bool
<=n
1))
               forall a b. (a -> b) -> a -> b
$ forall d. (Floating d, Ord d) => d -> d -> d -> d -> [d]
cubForm (-  n
x1y forall a. Num a => a -> a -> a
+ n
3forall a. Num a => a -> a -> a
*n
c1y forall a. Num a => a -> a -> a
- n
3forall a. Num a => a -> a -> a
*n
c2y forall a. Num a => a -> a -> a
+ n
x2y)
                         ( n
3forall a. Num a => a -> a -> a
*n
x1y forall a. Num a => a -> a -> a
- n
6forall a. Num a => a -> a -> a
*n
c1y forall a. Num a => a -> a -> a
+ n
3forall a. Num a => a -> a -> a
*n
c2y)
                         (-n
3forall a. Num a => a -> a -> a
*n
x1y forall a. Num a => a -> a -> a
+ n
3forall a. Num a => a -> a -> a
*n
c1y)
                         (n
x1y forall a. Num a => a -> a -> a
- n
y)
            testT :: n -> Crossings
testT n
t = let (forall n. P2 n -> (n, n)
unp2 -> (n
px,n
_)) = FixedSegment V2 n
c forall p. Parametric p => p -> N p -> Codomain p (N p)
`atParam` n
t
                      in  if n
px forall a. Ord a => a -> a -> Bool
> n
x then n -> Crossings
signFromDerivAt n
t else Crossings
0
            signFromDerivAt :: n -> Crossings
signFromDerivAt n
t =
              let v :: V2 n
v =  (n
3forall a. Num a => a -> a -> a
*n
tforall a. Num a => a -> a -> a
*n
t) forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^ ((-n
1)forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
x1 forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^+^ n
3forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
c1 forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^-^ n
3forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
c2 forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^+^ V2 n
x2)
                   forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^+^ (n
2forall a. Num a => a -> a -> a
*n
t)   forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^ (n
3forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
x1 forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^-^ n
6forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
c1 forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^+^ n
3forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
c2)
                   forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^+^            ((-n
3)forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
x1 forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
^+^ n
3forall (f :: * -> *) a. (Functor f, Num a) => a -> f a -> f a
*^V2 n
c1)
                  ang :: n
ang = V2 n
v forall s a. s -> Getting a s a -> a
^. forall (t :: * -> *) n.
(HasTheta t, RealFloat n) =>
Lens' (t n) (Angle n)
_theta forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall n. Iso' (Angle n) n
rad
              in  case () of ()
_ | n
0      forall a. Ord a => a -> a -> Bool
< n
ang Bool -> Bool -> Bool
&& n
ang forall a. Ord a => a -> a -> Bool
< forall a. Floating a => a
tauforall a. Fractional a => a -> a -> a
/n
2 Bool -> Bool -> Bool
&& n
t forall a. Ord a => a -> a -> Bool
< n
1 ->  Crossings
1
                               | -forall a. Floating a => a
tauforall a. Fractional a => a -> a -> a
/n
2 forall a. Ord a => a -> a -> Bool
< n
ang Bool -> Bool -> Bool
&& n
ang forall a. Ord a => a -> a -> Bool
< n
0     Bool -> Bool -> Bool
&& n
t forall a. Ord a => a -> a -> Bool
> n
0 -> -Crossings
1
                               | Bool
otherwise                            ->  Crossings
0

    isLeft :: Point V2 n -> Point V2 n -> n
isLeft Point V2 n
a Point V2 n
b = forall n. Num n => V2 n -> V2 n -> n
cross2 (Point V2 n
b forall (p :: * -> *) a. (Affine p, Num a) => p a -> p a -> Diff p a
.-. Point V2 n
a) (Point V2 n
p forall (p :: * -> *) a. (Affine p, Num a) => p a -> p a -> Diff p a
.-. Point V2 n
a)

------------------------------------------------------------
--  Clipping  ----------------------------------------------
------------------------------------------------------------

-- | @Clip@ tracks the accumulated clipping paths applied to a
--   diagram.  Note that the semigroup structure on @Clip@ is list
--   concatenation, so applying multiple clipping paths is sensible.
--   The clipping region is the intersection of all the applied
--   clipping paths.
newtype Clip n = Clip [Path V2 n]
  deriving (Typeable, NonEmpty (Clip n) -> Clip n
Clip n -> Clip n -> Clip n
forall b. Integral b => b -> Clip n -> Clip n
forall n. NonEmpty (Clip n) -> Clip n
forall n. Clip n -> Clip n -> Clip n
forall a.
(a -> a -> a)
-> (NonEmpty a -> a)
-> (forall b. Integral b => b -> a -> a)
-> Semigroup a
forall n b. Integral b => b -> Clip n -> Clip n
stimes :: forall b. Integral b => b -> Clip n -> Clip n
$cstimes :: forall n b. Integral b => b -> Clip n -> Clip n
sconcat :: NonEmpty (Clip n) -> Clip n
$csconcat :: forall n. NonEmpty (Clip n) -> Clip n
<> :: Clip n -> Clip n -> Clip n
$c<> :: forall n. Clip n -> Clip n -> Clip n
Semigroup)

makeWrapped ''Clip

instance Typeable n => AttributeClass (Clip n)

instance AsEmpty (Clip n) where
  _Empty :: Prism' (Clip n) ()
_Empty = forall n n'. Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n']
_Clip forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. AsEmpty a => Prism' a ()
_Empty

type instance V (Clip n) = V2
type instance N (Clip n) = n

instance (OrderedField n) => Transformable (Clip n) where
  transform :: Transformation (V (Clip n)) (N (Clip n)) -> Clip n -> Clip n
transform Transformation (V (Clip n)) (N (Clip n))
t (Clip [Path V2 n]
ps) = forall n. [Path V2 n] -> Clip n
Clip (forall t. Transformable t => Transformation (V t) (N t) -> t -> t
transform Transformation (V (Clip n)) (N (Clip n))
t [Path V2 n]
ps)

-- | A point inside a clip if the point is in 'All' invididual clipping
--   paths.
instance RealFloat n => HasQuery (Clip n) All where
  getQuery :: Clip n -> Query (V (Clip n)) (N (Clip n)) All
getQuery (Clip [Path V2 n]
paths) = forall (v :: * -> *) n m. (Point v n -> m) -> Query v n m
Query forall a b. (a -> b) -> a -> b
$ \Point (V (Clip n)) (N (Clip n))
p ->
    forall (t :: * -> *) m a.
(Foldable t, Monoid m) =>
(a -> m) -> t a -> m
F.foldMap (Bool -> All
All forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a b c. (a -> b -> c) -> b -> a -> c
flip forall t. HasQuery t Crossings => t -> Point (V t) (N t) -> Bool
isInsideWinding Point (V (Clip n)) (N (Clip n))
p) [Path V2 n]
paths

_Clip :: Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n']
_Clip :: forall n n'. Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n']
_Clip = forall s t. Rewrapping s t => Iso s t (Unwrapped s) (Unwrapped t)
_Wrapped

-- | Lens onto the Clip in a style. An empty list means no clipping.
_clip :: (Typeable n, OrderedField n) => Lens' (Style V2 n) [Path V2 n]
_clip :: forall n.
(Typeable n, OrderedField n) =>
Lens' (Style V2 n) [Path V2 n]
_clip = forall a (v :: * -> *) n.
(V a ~ v, N a ~ n, AttributeClass a, Transformable a) =>
Lens' (Style v n) (Maybe a)
atTAttr forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. APrism' a () -> Iso' (Maybe a) a
non' forall a. AsEmpty a => Prism' a ()
_Empty forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall n n'. Iso (Clip n) (Clip n') [Path V2 n] [Path V2 n']
_Clip

-- | Clip a diagram by the given path:
--
--   * Only the parts of the diagram which lie in the interior of the
--     path will be drawn.
--
--   * The envelope of the diagram is unaffected.
clipBy :: (HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) => Path V2 n -> a -> a
clipBy :: forall a n.
(HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) =>
Path V2 n -> a -> a
clipBy = forall a d.
(AttributeClass a, Transformable a, V a ~ V d, N a ~ N d,
 HasStyle d) =>
a -> d -> d
applyTAttr forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall n. [Path V2 n] -> Clip n
Clip forall b c a. (b -> c) -> (a -> b) -> a -> c
. (forall a. a -> [a] -> [a]
:[])

-- | Clip a diagram to the given path setting its envelope to the
--   pointwise minimum of the envelopes of the diagram and path. The
--   trace consists of those parts of the original diagram's trace
--   which fall within the clipping path, or parts of the path's trace
--   within the original diagram.
clipTo :: TypeableFloat n
  => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
clipTo :: forall n b.
TypeableFloat n =>
Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
clipTo Path V2 n
p QDiagram b V2 n Any
d = forall b (v :: * -> *) n m.
(OrderedField n, Metric v, Semigroup m) =>
Trace v n -> QDiagram b v n m -> QDiagram b v n m
setTrace Trace V2 n
intersectionTrace forall b c a. (b -> c) -> (a -> b) -> a -> c
. QDiagram b V2 n Any -> QDiagram b V2 n Any
toEnvelope forall a b. (a -> b) -> a -> b
$ forall a n.
(HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) =>
Path V2 n -> a -> a
clipBy Path V2 n
p QDiagram b V2 n Any
d
  where
    envP :: Maybe (V2 n -> n)
envP = forall (v :: * -> *) n. Envelope v n -> Maybe (v n -> n)
appEnvelope forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Enveloped a => a -> Envelope (V a) (N a)
getEnvelope forall a b. (a -> b) -> a -> b
$ Path V2 n
p
    envD :: Maybe (V2 n -> n)
envD = forall (v :: * -> *) n. Envelope v n -> Maybe (v n -> n)
appEnvelope forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a. Enveloped a => a -> Envelope (V a) (N a)
getEnvelope forall a b. (a -> b) -> a -> b
$ QDiagram b V2 n Any
d
    toEnvelope :: QDiagram b V2 n Any -> QDiagram b V2 n Any
toEnvelope = case (Maybe (V2 n -> n)
envP, Maybe (V2 n -> n)
envD) of
      (Just V2 n -> n
eP, Just V2 n -> n
eD) -> forall b (v :: * -> *) n m.
(OrderedField n, Metric v, Monoid' m) =>
Envelope v n -> QDiagram b v n m -> QDiagram b v n m
setEnvelope forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n. (v n -> n) -> Envelope v n
mkEnvelope forall a b. (a -> b) -> a -> b
$ \V2 n
v -> forall a. Ord a => a -> a -> a
min (V2 n -> n
eP V2 n
v) (V2 n -> n
eD V2 n
v)
      (Maybe (V2 n -> n)
_, Maybe (V2 n -> n)
_)             -> forall a. a -> a
id
    intersectionTrace :: Trace V2 n
intersectionTrace = forall (v :: * -> *) n.
(Point v n -> v n -> SortedList n) -> Trace v n
Trace Point V2 n -> V2 n -> SortedList n
traceIntersections
    traceIntersections :: Point V2 n -> V2 n -> SortedList n
traceIntersections Point V2 n
pt V2 n
v =
        -- on boundary of d, inside p
        forall b a. Ord b => ([a] -> [b]) -> SortedList a -> SortedList b
onSortedList (forall a. (a -> Bool) -> [a] -> [a]
filter n -> Bool
pInside) (forall (v :: * -> *) n.
Trace v n -> Point v n -> v n -> SortedList n
appTrace (forall a. Traced a => a -> Trace (V a) (N a)
getTrace QDiagram b V2 n Any
d) Point V2 n
pt V2 n
v) forall a. Semigroup a => a -> a -> a
<>
        -- or on boundary of p, inside d
        forall b a. Ord b => ([a] -> [b]) -> SortedList a -> SortedList b
onSortedList (forall a. (a -> Bool) -> [a] -> [a]
filter n -> Bool
dInside) (forall (v :: * -> *) n.
Trace v n -> Point v n -> v n -> SortedList n
appTrace (forall a. Traced a => a -> Trace (V a) (N a)
getTrace Path V2 n
p) Point V2 n
pt V2 n
v) where
          newPt :: n -> Point V2 n
newPt n
dist = Point V2 n
pt forall (p :: * -> *) a. (Affine p, Num a) => p a -> Diff p a -> p a
.+^ V2 n
v forall (f :: * -> *) a. (Functor f, Num a) => f a -> a -> f a
^* n
dist
          pInside :: n -> Bool
pInside n
dDist = forall n.
RealFloat n =>
FillRule -> Path V2 n -> Point V2 n -> Bool
runFillRule FillRule
Winding Path V2 n
p (n -> Point V2 n
newPt n
dDist)
          dInside :: n -> Bool
dInside n
pDist = Any -> Bool
getAny forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall t m. HasQuery t m => t -> Point (V t) (N t) -> m
sample QDiagram b V2 n Any
d forall a b. (a -> b) -> a -> b
$ n -> Point V2 n
newPt n
pDist

-- | Clip a diagram to the clip path taking the envelope and trace of the clip
--   path.
clipped :: TypeableFloat n
  => Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
clipped :: forall n b.
TypeableFloat n =>
Path V2 n -> QDiagram b V2 n Any -> QDiagram b V2 n Any
clipped Path V2 n
p = forall (v :: * -> *) n a m b.
(InSpace v n a, Metric v, OrderedField n, Monoid' m, Traced a) =>
a -> QDiagram b v n m -> QDiagram b v n m
withTrace Path V2 n
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall (v :: * -> *) n a m b.
(InSpace v n a, Monoid' m, Enveloped a) =>
a -> QDiagram b v n m -> QDiagram b v n m
withEnvelope Path V2 n
p forall b c a. (b -> c) -> (a -> b) -> a -> c
. forall a n.
(HasStyle a, V a ~ V2, N a ~ n, TypeableFloat n) =>
Path V2 n -> a -> a
clipBy Path V2 n
p

------------------------------------------------------------
--  Intersections  -----------------------------------------
------------------------------------------------------------

-- | Find the intersect points of two objects that can be converted to a path.
intersectPoints :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n)
  => t -> s -> [P2 n]
intersectPoints :: forall n t s.
(InSpace V2 n t, SameSpace t s, ToPath t, ToPath s,
 OrderedField n) =>
t -> s -> [P2 n]
intersectPoints = forall n t s.
(InSpace V2 n t, SameSpace t s, ToPath t, ToPath s,
 OrderedField n) =>
n -> t -> s -> [P2 n]
intersectPoints' n
1e-8

-- | Find the intersect points of two objects that can be converted to a path
--   within the given tolerance.
intersectPoints' :: (InSpace V2 n t, SameSpace t s, ToPath t, ToPath s, OrderedField n)
  => n -> t -> s -> [P2 n]
intersectPoints' :: forall n t s.
(InSpace V2 n t, SameSpace t s, ToPath t, ToPath s,
 OrderedField n) =>
n -> t -> s -> [P2 n]
intersectPoints' n
eps t
t s
s = forall n. OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP' n
eps (forall t.
(ToPath t, Metric (V t), OrderedField (N t)) =>
t -> Path (V t) (N t)
toPath t
t) (forall t.
(ToPath t, Metric (V t), OrderedField (N t)) =>
t -> Path (V t) (N t)
toPath s
s)

-- | Compute the intersect points between two paths.
intersectPointsP :: OrderedField n => Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP :: forall n. OrderedField n => Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP = forall n. OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP' n
1e-8

-- | Compute the intersect points between two paths within given tolerance.
intersectPointsP' :: OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP' :: forall n. OrderedField n => n -> Path V2 n -> Path V2 n -> [P2 n]
intersectPointsP' n
eps Path V2 n
as Path V2 n
bs = do
  Located (Trail V2 n)
a <- forall (v :: * -> *) n. Path v n -> [Located (Trail v n)]
pathTrails Path V2 n
as
  Located (Trail V2 n)
b <- forall (v :: * -> *) n. Path v n -> [Located (Trail v n)]
pathTrails Path V2 n
bs
  forall n.
OrderedField n =>
n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT' n
eps Located (Trail V2 n)
a Located (Trail V2 n)
b

-- | Compute the intersect points between two located trails.
intersectPointsT :: OrderedField n => Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT :: forall n.
OrderedField n =>
Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT = forall n.
OrderedField n =>
n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT' n
1e-8

-- | Compute the intersect points between two located trails within the given
--   tolerance.
intersectPointsT' :: OrderedField n => n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT' :: forall n.
OrderedField n =>
n -> Located (Trail V2 n) -> Located (Trail V2 n) -> [P2 n]
intersectPointsT' n
eps Located (Trail V2 n)
as Located (Trail V2 n)
bs = do
  FixedSegment V2 n
a <- forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Located (Trail v n) -> [FixedSegment v n]
fixTrail Located (Trail V2 n)
as
  FixedSegment V2 n
b <- forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Located (Trail v n) -> [FixedSegment v n]
fixTrail Located (Trail V2 n)
bs
  forall n.
OrderedField n =>
n -> FixedSegment V2 n -> FixedSegment V2 n -> [P2 n]
intersectPointsS' n
eps FixedSegment V2 n
a FixedSegment V2 n
b