{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ViewPatterns #-}

-- |
-- Module      :  Diagrams.TwoD.Polygons
-- Copyright   :  (c) 2011 diagrams-lib team (see LICENSE)
-- License     :  BSD-style (see LICENSE)
-- Maintainer  :  diagrams-discuss@googlegroups.com
--
-- This module defines a general API for creating various types of
-- polygons.
module Diagrams.TwoD.Polygons (
  -- * Polygons
  PolyType (..),
  PolyOrientation (..),
  PolygonOpts (..),
  polyType,
  polyOrient,
  polyCenter,
  polygon,
  polyTrail,

  -- ** Generating polygon vertices
  polyPolarTrail,
  polySidesTrail,
  polyRegularTrail,
  orient,

  -- * Star polygons
  StarOpts (..),
  star,

  -- ** Function graphs
  -- $graphs
  GraphPart (..),
  orbits,
  mkGraph,
) where

import Control.Lens (
  Lens',
  generateSignatures,
  lensRules,
  makeLensesWith,
  view,
  (.~),
  (^.),
 )
import Control.Monad (forM, liftM)
import Control.Monad.ST (ST, runST)
import Data.Array.ST (
  STUArray,
  newArray,
  readArray,
  writeArray,
 )
import Data.Default
import Data.List (maximumBy, minimumBy)
import Data.List.NonEmpty (NonEmpty (..))
import qualified Data.List.NonEmpty as NE
import Data.Maybe (catMaybes)
import Data.Ord (comparing)

import Diagrams.Angle
import Diagrams.Core
import Diagrams.Located
import Diagrams.Path
import Diagrams.Points (centroid)
import Diagrams.Trail
import Diagrams.TrailLike
import Diagrams.TwoD.Types
import Diagrams.TwoD.Vector (leftTurn, unitX, unitY, unit_Y)
import Diagrams.Util (tau, (#))

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

-- | Method used to determine the vertices of a polygon.
data PolyType n
  = -- | A \"polar\" polygon.
    --
    --   * The first argument is a list of /central/
    --     /angles/ from each vertex to the next.
    --
    --   * The second argument is a list of /radii/ from
    --     the origin to each successive vertex.
    --
    --   To construct an /n/-gon, use a list of /n-1/
    --   angles and /n/ radii.  Extra angles or radii
    --   are ignored.
    --
    --   Cyclic polygons (with all vertices lying on a
    --   circle) can be constructed using a second
    --   argument of @(repeat r)@.
    PolyPolar [Angle n] [n]
  | -- | A polygon determined by the distance between
    --   successive vertices and the external angles formed
    --   by each three successive vertices. In other
    --   words, a polygon specified by \"turtle
    --   graphics\": go straight ahead x1 units; turn by
    --   external angle a1; go straight ahead x2 units; turn by
    --   external angle a2; etc. The polygon will be centered
    --   at the /centroid/ of its vertices.
    --
    --   * The first argument is a list of /vertex/
    --     /angles/, giving the external angle at each vertex
    --     from the previous vertex to the next.  The
    --     first angle in the list is the external angle at
    --     the /second/ vertex; the first edge always starts
    --     out heading in the positive y direction from
    --     the first vertex.
    --
    --   * The second argument is a list of distances
    --     between successive vertices.
    --
    --   To construct an /n/-gon, use a list of /n-2/
    --   angles and /n-1/ edge lengths.  Extra angles or
    --   lengths are ignored.
    PolySides [Angle n] [n]
  | -- | A regular polygon with the given number of
    --   sides (first argument) and the given radius
    --   (second argument).
    PolyRegular Int n

-- | Determine how a polygon should be oriented.
data PolyOrientation n
  = -- | No special orientation; the first
    --   vertex will be at (1,0).
    NoOrient
  | -- | Orient /horizontally/, so the
    --   bottommost edge is parallel to
    --   the x-axis.
    --   This is the default.
    OrientH
  | -- | Orient /vertically/, so the
    --   leftmost edge is parallel to the
    --   y-axis.
    OrientV
  | -- | Orient so some edge is
    --   /facing/ /in/ /the/ /direction/
    --   /of/, that is, perpendicular
    --   to, the given vector.
    OrientTo (V2 n)
  deriving (PolyOrientation n -> PolyOrientation n -> Bool
(PolyOrientation n -> PolyOrientation n -> Bool)
-> (PolyOrientation n -> PolyOrientation n -> Bool)
-> Eq (PolyOrientation n)
forall n. Eq n => PolyOrientation n -> PolyOrientation n -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: forall n. Eq n => PolyOrientation n -> PolyOrientation n -> Bool
== :: PolyOrientation n -> PolyOrientation n -> Bool
$c/= :: forall n. Eq n => PolyOrientation n -> PolyOrientation n -> Bool
/= :: PolyOrientation n -> PolyOrientation n -> Bool
Eq, Eq (PolyOrientation n)
Eq (PolyOrientation n) =>
(PolyOrientation n -> PolyOrientation n -> Ordering)
-> (PolyOrientation n -> PolyOrientation n -> Bool)
-> (PolyOrientation n -> PolyOrientation n -> Bool)
-> (PolyOrientation n -> PolyOrientation n -> Bool)
-> (PolyOrientation n -> PolyOrientation n -> Bool)
-> (PolyOrientation n -> PolyOrientation n -> PolyOrientation n)
-> (PolyOrientation n -> PolyOrientation n -> PolyOrientation n)
-> Ord (PolyOrientation n)
PolyOrientation n -> PolyOrientation n -> Bool
PolyOrientation n -> PolyOrientation n -> Ordering
PolyOrientation n -> PolyOrientation n -> PolyOrientation n
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
forall n. Ord n => Eq (PolyOrientation n)
forall n. Ord n => PolyOrientation n -> PolyOrientation n -> Bool
forall n.
Ord n =>
PolyOrientation n -> PolyOrientation n -> Ordering
forall n.
Ord n =>
PolyOrientation n -> PolyOrientation n -> PolyOrientation n
$ccompare :: forall n.
Ord n =>
PolyOrientation n -> PolyOrientation n -> Ordering
compare :: PolyOrientation n -> PolyOrientation n -> Ordering
$c< :: forall n. Ord n => PolyOrientation n -> PolyOrientation n -> Bool
< :: PolyOrientation n -> PolyOrientation n -> Bool
$c<= :: forall n. Ord n => PolyOrientation n -> PolyOrientation n -> Bool
<= :: PolyOrientation n -> PolyOrientation n -> Bool
$c> :: forall n. Ord n => PolyOrientation n -> PolyOrientation n -> Bool
> :: PolyOrientation n -> PolyOrientation n -> Bool
$c>= :: forall n. Ord n => PolyOrientation n -> PolyOrientation n -> Bool
>= :: PolyOrientation n -> PolyOrientation n -> Bool
$cmax :: forall n.
Ord n =>
PolyOrientation n -> PolyOrientation n -> PolyOrientation n
max :: PolyOrientation n -> PolyOrientation n -> PolyOrientation n
$cmin :: forall n.
Ord n =>
PolyOrientation n -> PolyOrientation n -> PolyOrientation n
min :: PolyOrientation n -> PolyOrientation n -> PolyOrientation n
Ord, Int -> PolyOrientation n -> ShowS
[PolyOrientation n] -> ShowS
PolyOrientation n -> String
(Int -> PolyOrientation n -> ShowS)
-> (PolyOrientation n -> String)
-> ([PolyOrientation n] -> ShowS)
-> Show (PolyOrientation n)
forall n. Show n => Int -> PolyOrientation n -> ShowS
forall n. Show n => [PolyOrientation n] -> ShowS
forall n. Show n => PolyOrientation n -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall n. Show n => Int -> PolyOrientation n -> ShowS
showsPrec :: Int -> PolyOrientation n -> ShowS
$cshow :: forall n. Show n => PolyOrientation n -> String
show :: PolyOrientation n -> String
$cshowList :: forall n. Show n => [PolyOrientation n] -> ShowS
showList :: [PolyOrientation n] -> ShowS
Show, ReadPrec [PolyOrientation n]
ReadPrec (PolyOrientation n)
Int -> ReadS (PolyOrientation n)
ReadS [PolyOrientation n]
(Int -> ReadS (PolyOrientation n))
-> ReadS [PolyOrientation n]
-> ReadPrec (PolyOrientation n)
-> ReadPrec [PolyOrientation n]
-> Read (PolyOrientation n)
forall n. Read n => ReadPrec [PolyOrientation n]
forall n. Read n => ReadPrec (PolyOrientation n)
forall n. Read n => Int -> ReadS (PolyOrientation n)
forall n. Read n => ReadS [PolyOrientation n]
forall a.
(Int -> ReadS a)
-> ReadS [a] -> ReadPrec a -> ReadPrec [a] -> Read a
$creadsPrec :: forall n. Read n => Int -> ReadS (PolyOrientation n)
readsPrec :: Int -> ReadS (PolyOrientation n)
$creadList :: forall n. Read n => ReadS [PolyOrientation n]
readList :: ReadS [PolyOrientation n]
$creadPrec :: forall n. Read n => ReadPrec (PolyOrientation n)
readPrec :: ReadPrec (PolyOrientation n)
$creadListPrec :: forall n. Read n => ReadPrec [PolyOrientation n]
readListPrec :: ReadPrec [PolyOrientation n]
Read)

-- | Options for specifying a polygon.
data PolygonOpts n = PolygonOpts
  { forall n. PolygonOpts n -> PolyType n
_polyType :: PolyType n
  , forall n. PolygonOpts n -> PolyOrientation n
_polyOrient :: PolyOrientation n
  , forall n. PolygonOpts n -> Point V2 n
_polyCenter :: Point V2 n
  }

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

-- | Specification for the polygon's vertices.
polyType :: Lens' (PolygonOpts n) (PolyType n)

-- | Should a rotation be applied to the polygon in order to orient it in a
--   particular way?
polyOrient :: Lens' (PolygonOpts n) (PolyOrientation n)

-- | Should a translation be applied to the polygon in order to place the center
--   at a particular location?
polyCenter :: Lens' (PolygonOpts n) (Point V2 n)

-- | The default polygon is a regular pentagon of radius 1, centered
--   at the origin, aligned to the x-axis.
instance Num n => Default (PolygonOpts n) where
  def :: PolygonOpts n
def = PolyType n -> PolyOrientation n -> Point V2 n -> PolygonOpts n
forall n.
PolyType n -> PolyOrientation n -> Point V2 n -> PolygonOpts n
PolygonOpts (Int -> n -> PolyType n
forall n. Int -> n -> PolyType n
PolyRegular Int
5 n
1) PolyOrientation n
forall n. PolyOrientation n
OrientH Point V2 n
forall (f :: * -> *) a. (Additive f, Num a) => Point f a
origin

-- | Generate a polygon.  See 'PolygonOpts' for more information.
polyTrail :: OrderedField n => PolygonOpts n -> Located (Trail V2 n)
polyTrail :: forall n. OrderedField n => PolygonOpts n -> Located (Trail V2 n)
polyTrail PolygonOpts n
po = Transformation
  (V (Located (Trail V2 n))) (N (Located (Trail V2 n)))
-> Located (Trail V2 n) -> Located (Trail V2 n)
forall t. Transformable t => Transformation (V t) (N t) -> t -> t
transform Transformation
  (V (Located (Trail V2 n))) (N (Located (Trail V2 n)))
Transformation V2 n
ori Located (Trail V2 n)
tr
 where
  tr :: Located (Trail V2 n)
tr = case PolygonOpts n
po PolygonOpts n
-> Getting (PolyType n) (PolygonOpts n) (PolyType n) -> PolyType n
forall s a. s -> Getting a s a -> a
^. Getting (PolyType n) (PolygonOpts n) (PolyType n)
forall n (f :: * -> *).
Functor f =>
(PolyType n -> f (PolyType n))
-> PolygonOpts n -> f (PolygonOpts n)
polyType of
    PolyPolar [Angle n]
ans [n]
szs -> [Angle n] -> [n] -> Located (Trail V2 n)
forall n.
OrderedField n =>
[Angle n] -> [n] -> Located (Trail V2 n)
polyPolarTrail [Angle n]
ans [n]
szs
    PolySides [Angle n]
ans [n]
szs -> [Angle n] -> [n] -> Located (Trail V2 n)
forall n.
OrderedField n =>
[Angle n] -> [n] -> Located (Trail V2 n)
polySidesTrail [Angle n]
ans [n]
szs
    PolyRegular Int
n n
r -> Int -> n -> Located (Trail V2 n)
forall n. OrderedField n => Int -> n -> Located (Trail V2 n)
polyRegularTrail Int
n n
r
  ori :: Transformation V2 n
ori = case PolygonOpts n
po PolygonOpts n
-> Getting (PolyOrientation n) (PolygonOpts n) (PolyOrientation n)
-> PolyOrientation n
forall s a. s -> Getting a s a -> a
^. Getting (PolyOrientation n) (PolygonOpts n) (PolyOrientation n)
forall n (f :: * -> *).
Functor f =>
(PolyOrientation n -> f (PolyOrientation n))
-> PolygonOpts n -> f (PolygonOpts n)
polyOrient of
    PolyOrientation n
OrientH -> V2 n -> Located (Trail V2 n) -> Transformation V2 n
forall n.
OrderedField n =>
V2 n -> Located (Trail V2 n) -> Transformation V2 n
orient V2 n
forall (v :: * -> *) n. (R2 v, Additive v, Num n) => v n
unit_Y Located (Trail V2 n)
tr
    PolyOrientation n
OrientV -> V2 n -> Located (Trail V2 n) -> Transformation V2 n
forall n.
OrderedField n =>
V2 n -> Located (Trail V2 n) -> Transformation V2 n
orient V2 n
forall (v :: * -> *) n. (R1 v, Additive v, Num n) => v n
unitX Located (Trail V2 n)
tr
    OrientTo V2 n
v -> V2 n -> Located (Trail V2 n) -> Transformation V2 n
forall n.
OrderedField n =>
V2 n -> Located (Trail V2 n) -> Transformation V2 n
orient V2 n
v Located (Trail V2 n)
tr
    PolyOrientation n
NoOrient -> Transformation V2 n
forall a. Monoid a => a
mempty

-- | Generate the polygon described by the given options.
polygon :: (InSpace V2 n t, TrailLike t) => PolygonOpts n -> t
polygon :: forall n t. (InSpace V2 n t, TrailLike t) => PolygonOpts n -> t
polygon = Located (Trail (V t) (N t)) -> t
Located (Trail V2 n) -> t
forall t. TrailLike t => Located (Trail (V t) (N t)) -> t
trailLike (Located (Trail V2 n) -> t)
-> (PolygonOpts n -> Located (Trail V2 n)) -> PolygonOpts n -> t
forall b c a. (b -> c) -> (a -> b) -> a -> c
. PolygonOpts n -> Located (Trail V2 n)
forall n. OrderedField n => PolygonOpts n -> Located (Trail V2 n)
polyTrail

-- | Generate the located trail of a polygon specified by polar data
--   (central angles and radii). See 'PolyPolar'.
polyPolarTrail :: OrderedField n => [Angle n] -> [n] -> Located (Trail V2 n)
polyPolarTrail :: forall n.
OrderedField n =>
[Angle n] -> [n] -> Located (Trail V2 n)
polyPolarTrail [] [n]
_ = Trail V2 n
forall (v :: * -> *) n. (Metric v, OrderedField n) => Trail v n
emptyTrail Trail V2 n
-> Point (V (Trail V2 n)) (N (Trail V2 n)) -> Located (Trail V2 n)
forall a. a -> Point (V a) (N a) -> Located a
`at` Point (V (Trail V2 n)) (N (Trail V2 n))
Point V2 n
forall (f :: * -> *) a. (Additive f, Num a) => Point f a
origin
polyPolarTrail [Angle n]
_ [] = Trail V2 n
forall (v :: * -> *) n. (Metric v, OrderedField n) => Trail v n
emptyTrail Trail V2 n
-> Point (V (Trail V2 n)) (N (Trail V2 n)) -> Located (Trail V2 n)
forall a. a -> Point (V a) (N a) -> Located a
`at` Point (V (Trail V2 n)) (N (Trail V2 n))
Point V2 n
forall (f :: * -> *) a. (Additive f, Num a) => Point f a
origin
polyPolarTrail [Angle n]
ans (n
r : [n]
rs) = Trail V2 n
tr Trail V2 n
-> Point (V (Trail V2 n)) (N (Trail V2 n)) -> Located (Trail V2 n)
forall a. a -> Point (V a) (N a) -> Located a
`at` Point (V (Trail V2 n)) (N (Trail V2 n))
Point V2 n
p1
 where
  p1 :: Point V2 n
p1 = (n, n) -> Point V2 n
forall n. (n, n) -> P2 n
p2 (n
1, n
0) Point V2 n -> (Point V2 n -> Point V2 n) -> Point V2 n
forall a b. a -> (a -> b) -> b
# n -> Point V2 n -> Point V2 n
forall (v :: * -> *) n a.
(InSpace v n a, Eq n, Fractional n, Transformable a) =>
n -> a -> a
scale n
r
  tr :: Trail V2 n
tr =
    Trail V2 n -> Trail V2 n
forall (v :: * -> *) n. Trail v n -> Trail v n
closeTrail (Trail V2 n -> Trail V2 n)
-> ([Point V2 n] -> Trail V2 n) -> [Point V2 n] -> Trail V2 n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Point V2 n] -> Trail V2 n
forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
[Point v n] -> Trail v n
trailFromVertices ([Point V2 n] -> Trail V2 n) -> [Point V2 n] -> Trail V2 n
forall a b. (a -> b) -> a -> b
$
      (Angle n -> n -> Point V2 n) -> [Angle n] -> [n] -> [Point V2 n]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith
        (\Angle n
a n
l -> Angle n -> Point V2 n -> Point V2 n
forall n t.
(InSpace V2 n t, Transformable t, Floating n) =>
Angle n -> t -> t
rotate Angle n
a (Point V2 n -> Point V2 n)
-> (Point V2 n -> Point V2 n) -> Point V2 n -> Point V2 n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. n -> Point V2 n -> Point V2 n
forall (v :: * -> *) n a.
(InSpace v n a, Eq n, Fractional n, Transformable a) =>
n -> a -> a
scale n
l (Point V2 n -> Point V2 n) -> Point V2 n -> Point V2 n
forall a b. (a -> b) -> a -> b
$ (n, n) -> Point V2 n
forall n. (n, n) -> P2 n
p2 (n
1, n
0))
        ((Angle n -> Angle n -> Angle n)
-> Angle n -> [Angle n] -> [Angle n]
forall b a. (b -> a -> b) -> b -> [a] -> [b]
scanl Angle n -> Angle n -> Angle n
forall a. Num a => Angle a -> Angle a -> Angle a
forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
(^+^) Angle n
forall a. Num a => Angle a
forall (f :: * -> *) a. (Additive f, Num a) => f a
zero [Angle n]
ans)
        (n
r n -> [n] -> [n]
forall a. a -> [a] -> [a]
: [n]
rs)

-- | Generate the vertices of a polygon specified by side length and
--   angles, and a starting point for the trail such that the origin
--   is at the centroid of the vertices.  See 'PolySides'.
polySidesTrail :: OrderedField n => [Angle n] -> [n] -> Located (Trail V2 n)
polySidesTrail :: forall n.
OrderedField n =>
[Angle n] -> [n] -> Located (Trail V2 n)
polySidesTrail [Angle n]
ans [n]
ls = Trail V2 n
tr Trail V2 n
-> Point (V (Trail V2 n)) (N (Trail V2 n)) -> Located (Trail V2 n)
forall a. a -> Point (V a) (N a) -> Located a
`at` ([Point V2 n] -> Point V2 n
forall (v :: * -> *) n.
(Additive v, Fractional n) =>
[Point v n] -> Point v n
centroid [Point V2 n]
ps Point V2 n -> (Point V2 n -> Point V2 n) -> Point V2 n
forall a b. a -> (a -> b) -> b
# n -> Point V2 n -> Point V2 n
forall (v :: * -> *) n a.
(InSpace v n a, Eq n, Fractional n, Transformable a) =>
n -> a -> a
scale (-n
1))
 where
  ans' :: [Angle n]
ans' = (Angle n -> Angle n -> Angle n)
-> Angle n -> [Angle n] -> [Angle n]
forall b a. (b -> a -> b) -> b -> [a] -> [b]
scanl Angle n -> Angle n -> Angle n
forall a. Num a => Angle a -> Angle a -> Angle a
forall (f :: * -> *) a. (Additive f, Num a) => f a -> f a -> f a
(^+^) Angle n
forall a. Num a => Angle a
forall (f :: * -> *) a. (Additive f, Num a) => f a
zero [Angle n]
ans
  offsets :: [V2 n]
offsets = (Angle n -> V2 n -> V2 n) -> [Angle n] -> [V2 n] -> [V2 n]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith Angle n -> V2 n -> V2 n
forall n t.
(InSpace V2 n t, Transformable t, Floating n) =>
Angle n -> t -> t
rotate [Angle n]
ans' ((n -> V2 n) -> [n] -> [V2 n]
forall a b. (a -> b) -> [a] -> [b]
map (V2 n
forall (v :: * -> *) n. (R2 v, Additive v, Num n) => v n
unitY V2 n -> n -> V2 n
forall (f :: * -> *) a. (Functor f, Num a) => f a -> a -> f a
^*) [n]
ls)
  ps :: [Point V2 n]
ps = (Point V2 n -> V2 n -> Point V2 n)
-> Point V2 n -> [V2 n] -> [Point V2 n]
forall b a. (b -> a -> b) -> b -> [a] -> [b]
scanl Point V2 n -> V2 n -> Point V2 n
Point V2 n -> Diff (Point V2) n -> Point V2 n
forall a. Num a => Point V2 a -> Diff (Point V2) a -> Point V2 a
forall (p :: * -> *) a. (Affine p, Num a) => p a -> Diff p a -> p a
(.+^) Point V2 n
forall (f :: * -> *) a. (Additive f, Num a) => Point f a
origin [V2 n]
offsets
  tr :: Trail V2 n
tr = Trail V2 n -> Trail V2 n
forall (v :: * -> *) n. Trail v n -> Trail v n
closeTrail (Trail V2 n -> Trail V2 n)
-> ([V2 n] -> Trail V2 n) -> [V2 n] -> Trail V2 n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [V2 n] -> Trail V2 n
forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
[v n] -> Trail v n
trailFromOffsets ([V2 n] -> Trail V2 n) -> [V2 n] -> Trail V2 n
forall a b. (a -> b) -> a -> b
$ [V2 n]
offsets

-- | Generate the vertices of a regular polygon.  See 'PolyRegular'.
polyRegularTrail :: OrderedField n => Int -> n -> Located (Trail V2 n)
polyRegularTrail :: forall n. OrderedField n => Int -> n -> Located (Trail V2 n)
polyRegularTrail Int
n n
r =
  [Angle n] -> [n] -> Located (Trail V2 n)
forall n.
OrderedField n =>
[Angle n] -> [n] -> Located (Trail V2 n)
polyPolarTrail
    (Int -> Angle n -> [Angle n]
forall a. Int -> a -> [a]
replicate (Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1) (Angle n -> [Angle n]) -> Angle n -> [Angle n]
forall a b. (a -> b) -> a -> b
$ Angle n
forall v. Floating v => Angle v
fullTurn Angle n -> n -> Angle n
forall (f :: * -> *) a.
(Functor f, Fractional a) =>
f a -> a -> f a
^/ Int -> n
forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
n)
    (n -> [n]
forall a. a -> [a]
repeat n
r)

-- | Generate a transformation to orient a trail.  @orient v t@
--   generates the smallest rotation such that one of the segments
--   adjacent to the vertex furthest in the direction of @v@ is
--   perpendicular to @v@.
orient :: OrderedField n => V2 n -> Located (Trail V2 n) -> Transformation V2 n
orient :: forall n.
OrderedField n =>
V2 n -> Located (Trail V2 n) -> Transformation V2 n
orient V2 n
v = V2 n -> [Point V2 n] -> Transformation V2 n
forall n.
OrderedField n =>
V2 n -> [Point V2 n] -> Transformation V2 n
orientPoints V2 n
v ([Point V2 n] -> Transformation V2 n)
-> (Located (Trail V2 n) -> [Point V2 n])
-> Located (Trail V2 n)
-> Transformation V2 n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Located (Trail V2 n) -> [Point V2 n]
forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Located (Trail v n) -> [Point v n]
trailVertices

orientPoints :: OrderedField n => V2 n -> [Point V2 n] -> Transformation V2 n
orientPoints :: forall n.
OrderedField n =>
V2 n -> [Point V2 n] -> Transformation V2 n
orientPoints V2 n
_ [] = Transformation V2 n
forall a. Monoid a => a
mempty
orientPoints V2 n
_ [Point V2 n
_] = Transformation V2 n
forall a. Monoid a => a
mempty
orientPoints V2 n
v xs :: [Point V2 n]
xs@(Point V2 n
y : [Point V2 n]
ys) = Angle n -> Transformation V2 n
forall n. Floating n => Angle n -> Transformation V2 n
rotation Angle n
a
 where
  (Point V2 n
n1, Point V2 n
x, Point V2 n
n2) =
    ((Point V2 n, Point V2 n, Point V2 n)
 -> (Point V2 n, Point V2 n, Point V2 n) -> Ordering)
-> [(Point V2 n, Point V2 n, Point V2 n)]
-> (Point V2 n, Point V2 n, Point V2 n)
forall (t :: * -> *) a.
Foldable t =>
(a -> a -> Ordering) -> t a -> a
maximumBy
      (((Point V2 n, Point V2 n, Point V2 n) -> n)
-> (Point V2 n, Point V2 n, Point V2 n)
-> (Point V2 n, Point V2 n, Point V2 n)
-> Ordering
forall a b. Ord a => (b -> a) -> b -> b -> Ordering
comparing (V2 n -> Point V2 n -> n
forall {f :: * -> *} {a}.
(Metric f, Floating a) =>
f a -> Point f a -> a
distAlong V2 n
v (Point V2 n -> n)
-> ((Point V2 n, Point V2 n, Point V2 n) -> Point V2 n)
-> (Point V2 n, Point V2 n, Point V2 n)
-> n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Point V2 n, Point V2 n, Point V2 n) -> Point V2 n
forall {a} {b} {c}. (a, b, c) -> b
sndOf3))
      ([Point V2 n]
-> [Point V2 n]
-> [Point V2 n]
-> [(Point V2 n, Point V2 n, Point V2 n)]
forall a b c. [a] -> [b] -> [c] -> [(a, b, c)]
zip3 ([Point V2 n]
ys [Point V2 n] -> [Point V2 n] -> [Point V2 n]
forall a. [a] -> [a] -> [a]
++ [Point V2 n
y]) [Point V2 n]
xs (NonEmpty (Point V2 n) -> Point V2 n
forall a. NonEmpty a -> a
NE.last (Point V2 n
y Point V2 n -> [Point V2 n] -> NonEmpty (Point V2 n)
forall a. a -> [a] -> NonEmpty a
:| [Point V2 n]
ys) Point V2 n -> [Point V2 n] -> [Point V2 n]
forall a. a -> [a] -> [a]
: NonEmpty (Point V2 n) -> [Point V2 n]
forall a. NonEmpty a -> [a]
NE.init (Point V2 n
y Point V2 n -> [Point V2 n] -> NonEmpty (Point V2 n)
forall a. a -> [a] -> NonEmpty a
:| [Point V2 n]
ys)))
  distAlong :: f a -> Point f a -> a
distAlong f a
w ((Point f a -> Point f a -> Diff (Point f) a
forall a. Num a => Point f a -> Point f a -> Diff (Point f) a
forall (p :: * -> *) a. (Affine p, Num a) => p a -> p a -> Diff p a
.-. Point f a
forall (f :: * -> *) a. (Additive f, Num a) => Point f a
origin) -> Diff (Point f) a
p) = a -> a
forall a. Num a => a -> a
signum (f a
w f a -> f a -> a
forall a. Num a => f a -> f a -> a
forall (f :: * -> *) a. (Metric f, Num a) => f a -> f a -> a
`dot` f a
Diff (Point f) a
p) a -> a -> a
forall a. Num a => a -> a -> a
* f a -> a
forall a. Floating a => f a -> a
forall (f :: * -> *) a. (Metric f, Floating a) => f a -> a
norm (f a -> f a -> f a
forall (v :: * -> *) a.
(Metric v, Fractional a) =>
v a -> v a -> v a
project f a
w f a
Diff (Point f) a
p)
  sndOf3 :: (a, b, c) -> b
sndOf3 (a
_, b
b, c
_) = b
b
  -- a :: Angle (Scalar v)
  a :: Angle n
a =
    (Angle n -> Angle n -> Ordering) -> [Angle n] -> Angle n
forall (t :: * -> *) a.
Foldable t =>
(a -> a -> Ordering) -> t a -> a
minimumBy ((Angle n -> n) -> Angle n -> Angle n -> Ordering
forall a b. Ord a => (b -> a) -> b -> b -> Ordering
comparing ((Angle n -> n) -> Angle n -> Angle n -> Ordering)
-> (Angle n -> n) -> Angle n -> Angle n -> Ordering
forall a b. (a -> b) -> a -> b
$ n -> n
forall a. Num a => a -> a
abs (n -> n) -> (Angle n -> n) -> Angle n -> n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Getting n (Angle n) n -> Angle n -> n
forall s (m :: * -> *) a. MonadReader s m => Getting a s a -> m a
view Getting n (Angle n) n
forall n (p :: * -> * -> *) (f :: * -> *).
(Profunctor p, Functor f) =>
p n (f n) -> p (Angle n) (f (Angle n))
rad)
      ([Angle n] -> Angle n)
-> ([Point V2 n] -> [Angle n]) -> [Point V2 n] -> Angle n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Point V2 n -> Angle n) -> [Point V2 n] -> [Angle n]
forall a b. (a -> b) -> [a] -> [b]
map (V2 n -> Angle n
angleFromNormal (V2 n -> Angle n) -> (Point V2 n -> V2 n) -> Point V2 n -> Angle n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Point V2 n -> Point V2 n -> Diff (Point V2) n
forall a. Num a => Point V2 a -> Point V2 a -> Diff (Point V2) a
forall (p :: * -> *) a. (Affine p, Num a) => p a -> p a -> Diff p a
.-. Point V2 n
x))
      ([Point V2 n] -> Angle n) -> [Point V2 n] -> Angle n
forall a b. (a -> b) -> a -> b
$ [Point V2 n
n1, Point V2 n
n2]
  v' :: V2 n
v' = V2 n -> V2 n
forall a. Floating a => V2 a -> V2 a
forall (f :: * -> *) a. (Metric f, Floating a) => f a -> f a
signorm V2 n
v
  -- angleFromNormal :: v -> Angle (Scalar v)
  angleFromNormal :: V2 n -> Angle n
angleFromNormal V2 n
o
    | V2 n -> V2 n -> Bool
forall n. (Num n, Ord n) => V2 n -> V2 n -> Bool
leftTurn V2 n
o' V2 n
v' = Angle n
phi
    | Bool
otherwise = Angle n -> Angle n
forall (f :: * -> *) a. (Functor f, Num a) => f a -> f a
negated Angle n
phi
   where
    o' :: V2 n
o' = V2 n -> V2 n
forall a. Floating a => V2 a -> V2 a
forall (f :: * -> *) a. (Metric f, Floating a) => f a -> f a
signorm V2 n
o
    theta :: n
theta = n -> n
forall a. Floating a => a -> a
acos (V2 n
v' V2 n -> V2 n -> n
forall a. Num a => V2 a -> V2 a -> a
forall (f :: * -> *) a. (Metric f, Num a) => f a -> f a -> a
`dot` V2 n
o')
    -- phi :: Angle (Scalar v)
    phi :: Angle n
phi
      | n
theta n -> n -> Bool
forall a. Ord a => a -> a -> Bool
<= n
forall a. Floating a => a
tau n -> n -> n
forall a. Fractional a => a -> a -> a
/ n
4 = n
forall a. Floating a => a
tau n -> n -> n
forall a. Fractional a => a -> a -> a
/ n
4 n -> n -> n
forall a. Num a => a -> a -> a
- n
theta n -> AReview (Angle n) n -> Angle n
forall b a. b -> AReview a b -> a
@@ AReview (Angle n) n
forall n (p :: * -> * -> *) (f :: * -> *).
(Profunctor p, Functor f) =>
p n (f n) -> p (Angle n) (f (Angle n))
rad
      | Bool
otherwise = n
theta n -> n -> n
forall a. Num a => a -> a -> a
- n
forall a. Floating a => a
tau n -> n -> n
forall a. Fractional a => a -> a -> a
/ n
4 n -> AReview (Angle n) n -> Angle n
forall b a. b -> AReview a b -> a
@@ AReview (Angle n) n
forall n (p :: * -> * -> *) (f :: * -> *).
(Profunctor p, Functor f) =>
p n (f n) -> p (Angle n) (f (Angle n))
rad

------------------------------------------------------------
-- Function graphs
------------------------------------------------------------

-- $graphs
-- These functions are used to implement 'star', but are exported on
-- the offchance that someone else finds them useful.

-- | Pieces of a function graph can either be cycles or \"hairs\".
data GraphPart a
  = Cycle [a]
  | Hair [a]
  deriving (Int -> GraphPart a -> ShowS
[GraphPart a] -> ShowS
GraphPart a -> String
(Int -> GraphPart a -> ShowS)
-> (GraphPart a -> String)
-> ([GraphPart a] -> ShowS)
-> Show (GraphPart a)
forall a. Show a => Int -> GraphPart a -> ShowS
forall a. Show a => [GraphPart a] -> ShowS
forall a. Show a => GraphPart a -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: forall a. Show a => Int -> GraphPart a -> ShowS
showsPrec :: Int -> GraphPart a -> ShowS
$cshow :: forall a. Show a => GraphPart a -> String
show :: GraphPart a -> String
$cshowList :: forall a. Show a => [GraphPart a] -> ShowS
showList :: [GraphPart a] -> ShowS
Show, (forall a b. (a -> b) -> GraphPart a -> GraphPart b)
-> (forall a b. a -> GraphPart b -> GraphPart a)
-> Functor GraphPart
forall a b. a -> GraphPart b -> GraphPart a
forall a b. (a -> b) -> GraphPart a -> GraphPart b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
$cfmap :: forall a b. (a -> b) -> GraphPart a -> GraphPart b
fmap :: forall a b. (a -> b) -> GraphPart a -> GraphPart b
$c<$ :: forall a b. a -> GraphPart b -> GraphPart a
<$ :: forall a b. a -> GraphPart b -> GraphPart a
Functor)

-- | @orbits f n@ computes the graph of @f@ on the integers mod @n@.
orbits :: (Int -> Int) -> Int -> [GraphPart Int]
orbits :: (Int -> Int) -> Int -> [GraphPart Int]
orbits Int -> Int
f Int
n = (forall s. ST s [GraphPart Int]) -> [GraphPart Int]
forall a. (forall s. ST s a) -> a
runST ST s [GraphPart Int]
forall s. ST s [GraphPart Int]
genOrbits
 where
  f_n :: Int -> Int
f_n Int
i = Int -> Int
f Int
i Int -> Int -> Int
forall a. Integral a => a -> a -> a
`mod` Int
n

  genOrbits :: ST s [GraphPart Int]
  genOrbits :: forall s. ST s [GraphPart Int]
genOrbits = (Int, Int) -> Bool -> ST s (STUArray s Int Bool)
forall i. Ix i => (i, i) -> Bool -> ST s (STUArray s i Bool)
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
(i, i) -> e -> m (a i e)
newArray (Int
0, Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1) Bool
False ST s (STUArray s Int Bool)
-> (STUArray s Int Bool -> ST s [GraphPart Int])
-> ST s [GraphPart Int]
forall a b. ST s a -> (a -> ST s b) -> ST s b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= STUArray s Int Bool -> ST s [GraphPart Int]
forall s. STUArray s Int Bool -> ST s [GraphPart Int]
genOrbits'

  genOrbits' :: STUArray s Int Bool -> ST s [GraphPart Int]
  genOrbits' :: forall s. STUArray s Int Bool -> ST s [GraphPart Int]
genOrbits' STUArray s Int Bool
marks = ([Maybe [GraphPart Int]] -> [GraphPart Int])
-> ST s [Maybe [GraphPart Int]] -> ST s [GraphPart Int]
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM ([[GraphPart Int]] -> [GraphPart Int]
forall (t :: * -> *) a. Foldable t => t [a] -> [a]
concat ([[GraphPart Int]] -> [GraphPart Int])
-> ([Maybe [GraphPart Int]] -> [[GraphPart Int]])
-> [Maybe [GraphPart Int]]
-> [GraphPart Int]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Maybe [GraphPart Int]] -> [[GraphPart Int]]
forall a. [Maybe a] -> [a]
catMaybes) ([Int]
-> (Int -> ST s (Maybe [GraphPart Int]))
-> ST s [Maybe [GraphPart Int]]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
t a -> (a -> m b) -> m (t b)
forM [Int
0 .. Int
n Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1] (STUArray s Int Bool -> Int -> ST s (Maybe [GraphPart Int])
forall s.
STUArray s Int Bool -> Int -> ST s (Maybe [GraphPart Int])
genPart STUArray s Int Bool
marks))

  genPart :: STUArray s Int Bool -> Int -> ST s (Maybe [GraphPart Int])
  genPart :: forall s.
STUArray s Int Bool -> Int -> ST s (Maybe [GraphPart Int])
genPart STUArray s Int Bool
marks Int
i = do
    [Int]
tr <- Int -> STUArray s Int Bool -> ST s [Int]
forall s. Int -> STUArray s Int Bool -> ST s [Int]
markRho Int
i STUArray s Int Bool
marks
    case [Int]
tr of
      [] -> Maybe [GraphPart Int] -> ST s (Maybe [GraphPart Int])
forall a. a -> ST s a
forall (m :: * -> *) a. Monad m => a -> m a
return Maybe [GraphPart Int]
forall a. Maybe a
Nothing
      [Int]
_ -> Maybe [GraphPart Int] -> ST s (Maybe [GraphPart Int])
forall a. a -> ST s a
forall (m :: * -> *) a. Monad m => a -> m a
return (Maybe [GraphPart Int] -> ST s (Maybe [GraphPart Int]))
-> ([Int] -> Maybe [GraphPart Int])
-> [Int]
-> ST s (Maybe [GraphPart Int])
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [GraphPart Int] -> Maybe [GraphPart Int]
forall a. a -> Maybe a
Just ([GraphPart Int] -> Maybe [GraphPart Int])
-> ([Int] -> [GraphPart Int]) -> [Int] -> Maybe [GraphPart Int]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Int] -> [GraphPart Int]
splitParts ([Int] -> ST s (Maybe [GraphPart Int]))
-> [Int] -> ST s (Maybe [GraphPart Int])
forall a b. (a -> b) -> a -> b
$ [Int]
tr

  markRho :: Int -> STUArray s Int Bool -> ST s [Int]
  markRho :: forall s. Int -> STUArray s Int Bool -> ST s [Int]
markRho Int
i STUArray s Int Bool
marks = do
    Bool
isMarked <- STUArray s Int Bool -> Int -> ST s Bool
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> i -> m e
readArray STUArray s Int Bool
marks Int
i
    if Bool
isMarked
      then [Int] -> ST s [Int]
forall a. a -> ST s a
forall (m :: * -> *) a. Monad m => a -> m a
return []
      else
        STUArray s Int Bool -> Int -> Bool -> ST s ()
forall (a :: * -> * -> *) e (m :: * -> *) i.
(MArray a e m, Ix i) =>
a i e -> i -> e -> m ()
writeArray STUArray s Int Bool
marks Int
i Bool
True
          ST s () -> ST s [Int] -> ST s [Int]
forall a b. ST s a -> ST s b -> ST s b
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> ([Int] -> [Int]) -> ST s [Int] -> ST s [Int]
forall (m :: * -> *) a1 r. Monad m => (a1 -> r) -> m a1 -> m r
liftM (Int
i Int -> [Int] -> [Int]
forall a. a -> [a] -> [a]
:) (Int -> STUArray s Int Bool -> ST s [Int]
forall s. Int -> STUArray s Int Bool -> ST s [Int]
markRho (Int -> Int
f_n Int
i) STUArray s Int Bool
marks)

  splitParts :: [Int] -> [GraphPart Int]
  splitParts :: [Int] -> [GraphPart Int]
splitParts [Int]
tr = [GraphPart Int]
hair [GraphPart Int] -> [GraphPart Int] -> [GraphPart Int]
forall a. [a] -> [a] -> [a]
++ [GraphPart Int]
cyc
   where
    hair :: [GraphPart Int]
hair
      | Bool -> Bool
not ([Int] -> Bool
forall a. [a] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [Int]
tl) = [[Int] -> GraphPart Int
forall a. [a] -> GraphPart a
Hair ([Int] -> GraphPart Int) -> [Int] -> GraphPart Int
forall a b. (a -> b) -> a -> b
$ [Int]
tl [Int] -> [Int] -> [Int]
forall a. [a] -> [a] -> [a]
++ [Int -> Int
f_n ([Int] -> Int
forall a. HasCallStack => [a] -> a
last [Int]
tl)]]
      | Bool
otherwise = []
    cyc :: [GraphPart Int]
cyc
      | Bool -> Bool
not ([Int] -> Bool
forall a. [a] -> Bool
forall (t :: * -> *) a. Foldable t => t a -> Bool
null [Int]
body) = [[Int] -> GraphPart Int
forall a. [a] -> GraphPart a
Cycle [Int]
body]
      | Bool
otherwise = []
    l :: Int
l = [Int] -> Int
forall a. HasCallStack => [a] -> a
last [Int]
tr
    ([Int]
tl, [Int]
body) = (Int -> Bool) -> [Int] -> ([Int], [Int])
forall a. (a -> Bool) -> [a] -> ([a], [a])
span (Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
/= Int -> Int
f_n Int
l) [Int]
tr

-- | Generate a function graph from the given function and labels.
mkGraph :: (Int -> Int) -> [a] -> [GraphPart a]
mkGraph :: forall a. (Int -> Int) -> [a] -> [GraphPart a]
mkGraph Int -> Int
f [a]
xs = ((GraphPart Int -> GraphPart a) -> [GraphPart Int] -> [GraphPart a]
forall a b. (a -> b) -> [a] -> [b]
map ((GraphPart Int -> GraphPart a)
 -> [GraphPart Int] -> [GraphPart a])
-> ((Int -> a) -> GraphPart Int -> GraphPart a)
-> (Int -> a)
-> [GraphPart Int]
-> [GraphPart a]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Int -> a) -> GraphPart Int -> GraphPart a
forall a b. (a -> b) -> GraphPart a -> GraphPart b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap) ([a]
xs [a] -> Int -> a
forall a. HasCallStack => [a] -> Int -> a
!!) ([GraphPart Int] -> [GraphPart a])
-> [GraphPart Int] -> [GraphPart a]
forall a b. (a -> b) -> a -> b
$ (Int -> Int) -> Int -> [GraphPart Int]
orbits Int -> Int
f ([a] -> Int
forall a. [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [a]
xs)

------------------------------------------------------------
--  Star polygons
------------------------------------------------------------

-- | Options for creating \"star\" polygons, where the edges connect
--   possibly non-adjacent vertices.
data StarOpts
  = -- | Specify the order in which the vertices should be
    --   connected by a function that maps each vertex
    --   index to the index of the vertex that should come
    --   next.  Indexing of vertices begins at 0.
    StarFun (Int -> Int)
  | -- | Specify a star polygon by a \"skip\".  A skip of
    --   1 indicates a normal polygon, where edges go
    --   between successive vertices.  A skip of 2 means
    --   that edges will connect every second vertex,
    --   skipping one in between.  Generally, a skip of
    --   /n/ means that edges will connect every /n/th
    --   vertex.
    StarSkip Int

-- | Create a generalized /star/ /polygon/.  The 'StarOpts' are used
--   to determine in which order the given vertices should be
--   connected.  The intention is that the second argument of type
--   @[Point v]@ could be generated by a call to 'polygon', 'regPoly', or
--   the like, since a list of vertices is 'TrailLike'.  But of course
--   the list can be generated any way you like.  A @'Path' 'v'@ is
--   returned (instead of any 'TrailLike') because the resulting path
--   may have more than one component, for example if the vertices are
--   to be connected in several disjoint cycles.
star :: OrderedField n => StarOpts -> [Point V2 n] -> Path V2 n
star :: forall n. OrderedField n => StarOpts -> [Point V2 n] -> Path V2 n
star StarOpts
sOpts [Point V2 n]
vs = [GraphPart (Point V2 n)] -> Path V2 n
graphToPath ([GraphPart (Point V2 n)] -> Path V2 n)
-> [GraphPart (Point V2 n)] -> Path V2 n
forall a b. (a -> b) -> a -> b
$ (Int -> Int) -> [Point V2 n] -> [GraphPart (Point V2 n)]
forall a. (Int -> Int) -> [a] -> [GraphPart a]
mkGraph Int -> Int
f [Point V2 n]
vs
 where
  f :: Int -> Int
f = case StarOpts
sOpts of
    StarFun Int -> Int
g -> Int -> Int
g
    StarSkip Int
k -> (Int -> Int -> Int
forall a. Num a => a -> a -> a
+ Int
k)
  graphToPath :: [GraphPart (Point V2 n)] -> Path V2 n
graphToPath = [Path V2 n] -> Path V2 n
forall a. Monoid a => [a] -> a
mconcat ([Path V2 n] -> Path V2 n)
-> ([GraphPart (Point V2 n)] -> [Path V2 n])
-> [GraphPart (Point V2 n)]
-> Path V2 n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (GraphPart (Point V2 n) -> Path V2 n)
-> [GraphPart (Point V2 n)] -> [Path V2 n]
forall a b. (a -> b) -> [a] -> [b]
map GraphPart (Point V2 n) -> Path V2 n
forall {v :: * -> *} {n}.
(Metric v, Floating n, Ord n) =>
GraphPart (Point v n) -> Path v n
partToPath

  partToPath :: GraphPart (Point v n) -> Path v n
partToPath (Cycle [Point v n]
ps) =
    Located (Trail v n) -> Path v n
forall (v :: * -> *) n.
(Metric v, OrderedField n) =>
Located (Trail v n) -> Path v n
pathFromLocTrail
      (Located (Trail v n) -> Path v n)
-> ([Point v n] -> Located (Trail v n)) -> [Point v n] -> Path v n
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Trail v n -> Trail v n)
-> Located (Trail v n) -> Located (Trail v n)
forall a b. SameSpace a b => (a -> b) -> Located a -> Located b
mapLoc Trail v n -> Trail v n
forall (v :: * -> *) n. Trail v n -> Trail v n
closeTrail
      (Located (Trail v n) -> Located (Trail v n))
-> ([Point v n] -> Located (Trail v n))
-> [Point v n]
-> Located (Trail v n)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Point v n] -> Located (Trail v n)
[Point (V (Located (Trail v n))) (N (Located (Trail v n)))]
-> Located (Trail v n)
forall t. TrailLike t => [Point (V t) (N t)] -> t
fromVertices
      ([Point v n] -> Path v n) -> [Point v n] -> Path v n
forall a b. (a -> b) -> a -> b
$ [Point v n]
ps
  partToPath (Hair [Point v n]
ps) = [Point (V (Path v n)) (N (Path v n))] -> Path v n
forall t. TrailLike t => [Point (V t) (N t)] -> t
fromVertices [Point v n]
[Point (V (Path v n)) (N (Path v n))]
ps